https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=AMC37.5&feedformat=atomAoPS Wiki - User contributions [en]2021-10-26T14:04:28ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=The_Number_Devil&diff=13374The Number Devil2007-02-25T01:31:52Z<p>AMC37.5: mention english translation</p>
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<div>'''The Number Devil: A Mathematical Adventure''' is a fictional book by Hans Magnus Enzensberger involving mathematics.<br />
<br />
An English translation exists.</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=The_Number_Devil&diff=13373The Number Devil2007-02-25T01:31:26Z<p>AMC37.5: create article with description</p>
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<div>'''The Number Devil: A Mathematical Adventure''' is a fictional book by Hans Magnus Enzensberger involving mathematics.</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=User:AMC37.5&diff=13370User:AMC37.52007-02-25T01:19:47Z<p>AMC37.5: pi</p>
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<div><pre><br />
^<br />
--------------|<br />
</pre><br />
That is not my score.<br />
<br />
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986<br />
<br />
As of Feb. 24, 2007 I am the first user on AOPS Wiki in alphabetical order.<br />
<br />
I know more <big><big><big><math>\pi</math></big></big></big> than you.</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=User:AMC37.5&diff=13369User:AMC37.52007-02-25T01:13:11Z<p>AMC37.5: As of Feb. 24, 2007 I am the first user on AOPS Wiki in alphabetical order.</p>
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<div><pre><br />
^<br />
--------------|<br />
</pre><br />
That is not my score.<br />
<br />
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986<br />
<br />
As of Feb. 24, 2007 I am the first user on AOPS Wiki in alphabetical order.</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=User_talk:Joml88&diff=13368User talk:Joml882007-02-25T01:11:49Z<p>AMC37.5: moved from bad title</p>
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<div>Eh, Joe, I didn't know you were employed by AoPS. What all do you do for them?\ --[[User:solafidefarms|solafidefarms]]<br />
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Of course, he works for them on the Wiki! Probably the classroom as well. --[[User:Mysmartmouth|Sean]] 08:29, 24 June 2006 (EDT)<br />
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I assist two AoPS classes. [[User:Joml88|Joe]] 08:32, 24 June 2006 (EDT)<br />
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ind33d. --[[User:Iversonfan2005]]<br />
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Yeah, Joe rules. FYI, Joe, you accidentally named the [[Power of a Point Theorem]] introductory problems using different standards.--[[User:MCrawford|MCrawford]] 23:42, 30 June 2006 (EDT)<br />
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Thanks. That's what I get for trying to work on the wiki when extremely tired...can't even focus enough to do repetitive work right! OK, well it's fixed now :) [[User:Joml88|Joe]] 07:43, 1 July 2006 (EDT)<br />
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Yeah, it's because I go around leaving messages like this all over the place. (It also helped that someone finally created a page for the 2006AMC10 which had been tops.) Is there any way to make the default link in my signature go to my usertalk page instead of my user page? --[[User:JBL|JBL]] 09:57, 1 August 2006 (EDT)<br />
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== Furman Tourney ==<br />
<br />
It might be best to give the exams their own page, and then have sub-pages to the indivudual problems with solutions. That way, a student can use the wiki to take the exam as a practice test.--[[User:MCrawford|MCrawford]] 16:23, 21 July 2006 (EDT)<br />
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== Pigeonhole ==<br />
Pigeonhole page already exists -- now we have two, one with capital Principle and one with lowercase principle. Perhaps you could merge content? (I think I would write Principle, but whichever way you want.) --[[User:JBL|JBL]] 10:26, 12 August 2006 (EDT)<br />
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= Moved from incorrectly titled talk page [[User:AMC37.5|AMC37.5]] 20:11, 24 February 2007 (EST) =<br />
==AMC Problems/Solutions Subpages==<br />
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OK, I see what you're saying about the subpages. What should I do with the pages that I already made? Should I make a redirect like you did with the 2006 ones, or should I just clear the pages? -[[user:matt276eagles|matt276eagles]], 00:07, 10 July 2006 (EDT)</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Srinivasa_Ramanujan&diff=13365Srinivasa Ramanujan2007-02-25T01:05:37Z<p>AMC37.5: remove extra space, add name</p>
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<div>''Srinivasa Ramanujan'' was an Indian [[mathematician]], 1887-1920, noted for his work in [[number theory]].<br />
<br />
Among his many accomplishments is the formula: <br />
<br />
<math>\frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum^\infty_{k=0} \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}</math>.<br />
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==Links==<br />
<br />
*[http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Ramanujan.html Biography of Ramanujan] on MacTutor.<br />
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{{stub}}</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Junior_Balkan_Mathematical_Olympiad&diff=13364Junior Balkan Mathematical Olympiad2007-02-25T00:52:16Z<p>AMC37.5: categorize</p>
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<div>The '''Junior Balkan Mathematical Olympiad''' ('''JBMO''') is an annual contest for students under the age of 15.5 from one of the [[#Member countries|member countries]] (Balkan area). In recent years the hosts have also invited some non-member guest countries.<br />
<br />
== Member countries ==<br />
===Albania===<br />
===Bosnia & Herzegovina===<br />
===Bulgaria===<br />
===Cyprus===<br />
''Main article: [[Cyprus_mathematics_competitions#Junior high-school (Gymnasium) Competitions|Junior high-school (Gymnasium) Maths Competitions in Cyprus]].<br />
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In Cyprus '''Four provincial competitions''' and a '''National (Pancyprian) competition''' are held every year. During this procedure 30 students are selected and Four '''Team Selection Tests''' are held to determine who will be the the six member of national team for JBMO<br />
<br />
*In every competition or test there are four problem usually covering [[geometry]], [[number theory]], [[algebra]], and [[combinatorics]] (elementary level) and last four hours each.<br />
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===Hellas===<br />
* Θαλής ([[Thales|Thalis]]) - first round<br />
* Ευκλείδης ([[Euclides|Efklidis]]) - second round<br />
* Αρχιμήδης ([[Archimedes|Archimidis]]) - third round<br />
<br />
===Former Yugoslav Republic of Macedonia===<br />
===Republic of Moldova===<br />
===Romania===<br />
<br />
===Serbia & Montenegro===<br />
===Turkey===<br />
==Past JBMOs==<br />
* The [[1997_BMO|1st JBMO]] was held in Belgrade, Yugoslavia in 1997.<br />
* The [[1998_BMO|2nd JBMO]] was held in Athens, Greece in 1998.<br />
* The [[1999_BMO|3rd JBMO]] was held in Plovdiv, Bulgaria in 1999.<br />
* The [[2000_BMO|4th JBMO]] was held in Ohrid, Former Yugoslav Republic of Macedonia in 2000.<br />
* The [[2001_BMO|5th JBMO]] was held in Nicosia, Cyprus in 2001.<br />
* The [[2002_BMO|6th JBMO]] was held in Târgu-Mureş, Romania in 2002.<br />
* The [[2003_BMO|7th JBMO]] was held in Izmir, Turkey in 2003.<br />
* The [[2004_BMO|8th JBMO]] was held in Novi Sad, Yugoslavia in 2004.<br />
* The [[2005_BMO|9th JBMO]] was held in Veria, Greece on 20-26 June , 2005. [http://www.hms.gr/jbmo2005/]<br />
* The [[2006_BMO|10th JBMO]] was held in Moldova on 25-30 June, 2006. [http://dbsrv.asm.md/jbmo/]<br />
* The [[2007_BMO|11th JBMO]] will held in 2007.<br />
<br />
==See also==<br />
*[[JBMO Problems and Solutions, with authors]]<br />
*[[Balkan Mathematical Olympiad]]<br />
*[[Mathematics competition resources]]<br />
*[[Math books]]<br />
*[[List of mathematics competitions]]<br />
<br />
[[Category:Mathematics competitions]]</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Ellipse&diff=13363Ellipse2007-02-25T00:50:49Z<p>AMC37.5: fix link</p>
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<div>An '''ellipse''' is a [[conic section]] formed by cutting through a [[cone]] at an [[angle]]. Equivalently, it is defined as the [[locus]], or [[set]], of all [[point]]s <math>P</math> such that the sum of the distances from <math>P</math> to two fixed [[focus|foci]] is a constant. (The equivalence of these two definitions is a non-trivial fact.)<br />
<br />
Ellipses tend to resemble [[circle]]s which have been "flattened" or "stretched." They occur in nature as well as in mathematics: as was proven in [[Kepler's Laws]], the planets all revolve about the sun in elliptical, not circular, orbits with the sun at one of the foci. Note that the circle is just a special case of the ellipse, just as a square is to a rectangle, and occurs when (in the first definition) the cut is [[perpendicular]] to the axis of the the cone, or (in the second definition) the two foci of the ellipse coincide.<br />
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For a given non-circular ellipse, there will be two points on the ellipse closest to the center and two points furthest away -- it will be "tall and skinny" or "short and fat." The segment connecting the center of the ellipse to one of the "farther away ends" is called the ''[[semimajor axis]]'' and the segment connecting the center to a closer end is called the ''[[semiminor axis]]''. These two segments are perpendicular. Drawing all four semi-axes divides the ellipse into 4 [[congruent (geometry)|congruent]] quarters.<br />
<br />
{{image}}<br />
<br />
Using the second definition of an ellipse given above, one may easily construct an ellipse from household materials. To draw an ellipse with two pushpins, a loop of string, pencil, and paper, stick the pushpins in the paper place the string on the paper so that both pushpins are inside it. The pushpins will be the foci of the ellipse, and the length of the string will determine the sum of the distances from a point on the ellipse to the two foci. Hold the pencil on the paper such that the string is taut against the pencil tip and the two pushpins. Then move the pencil tip while keeping the string taut. This will traces out an ellipse.<br />
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An ellipse in a [[Cartesian coordinate system]] with center <math>C = (h, k)</math> whose axes are parallel to the coordinate axes, with the vertical semi-axis of length <math>a</math> and the horizontal semi-axis of length <math>b</math> is given by the equation <math>\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1</math>. In particular, if the center of the ellipse is the origin this simplifies to <math>\frac{x^2}{a^2}+\frac{y^2}{b^2}=1</math>.<br />
<br />
The three-dimensional counterpart of the ellipse is the [[ellipsoid]].<br />
<br />
==See also==<br />
* [[Parabola]]<br />
* [[Conic section]]s<br />
* [[Geometry]]<br />
* [[Polynomial]]s</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Fundamental_Theorem_of_Calculus&diff=13362Fundamental Theorem of Calculus2007-02-25T00:50:14Z<p>AMC37.5: /* Intuitive Explanation */ lowercase section</p>
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<div>The '''Fundamental Theorem of Calculus''' establishes a link between the two central operations of [[calculus]]: [[derivative|differentiation]] and [[integral|integration]]. <br />
<br />
== Introductory Problems ==<br />
<br />
This section is for people who know what [[integral]]s are but don't know the Fundamental Theorem of Calculus yet, and would like to try to figure it out. (Actually there are two different but related Fundamental Theorems of Calculus. Questions 0 through 5 correspond to the "first" Fundamental Theorem of Calculus. The last question corresponds to the "second" Fundamental Theorem of Calculus.)<br />
<br />
* Evaluate <math>\int_2^5 x^3 dx</math> and <math>\int_{.2}^{.4} \cos(x) dx</math>. (The next few questions are meant as hints for how to do this.)<br />
# An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>e^{t^2}</math> meters/second. (Yes, probably no object really moves this way, but just pretend.) ''Approximately'' how far does the object move between times <math>t=1 </math> second and <math>t=2</math> seconds? (I picked <math>e^{t^2}</math> because I wanted a function that doesn't have a nice anti-derivative.) Interpret the distance that the object travels between times <math>t=1</math> and <math>t=2</math> geometrically, as an area under a curve.<br />
# An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>t^3</math> m/s. Exactly how far does the object go between times <math>t=2</math> sec and <math>t=5</math> sec? Interpret this distance geometrically, as an area under a curve.<br />
# Same as question 3, but this time the object's velocity at time <math>{t}</math> is <math>\cos{t}</math>, and you want to find out exactly how far the object moved between times <math>t=.2</math> and <math>t=.4</math>. Interpret the distance that the object moved geometrically, as an area under a curve.<br />
<br />
Can you do the main problem now?<br />
<br />
# Here's a slightly different way to think about the main problem, that doesn't use physics. How much does the function <math>f(x)= \frac{x^4}{4}</math> change over the interval from <math>x=2</math> to <math>x=5</math>? Obviously, the answer is <math>\frac{5^4}{4} - \frac{2^4}{4}</math> . But, there's another way to look at it: ''the total change is the sum of all the little changes''. Break the interval from <math>2</math> to <math>5</math> up into <math>30</math> little subintervals. Using the derivative, tell me: approximately how much does <math>{f}</math> change over each of these little subintervals? Adding up all of these little changes gives you a [[Riemann sum]] that approximates the total change of <math>{f}</math> over the whole interval. This Riemann sum also approximates a certain integral. What is that integral?<br />
<br />
The remaining question deals with the "second" Fundamental Theorem of Calculus.<br />
<br />
# Let <math>f: \mathbb{R} \to \mathbb{R}</math> be [[continuous function | continuous]]. Define <math>F(x) = \int_0^x f(s) ds</math> for all <math>x \ge 0</math>. Draw a picture to explain this definition of <math>{F}</math>. <math>F'(x)= \lim_{\Delta x \to 0} \frac{F(x+\Delta x) - F(x)}{\Delta x}</math>. Assuming <math>\Delta x</math> is a small number, represent <math>F(x+\Delta x) - F(x)</math> geometrically in your picture. Using your picture, approximately how large is <math>\frac{F(x+\Delta x) - F(x)}{\Delta x}</math>? Now the final question: What is <math>F'(x)</math>?<br />
<br />
== Statement==<br />
<br />
First Fundamental Theorem of Calculus:<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>. Then <math>\int_a^b F'(x)dx = F(b) - F(a)</math>. <br />
<br />
In other words, "the total change (on the right) is the sum of all the little changes (on the left)."<br />
<br />
<br />
Second Fundamental Theorem of Calculus:<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math>, <math>{a}<{b}</math>. Suppose <math>f:[a,b] \to \mathbb{R}</math> is [[continuous function | continuous]] on the whole interval <math>[a,b]</math>. Let <math>F(x) = \int_a^x f(s) ds</math> for all <math>x \in [a,b]</math>. Then <math>F</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and from the left for the derivatives at a and b, respectively), and <math>F'(x) = f(x)</math> for all <math>x \in [a,b]</math>.<br />
<br />
<br />
<br />
== Intuitive explanation ==<br />
<br />
The first Fundamental Theorem of Calculus basically says that "the total change is the sum of all the little changes."<br />
<br />
How much does a function <math>F</math> change over an interval <math>[a,b]</math>? Obviously, the answer is <math>F(b)-F(a)</math>. But there's another way to look at it. Break the interval <math>[a,b]</math> up into a whole bunch of tiny subintervals, each having a tiny width <math>\Delta x</math>. Let's say <math>[a,b]</math> has been broken up into <math>n</math> subintervals, so <math>\Delta x = \frac{b-a}{n}</math>. Let <math>x_0 = a, x_1 = a + \Delta x, x_2 = a + 2\Delta x, \ldots, x_i = x_0 + i\Delta x, \ldots, x_n = a + n\Delta x = b</math>.<br />
<br />
How much does <math>F</math> change over the tiny interval <math>[x_i,x_{i+1}]</math>? Of course, the answer is <math>F(x_{i+1})-F(x_i)</math>. But this is approximately <math>F'(x_i)\Delta x</math>. If <math>\Delta F_i</math> is the amount that <math>F</math> changes on the interval <math>[x_i, x_{i+1}]</math>, then <math>\Delta F_i \approx F'(x_i)\Delta x</math>.<br />
<br />
The total change of <math>F</math> over the interval <math>[a,b]</math> , <math>F(b)-F(a)</math>, is exactly equal to <math>\Delta F_0 + \Delta F_1 +\cdots + \Delta F_{n-1}</math> . Thus,<br />
<br />
<math>F(b)-F(a) \approx F'(x_0)\Delta x + F'(x_1) \Delta x + \cdots + F'(x_{n-1}) \Delta x</math>.<br />
<br />
What we have here on the right is a Riemann sum. It approximates a certain integral. What integral does it approximate? Well, it approximates <math>\int_a^b F'(x) dx</math> .<br />
<br />
If we repeat this process, using more and more subintervals, then our approximations will get better and better, and the Riemann sums will approximate that integral better and better, and in the limit we will find that <math>F(b)-F(a) = \int_a^b F'(x) dx</math>.<br />
<br />
This can be made into a rigorous proof, if you use the [[Mean Value Theorem]]. The standard proof of the first Fundamental Theorem of Calculus, using the Mean Value Theorem, can be thought of in this way.<br />
<br />
In order to get an intuitive understanding of the second Fundamental Theorem of Calculus, I recommend just thinking about problem 6. The idea presented there can also be turned into a rigorous proof. (The standard proof can be thought of in this way.)<br />
<br />
== Proof ==<br />
<br />
Here's a proof of the first Fundamental Theorem of Calculus.<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>.<br />
<br />
Let <math>\epsilon > 0</math>. There exists <math>\delta > 0</math> such that if <math>a=x_0, x_1, x_2, \ldots, x_n=b</math> is a partition of <math>[a,b]</math> , and <math>\Delta x_0=x_1-x_0, \Delta x_1 = x_2-x_1, \ldots, \Delta x_{n-1}=x_n - x_{n-1}=b-x_{n-1}</math> , and <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>, and <math>\xi_i</math> is in <math>[x_i,x_{i+1}]</math> for all <math>i</math>, <math>0 \le i < n</math>, THEN the Riemann sum <br />
<br />
<math>F'(\xi_0) \Delta x_0 + F'(\xi_1) \Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math> <br />
<br />
is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
(In fact, this is sometimes taken as the definition of the statement "<math>F'</math> is Riemann integrable on the interval <math>[a,b]</math>.")<br />
<br />
So, let <math>a=x_0, x_1,\ldots, x_n=b</math> be a partition of <math>[a,b]</math> such that <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>.<br />
<br />
For each <math>i</math>, <math>0\le i < n</math>, let <math>\Delta F_i = F(x_{i+1})-F(x_i)</math> be the amount that <math>F</math> changes over the interval <math>[x_i,x_{i+1}]</math>. Then<br />
<br />
<math>F(b) - F(a)=\Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math>.<br />
<br />
According to the Mean Value Theorem, for each <math>i</math>, <math>0 \le i < n</math>, there exists <math>\xi_i \in (x_i, x_{i+1})</math> such that <math>\Delta F_i = F(x_{i+1}) - F(x_i) = F'(\xi_i)\Delta x_i</math>. <br />
<br />
(This is similar to the part of the intuitive argument where we said that <math>\Delta F_i \approx F'(x_i) \Delta x_i</math>. However, this is better. The Mean Value Theorem, fortunately, gives us exact equality, rather than just an approximation.)<br />
<br />
Thus,<br />
<br />
<math>F(b)-F(a) = \Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math><br />
<math>= F'(\xi_0) \Delta x_0 + F'(\xi_1)\Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math>.<br />
<br />
This last expression, on the right, is a Riemann sum, and it is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
THEREFORE, we have found that <math>F(b) - F(a)</math> is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
But <math>\epsilon > 0</math> was arbitrary. The only way that <math>F(b) - F(a)</math> could be within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math> for any <math>\epsilon > 0</math> is if <math>F(b)-F(a)</math> is actually equal to <math>\int_a^b F'(x) dx</math>.<br />
<br />
So that means <math>\int_a^b F'(x) dx = F(b)-F(a)</math>.<br />
<br />
That concludes the proof of the first Fundamental Theorem of Calculus.<br />
<br />
For a proof of the second Fundamental Theorem of Calculus, I recommend looking in the book ''Calculus'' by Spivak. (Hopefully I or someone else will post a proof here eventually.)<br />
<br />
==Generalizations==<br />
<br />
==See also==</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Fundamental_Theorem_of_Calculus&diff=13361Fundamental Theorem of Calculus2007-02-25T00:49:52Z<p>AMC37.5: /* Introductory Problems */ convert to list</p>
<hr />
<div>The '''Fundamental Theorem of Calculus''' establishes a link between the two central operations of [[calculus]]: [[derivative|differentiation]] and [[integral|integration]]. <br />
<br />
== Introductory Problems ==<br />
<br />
This section is for people who know what [[integral]]s are but don't know the Fundamental Theorem of Calculus yet, and would like to try to figure it out. (Actually there are two different but related Fundamental Theorems of Calculus. Questions 0 through 5 correspond to the "first" Fundamental Theorem of Calculus. The last question corresponds to the "second" Fundamental Theorem of Calculus.)<br />
<br />
* Evaluate <math>\int_2^5 x^3 dx</math> and <math>\int_{.2}^{.4} \cos(x) dx</math>. (The next few questions are meant as hints for how to do this.)<br />
# An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>e^{t^2}</math> meters/second. (Yes, probably no object really moves this way, but just pretend.) ''Approximately'' how far does the object move between times <math>t=1 </math> second and <math>t=2</math> seconds? (I picked <math>e^{t^2}</math> because I wanted a function that doesn't have a nice anti-derivative.) Interpret the distance that the object travels between times <math>t=1</math> and <math>t=2</math> geometrically, as an area under a curve.<br />
# An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>t^3</math> m/s. Exactly how far does the object go between times <math>t=2</math> sec and <math>t=5</math> sec? Interpret this distance geometrically, as an area under a curve.<br />
# Same as question 3, but this time the object's velocity at time <math>{t}</math> is <math>\cos{t}</math>, and you want to find out exactly how far the object moved between times <math>t=.2</math> and <math>t=.4</math>. Interpret the distance that the object moved geometrically, as an area under a curve.<br />
<br />
Can you do the main problem now?<br />
<br />
# Here's a slightly different way to think about the main problem, that doesn't use physics. How much does the function <math>f(x)= \frac{x^4}{4}</math> change over the interval from <math>x=2</math> to <math>x=5</math>? Obviously, the answer is <math>\frac{5^4}{4} - \frac{2^4}{4}</math> . But, there's another way to look at it: ''the total change is the sum of all the little changes''. Break the interval from <math>2</math> to <math>5</math> up into <math>30</math> little subintervals. Using the derivative, tell me: approximately how much does <math>{f}</math> change over each of these little subintervals? Adding up all of these little changes gives you a [[Riemann sum]] that approximates the total change of <math>{f}</math> over the whole interval. This Riemann sum also approximates a certain integral. What is that integral?<br />
<br />
The remaining question deals with the "second" Fundamental Theorem of Calculus.<br />
<br />
# Let <math>f: \mathbb{R} \to \mathbb{R}</math> be [[continuous function | continuous]]. Define <math>F(x) = \int_0^x f(s) ds</math> for all <math>x \ge 0</math>. Draw a picture to explain this definition of <math>{F}</math>. <math>F'(x)= \lim_{\Delta x \to 0} \frac{F(x+\Delta x) - F(x)}{\Delta x}</math>. Assuming <math>\Delta x</math> is a small number, represent <math>F(x+\Delta x) - F(x)</math> geometrically in your picture. Using your picture, approximately how large is <math>\frac{F(x+\Delta x) - F(x)}{\Delta x}</math>? Now the final question: What is <math>F'(x)</math>?<br />
<br />
== Statement==<br />
<br />
First Fundamental Theorem of Calculus:<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>. Then <math>\int_a^b F'(x)dx = F(b) - F(a)</math>. <br />
<br />
In other words, "the total change (on the right) is the sum of all the little changes (on the left)."<br />
<br />
<br />
Second Fundamental Theorem of Calculus:<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math>, <math>{a}<{b}</math>. Suppose <math>f:[a,b] \to \mathbb{R}</math> is [[continuous function | continuous]] on the whole interval <math>[a,b]</math>. Let <math>F(x) = \int_a^x f(s) ds</math> for all <math>x \in [a,b]</math>. Then <math>F</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and from the left for the derivatives at a and b, respectively), and <math>F'(x) = f(x)</math> for all <math>x \in [a,b]</math>.<br />
<br />
<br />
<br />
== Intuitive Explanation ==<br />
<br />
The first Fundamental Theorem of Calculus basically says that "the total change is the sum of all the little changes."<br />
<br />
How much does a function <math>F</math> change over an interval <math>[a,b]</math>? Obviously, the answer is <math>F(b)-F(a)</math>. But there's another way to look at it. Break the interval <math>[a,b]</math> up into a whole bunch of tiny subintervals, each having a tiny width <math>\Delta x</math>. Let's say <math>[a,b]</math> has been broken up into <math>n</math> subintervals, so <math>\Delta x = \frac{b-a}{n}</math>. Let <math>x_0 = a, x_1 = a + \Delta x, x_2 = a + 2\Delta x, \ldots, x_i = x_0 + i\Delta x, \ldots, x_n = a + n\Delta x = b</math>.<br />
<br />
How much does <math>F</math> change over the tiny interval <math>[x_i,x_{i+1}]</math>? Of course, the answer is <math>F(x_{i+1})-F(x_i)</math>. But this is approximately <math>F'(x_i)\Delta x</math>. If <math>\Delta F_i</math> is the amount that <math>F</math> changes on the interval <math>[x_i, x_{i+1}]</math>, then <math>\Delta F_i \approx F'(x_i)\Delta x</math>.<br />
<br />
The total change of <math>F</math> over the interval <math>[a,b]</math> , <math>F(b)-F(a)</math>, is exactly equal to <math>\Delta F_0 + \Delta F_1 +\cdots + \Delta F_{n-1}</math> . Thus,<br />
<br />
<math>F(b)-F(a) \approx F'(x_0)\Delta x + F'(x_1) \Delta x + \cdots + F'(x_{n-1}) \Delta x</math>.<br />
<br />
What we have here on the right is a Riemann sum. It approximates a certain integral. What integral does it approximate? Well, it approximates <math>\int_a^b F'(x) dx</math> .<br />
<br />
If we repeat this process, using more and more subintervals, then our approximations will get better and better, and the Riemann sums will approximate that integral better and better, and in the limit we will find that <math>F(b)-F(a) = \int_a^b F'(x) dx</math>.<br />
<br />
This can be made into a rigorous proof, if you use the [[Mean Value Theorem]]. The standard proof of the first Fundamental Theorem of Calculus, using the Mean Value Theorem, can be thought of in this way.<br />
<br />
In order to get an intuitive understanding of the second Fundamental Theorem of Calculus, I recommend just thinking about problem 6. The idea presented there can also be turned into a rigorous proof. (The standard proof can be thought of in this way.)<br />
<br />
<br />
<br />
== Proof ==<br />
<br />
Here's a proof of the first Fundamental Theorem of Calculus.<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>.<br />
<br />
Let <math>\epsilon > 0</math>. There exists <math>\delta > 0</math> such that if <math>a=x_0, x_1, x_2, \ldots, x_n=b</math> is a partition of <math>[a,b]</math> , and <math>\Delta x_0=x_1-x_0, \Delta x_1 = x_2-x_1, \ldots, \Delta x_{n-1}=x_n - x_{n-1}=b-x_{n-1}</math> , and <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>, and <math>\xi_i</math> is in <math>[x_i,x_{i+1}]</math> for all <math>i</math>, <math>0 \le i < n</math>, THEN the Riemann sum <br />
<br />
<math>F'(\xi_0) \Delta x_0 + F'(\xi_1) \Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math> <br />
<br />
is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
(In fact, this is sometimes taken as the definition of the statement "<math>F'</math> is Riemann integrable on the interval <math>[a,b]</math>.")<br />
<br />
So, let <math>a=x_0, x_1,\ldots, x_n=b</math> be a partition of <math>[a,b]</math> such that <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>.<br />
<br />
For each <math>i</math>, <math>0\le i < n</math>, let <math>\Delta F_i = F(x_{i+1})-F(x_i)</math> be the amount that <math>F</math> changes over the interval <math>[x_i,x_{i+1}]</math>. Then<br />
<br />
<math>F(b) - F(a)=\Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math>.<br />
<br />
According to the Mean Value Theorem, for each <math>i</math>, <math>0 \le i < n</math>, there exists <math>\xi_i \in (x_i, x_{i+1})</math> such that <math>\Delta F_i = F(x_{i+1}) - F(x_i) = F'(\xi_i)\Delta x_i</math>. <br />
<br />
(This is similar to the part of the intuitive argument where we said that <math>\Delta F_i \approx F'(x_i) \Delta x_i</math>. However, this is better. The Mean Value Theorem, fortunately, gives us exact equality, rather than just an approximation.)<br />
<br />
Thus,<br />
<br />
<math>F(b)-F(a) = \Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math><br />
<math>= F'(\xi_0) \Delta x_0 + F'(\xi_1)\Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math>.<br />
<br />
This last expression, on the right, is a Riemann sum, and it is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
THEREFORE, we have found that <math>F(b) - F(a)</math> is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
But <math>\epsilon > 0</math> was arbitrary. The only way that <math>F(b) - F(a)</math> could be within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math> for any <math>\epsilon > 0</math> is if <math>F(b)-F(a)</math> is actually equal to <math>\int_a^b F'(x) dx</math>.<br />
<br />
So that means <math>\int_a^b F'(x) dx = F(b)-F(a)</math>.<br />
<br />
That concludes the proof of the first Fundamental Theorem of Calculus.<br />
<br />
For a proof of the second Fundamental Theorem of Calculus, I recommend looking in the book ''Calculus'' by Spivak. (Hopefully I or someone else will post a proof here eventually.)<br />
<br />
==Generalizations==<br />
<br />
==See also==</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Fundamental_Theorem_of_Calculus&diff=13360Fundamental Theorem of Calculus2007-02-25T00:48:29Z<p>AMC37.5: /* Introductory Problems */ fix link, decapitalize Riemann sum</p>
<hr />
<div>The '''Fundamental Theorem of Calculus''' establishes a link between the two central operations of [[calculus]]: [[derivative|differentiation]] and [[integral|integration]]. <br />
<br />
== Introductory Problems ==<br />
<br />
This section is for people who know what [[integral]]s are but don't know the Fundamental Theorem of Calculus yet, and would like to try to figure it out. (Actually there are two different but related Fundamental Theorems of Calculus. Questions 0 through 5 correspond to the "first" Fundamental Theorem of Calculus. The last question corresponds to the "second" Fundamental Theorem of Calculus.)<br />
<br />
0) Evaluate <math>\int_2^5 x^3 dx</math> and <math>\int_{.2}^{.4} \cos(x) dx</math>. (The next few questions are meant as hints for how to do this.)<br />
<br />
1) An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>e^{t^2}</math> meters/second. (Yes, probably no object really moves this way, but just pretend.) ''Approximately'' how far does the object move between times <math>t=1 </math> second and <math>t=2</math> seconds? (I picked <math>e^{t^2}</math> because I wanted a function that doesn't have a nice anti-derivative.) Interpret the distance that the object travels between times <math>t=1</math> and <math>t=2</math> geometrically, as an area under a curve.<br />
<br />
2) An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>t^3</math> m/s. Exactly how far does the object go between times <math>t=2</math> sec and <math>t=5</math> sec? Interpret this distance geometrically, as an area under a curve.<br />
<br />
3) Same as question 3, but this time the object's velocity at time <math>{t}</math> is <math>\cos{t}</math>, and you want to find out exactly how far the object moved between times <math>t=.2</math> and <math>t=.4</math>. Interpret the distance that the object moved geometrically, as an area under a curve.<br />
<br />
4) Can you do problem 0) now?<br />
<br />
5) Here's a slightly different way to think about problem 0, that doesn't use physics. How much does the function <math>f(x)= \frac{x^4}{4}</math> change over the interval from <math>x=2</math> to <math>x=5</math>? Obviously, the answer is <math>\frac{5^4}{4} - \frac{2^4}{4}</math> . But, there's another way to look at it: ''the total change is the sum of all the little changes''. Break the interval from <math>2</math> to <math>5</math> up into <math>30</math> little subintervals. Using the derivative, tell me: approximately how much does <math>{f}</math> change over each of these little subintervals? Adding up all of these little changes gives you a [[Riemann sum]] that approximates the total change of <math>{f}</math> over the whole interval. This Riemann sum also approximates a certain integral. What is that integral?<br />
<br />
The remaining question deals with the "second" Fundamental Theorem of Calculus.<br />
<br />
6) Let <math>f: \mathbb{R} \to \mathbb{R}</math> be [[continuous function | continuous]]. Define <math>F(x) = \int_0^x f(s) ds</math> for all <math>x \ge 0</math>. Draw a picture to explain this definition of <math>{F}</math>. <math>F'(x)= \lim_{\Delta x \to 0} \frac{F(x+\Delta x) - F(x)}{\Delta x}</math>. Assuming <math>\Delta x</math> is a small number, represent <math>F(x+\Delta x) - F(x)</math> geometrically in your picture. Using your picture, approximately how large is <math>\frac{F(x+\Delta x) - F(x)}{\Delta x}</math>? Now the final question: What is <math>F'(x)</math>?<br />
<br />
== Statement==<br />
<br />
First Fundamental Theorem of Calculus:<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>. Then <math>\int_a^b F'(x)dx = F(b) - F(a)</math>. <br />
<br />
In other words, "the total change (on the right) is the sum of all the little changes (on the left)."<br />
<br />
<br />
Second Fundamental Theorem of Calculus:<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math>, <math>{a}<{b}</math>. Suppose <math>f:[a,b] \to \mathbb{R}</math> is [[continuous function | continuous]] on the whole interval <math>[a,b]</math>. Let <math>F(x) = \int_a^x f(s) ds</math> for all <math>x \in [a,b]</math>. Then <math>F</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and from the left for the derivatives at a and b, respectively), and <math>F'(x) = f(x)</math> for all <math>x \in [a,b]</math>.<br />
<br />
<br />
<br />
== Intuitive Explanation ==<br />
<br />
The first Fundamental Theorem of Calculus basically says that "the total change is the sum of all the little changes."<br />
<br />
How much does a function <math>F</math> change over an interval <math>[a,b]</math>? Obviously, the answer is <math>F(b)-F(a)</math>. But there's another way to look at it. Break the interval <math>[a,b]</math> up into a whole bunch of tiny subintervals, each having a tiny width <math>\Delta x</math>. Let's say <math>[a,b]</math> has been broken up into <math>n</math> subintervals, so <math>\Delta x = \frac{b-a}{n}</math>. Let <math>x_0 = a, x_1 = a + \Delta x, x_2 = a + 2\Delta x, \ldots, x_i = x_0 + i\Delta x, \ldots, x_n = a + n\Delta x = b</math>.<br />
<br />
How much does <math>F</math> change over the tiny interval <math>[x_i,x_{i+1}]</math>? Of course, the answer is <math>F(x_{i+1})-F(x_i)</math>. But this is approximately <math>F'(x_i)\Delta x</math>. If <math>\Delta F_i</math> is the amount that <math>F</math> changes on the interval <math>[x_i, x_{i+1}]</math>, then <math>\Delta F_i \approx F'(x_i)\Delta x</math>.<br />
<br />
The total change of <math>F</math> over the interval <math>[a,b]</math> , <math>F(b)-F(a)</math>, is exactly equal to <math>\Delta F_0 + \Delta F_1 +\cdots + \Delta F_{n-1}</math> . Thus,<br />
<br />
<math>F(b)-F(a) \approx F'(x_0)\Delta x + F'(x_1) \Delta x + \cdots + F'(x_{n-1}) \Delta x</math>.<br />
<br />
What we have here on the right is a Riemann sum. It approximates a certain integral. What integral does it approximate? Well, it approximates <math>\int_a^b F'(x) dx</math> .<br />
<br />
If we repeat this process, using more and more subintervals, then our approximations will get better and better, and the Riemann sums will approximate that integral better and better, and in the limit we will find that <math>F(b)-F(a) = \int_a^b F'(x) dx</math>.<br />
<br />
This can be made into a rigorous proof, if you use the [[Mean Value Theorem]]. The standard proof of the first Fundamental Theorem of Calculus, using the Mean Value Theorem, can be thought of in this way.<br />
<br />
In order to get an intuitive understanding of the second Fundamental Theorem of Calculus, I recommend just thinking about problem 6. The idea presented there can also be turned into a rigorous proof. (The standard proof can be thought of in this way.)<br />
<br />
<br />
<br />
== Proof ==<br />
<br />
Here's a proof of the first Fundamental Theorem of Calculus.<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>.<br />
<br />
Let <math>\epsilon > 0</math>. There exists <math>\delta > 0</math> such that if <math>a=x_0, x_1, x_2, \ldots, x_n=b</math> is a partition of <math>[a,b]</math> , and <math>\Delta x_0=x_1-x_0, \Delta x_1 = x_2-x_1, \ldots, \Delta x_{n-1}=x_n - x_{n-1}=b-x_{n-1}</math> , and <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>, and <math>\xi_i</math> is in <math>[x_i,x_{i+1}]</math> for all <math>i</math>, <math>0 \le i < n</math>, THEN the Riemann sum <br />
<br />
<math>F'(\xi_0) \Delta x_0 + F'(\xi_1) \Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math> <br />
<br />
is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
(In fact, this is sometimes taken as the definition of the statement "<math>F'</math> is Riemann integrable on the interval <math>[a,b]</math>.")<br />
<br />
So, let <math>a=x_0, x_1,\ldots, x_n=b</math> be a partition of <math>[a,b]</math> such that <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>.<br />
<br />
For each <math>i</math>, <math>0\le i < n</math>, let <math>\Delta F_i = F(x_{i+1})-F(x_i)</math> be the amount that <math>F</math> changes over the interval <math>[x_i,x_{i+1}]</math>. Then<br />
<br />
<math>F(b) - F(a)=\Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math>.<br />
<br />
According to the Mean Value Theorem, for each <math>i</math>, <math>0 \le i < n</math>, there exists <math>\xi_i \in (x_i, x_{i+1})</math> such that <math>\Delta F_i = F(x_{i+1}) - F(x_i) = F'(\xi_i)\Delta x_i</math>. <br />
<br />
(This is similar to the part of the intuitive argument where we said that <math>\Delta F_i \approx F'(x_i) \Delta x_i</math>. However, this is better. The Mean Value Theorem, fortunately, gives us exact equality, rather than just an approximation.)<br />
<br />
Thus,<br />
<br />
<math>F(b)-F(a) = \Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math><br />
<math>= F'(\xi_0) \Delta x_0 + F'(\xi_1)\Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math>.<br />
<br />
This last expression, on the right, is a Riemann sum, and it is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
THEREFORE, we have found that <math>F(b) - F(a)</math> is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
<br />
But <math>\epsilon > 0</math> was arbitrary. The only way that <math>F(b) - F(a)</math> could be within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math> for any <math>\epsilon > 0</math> is if <math>F(b)-F(a)</math> is actually equal to <math>\int_a^b F'(x) dx</math>.<br />
<br />
So that means <math>\int_a^b F'(x) dx = F(b)-F(a)</math>.<br />
<br />
That concludes the proof of the first Fundamental Theorem of Calculus.<br />
<br />
For a proof of the second Fundamental Theorem of Calculus, I recommend looking in the book ''Calculus'' by Spivak. (Hopefully I or someone else will post a proof here eventually.)<br />
<br />
==Generalizations==<br />
<br />
==See also==</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Fundamental_Theorem_of_Calculus&diff=13359Fundamental Theorem of Calculus2007-02-25T00:47:20Z<p>AMC37.5: fix links</p>
<hr />
<div>The '''Fundamental Theorem of Calculus''' establishes a link between the two central operations of [[calculus]]: [[derivative|differentiation]] and [[integral|integration]]. <br />
<br />
== Introductory Problems ==<br />
<br />
This section is for people who know what [[integral | integrals]] are but don't know the Fundamental Theorem of Calculus yet, and would like to try to figure it out. (Actually there are two different but related Fundamental Theorems of Calculus. Questions 0 through 5 correspond to the "first" Fundamental Theorem of Calculus. The last question corresponds to the "second" Fundamental Theorem of Calculus.)<br />
<br />
0) Evaluate <math>\int_2^5 x^3 dx</math> and <math>\int_{.2}^{.4} \cos(x) dx</math>. (The next few questions are meant as hints for how to do this.)<br />
<br />
1) An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>e^{t^2}</math> meters/second. (Yes, probably no object really moves this way, but just pretend.) ''Approximately'' how far does the object move between times <math>t=1 </math> second and <math>t=2</math> seconds? (I picked <math>e^{t^2}</math> because I wanted a function that doesn't have a nice anti-derivative.) Interpret the distance that the object travels between times <math>t=1</math> and <math>t=2</math> geometrically, as an area under a curve.<br />
<br />
2) An object is moving along a straight line, and its velocity at time <math>{t}</math> is <math>t^3</math> m/s. Exactly how far does the object go between times <math>t=2</math> sec and <math>t=5</math> sec? Interpret this distance geometrically, as an area under a curve.<br />
<br />
3) Same as question 3, but this time the object's velocity at time <math>{t}</math> is <math>\cos{t}</math>, and you want to find out exactly how far the object moved between times <math>t=.2</math> and <math>t=.4</math>. Interpret the distance that the object moved geometrically, as an area under a curve.<br />
<br />
4) Can you do problem 0) now?<br />
<br />
5) Here's a slightly different way to think about problem 0, that doesn't use physics. How much does the function <math>f(x)= \frac{x^4}{4}</math> change over the interval from <math>x=2</math> to <math>x=5</math>? Obviously, the answer is <math>\frac{5^4}{4} - \frac{2^4}{4}</math> . But, there's another way to look at it: ''the total change is the sum of all the little changes''. Break the interval from <math>2</math> to <math>5</math> up into <math>30</math> little subintervals. Using the derivative, tell me: approximately how much does <math>{f}</math> change over each of these little subintervals? Adding up all of these little changes gives you a [[Riemann Sum]] that approximates the total change of <math>{f}</math> over the whole interval. This Riemann Sum also approximates a certain integral. What is that integral?<br />
<br />
The remaining question deals with the "second" Fundamental Theorem of Calculus.<br />
<br />
6) Let <math>f: \mathbb{R} \to \mathbb{R}</math> be [[continuous function | continuous]]. Define <math>F(x) = \int_0^x f(s) ds</math> for all <math>x \ge 0</math>. Draw a picture to explain this definition of <math>{F}</math>. <math>F'(x)= \lim_{\Delta x \to 0} \frac{F(x+\Delta x) - F(x)}{\Delta x}</math>. Assuming <math>\Delta x</math> is a small number, represent <math>F(x+\Delta x) - F(x)</math> geometrically in your picture. Using your picture, approximately how large is <math>\frac{F(x+\Delta x) - F(x)}{\Delta x}</math>? Now the final question: What is <math>F'(x)</math>?<br />
<br />
== Statement==<br />
<br />
First Fundamental Theorem of Calculus:<br />
<br />
Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>. Then <math>\int_a^b F'(x)dx = F(b) - F(a)</math>. <br />
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In other words, "the total change (on the right) is the sum of all the little changes (on the left)."<br />
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Second Fundamental Theorem of Calculus:<br />
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Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math>, <math>{a}<{b}</math>. Suppose <math>f:[a,b] \to \mathbb{R}</math> is [[continuous function | continuous]] on the whole interval <math>[a,b]</math>. Let <math>F(x) = \int_a^x f(s) ds</math> for all <math>x \in [a,b]</math>. Then <math>F</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and from the left for the derivatives at a and b, respectively), and <math>F'(x) = f(x)</math> for all <math>x \in [a,b]</math>.<br />
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== Intuitive Explanation ==<br />
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The first Fundamental Theorem of Calculus basically says that "the total change is the sum of all the little changes."<br />
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How much does a function <math>F</math> change over an interval <math>[a,b]</math>? Obviously, the answer is <math>F(b)-F(a)</math>. But there's another way to look at it. Break the interval <math>[a,b]</math> up into a whole bunch of tiny subintervals, each having a tiny width <math>\Delta x</math>. Let's say <math>[a,b]</math> has been broken up into <math>n</math> subintervals, so <math>\Delta x = \frac{b-a}{n}</math>. Let <math>x_0 = a, x_1 = a + \Delta x, x_2 = a + 2\Delta x, \ldots, x_i = x_0 + i\Delta x, \ldots, x_n = a + n\Delta x = b</math>.<br />
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How much does <math>F</math> change over the tiny interval <math>[x_i,x_{i+1}]</math>? Of course, the answer is <math>F(x_{i+1})-F(x_i)</math>. But this is approximately <math>F'(x_i)\Delta x</math>. If <math>\Delta F_i</math> is the amount that <math>F</math> changes on the interval <math>[x_i, x_{i+1}]</math>, then <math>\Delta F_i \approx F'(x_i)\Delta x</math>.<br />
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The total change of <math>F</math> over the interval <math>[a,b]</math> , <math>F(b)-F(a)</math>, is exactly equal to <math>\Delta F_0 + \Delta F_1 +\cdots + \Delta F_{n-1}</math> . Thus,<br />
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<math>F(b)-F(a) \approx F'(x_0)\Delta x + F'(x_1) \Delta x + \cdots + F'(x_{n-1}) \Delta x</math>.<br />
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What we have here on the right is a Riemann sum. It approximates a certain integral. What integral does it approximate? Well, it approximates <math>\int_a^b F'(x) dx</math> .<br />
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If we repeat this process, using more and more subintervals, then our approximations will get better and better, and the Riemann sums will approximate that integral better and better, and in the limit we will find that <math>F(b)-F(a) = \int_a^b F'(x) dx</math>.<br />
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This can be made into a rigorous proof, if you use the [[Mean Value Theorem]]. The standard proof of the first Fundamental Theorem of Calculus, using the Mean Value Theorem, can be thought of in this way.<br />
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In order to get an intuitive understanding of the second Fundamental Theorem of Calculus, I recommend just thinking about problem 6. The idea presented there can also be turned into a rigorous proof. (The standard proof can be thought of in this way.)<br />
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== Proof ==<br />
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Here's a proof of the first Fundamental Theorem of Calculus.<br />
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Let <math>{a}</math>, <math>{b} \in \mathbb{R}</math> , <math>a<b</math>. Suppose <math>F:[a,b] \to \mathbb{R}</math> is differentiable on the whole interval <math>[a,b]</math> (using limits from the right and left for the derivatives at <math>{a}</math> and <math>{b}</math>, respectively), and suppose that <math>F'</math> is Riemann integrable on <math>[a,b]</math>.<br />
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Let <math>\epsilon > 0</math>. There exists <math>\delta > 0</math> such that if <math>a=x_0, x_1, x_2, \ldots, x_n=b</math> is a partition of <math>[a,b]</math> , and <math>\Delta x_0=x_1-x_0, \Delta x_1 = x_2-x_1, \ldots, \Delta x_{n-1}=x_n - x_{n-1}=b-x_{n-1}</math> , and <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>, and <math>\xi_i</math> is in <math>[x_i,x_{i+1}]</math> for all <math>i</math>, <math>0 \le i < n</math>, THEN the Riemann sum <br />
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<math>F'(\xi_0) \Delta x_0 + F'(\xi_1) \Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math> <br />
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is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
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(In fact, this is sometimes taken as the definition of the statement "<math>F'</math> is Riemann integrable on the interval <math>[a,b]</math>.")<br />
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So, let <math>a=x_0, x_1,\ldots, x_n=b</math> be a partition of <math>[a,b]</math> such that <math>\Delta x_i < \delta</math> for all <math>i</math>, <math>0 \le i < n</math>.<br />
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For each <math>i</math>, <math>0\le i < n</math>, let <math>\Delta F_i = F(x_{i+1})-F(x_i)</math> be the amount that <math>F</math> changes over the interval <math>[x_i,x_{i+1}]</math>. Then<br />
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<math>F(b) - F(a)=\Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math>.<br />
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According to the Mean Value Theorem, for each <math>i</math>, <math>0 \le i < n</math>, there exists <math>\xi_i \in (x_i, x_{i+1})</math> such that <math>\Delta F_i = F(x_{i+1}) - F(x_i) = F'(\xi_i)\Delta x_i</math>. <br />
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(This is similar to the part of the intuitive argument where we said that <math>\Delta F_i \approx F'(x_i) \Delta x_i</math>. However, this is better. The Mean Value Theorem, fortunately, gives us exact equality, rather than just an approximation.)<br />
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Thus,<br />
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<math>F(b)-F(a) = \Delta F_0 + \Delta F_1 + \cdots + \Delta F_{n-1}</math><br />
<math>= F'(\xi_0) \Delta x_0 + F'(\xi_1)\Delta x_1 + \cdots + F'(\xi_{n-1}) \Delta x_{n-1}</math>.<br />
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This last expression, on the right, is a Riemann sum, and it is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
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THEREFORE, we have found that <math>F(b) - F(a)</math> is within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math>.<br />
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But <math>\epsilon > 0</math> was arbitrary. The only way that <math>F(b) - F(a)</math> could be within <math>\epsilon</math> of <math>\int_a^b F'(x) dx</math> for any <math>\epsilon > 0</math> is if <math>F(b)-F(a)</math> is actually equal to <math>\int_a^b F'(x) dx</math>.<br />
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So that means <math>\int_a^b F'(x) dx = F(b)-F(a)</math>.<br />
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That concludes the proof of the first Fundamental Theorem of Calculus.<br />
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For a proof of the second Fundamental Theorem of Calculus, I recommend looking in the book ''Calculus'' by Spivak. (Hopefully I or someone else will post a proof here eventually.)<br />
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==Generalizations==<br />
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==See also==</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Discussion&diff=13358AoPS Wiki:Discussion2007-02-25T00:46:27Z<p>AMC37.5: /* Wiki-wide discussion board */ bug</p>
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<div>{{shortcut|[[AoPS:CP]]<br />[[AoPS:HELP]]}}<br />
<br />
<br />
=Pages to start off with=<br />
<Advertise your wikipage here><br />
<br />
[[Function]] really needs work. It's about 1/3rd written, and about 1/3rd of that is properly latexed. --[[User:Solafidefarms|solafidefarms]] 16:46, 22 June 2006 (EDT)<br />
[[Function]] is i think looks latexed--[[User:Anirudh|Anirudh]] 19:54, 30 December 2006 (EST)<br />
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Look at [[Special:Wantedpages]] to find interesting pages to work on. Or look at the list of stubs (visit the page Category:Stubs) to find pages in need of more content. Or, look at the list of [[Special:Newpages]] and look for the pages I've created, since most of them are just 2 sentences long. --[[User_talk:JBL|JBL]] 11:07, 12 July 2006 (EDT)<br />
<br />
=Things to do=<br />
Please add more to the list below<br />
<br />
== Suggestion - maybe add PDF's of contests ==<br />
Maybe we should add pdfs of the contests so people can download and print them?--[[User:Anirudh|Anirudh]] 22:00, 31 December 2006 (EST)<br />
:Just add them as TeX which can be rendered as a printable image. Acrobat is slow. [[User:AMC37.5|AMC37.5]] 01:32, 24 February 2007 (EST)<br />
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== Adding AMC Problems and Solutions! ==<br />
you should let awupu hve images too. --[[User:Anirudh|Anirudh]] 20:04, 27 November 2006 (EST)<br />
'''awupu2''': the AoPSWiki Unofficial Problem Uploader was just updated, and now automatically links to other wiki articles for you! See [http://mathideas.org/code/awupu/ awupu].<br />
--[[User:Chess64|Chess64]] 22:39, 5 November 2006 (EST)<br />
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Please see the [http://mathideas.org/code/awupu AoPSWiki Problem Uploader], which can help you save a lot of time when you are uploading MO problems. --[[User:Chess64|Chess64]] 20:27, 28 July 2006 (EDT)<br />
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Every member can contribute to this no matter what kind of math knowledge they have. This is also very important to the amount of information on the Wiki. Please go to the Contests Page and copy problems from the competitions to the pages they are missing from. (see below) If you have more time, please add a solution to the pages that are missing solutions. (also see below)<br />
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*2006<br />
**Missing Problems<br />
***2001 AMC 10 Problems 1-25<br />
***<s>2006 AMC 10B Problems 1-25</s><br />
***<s>2006 AMC 12A Problems 1-25</s><br />
***2006 AMC 12B Problems 1-25<br />
***2006 USAMO Problems 1-6<br />
***2006 USA TST Problems 1-6<br />
**Missing Solutions<br />
***2006 AMC 10A Solutions 7-25<br />
***<s>2006 AMC 10B Solutions 1-25</s><br />
***2006 AMC 12A Solutions 1-25<br />
***2006 AMC 12B Solutions 1-25<br />
***2006 AIME I Solutions 4, 7-11, 13-15<br />
***2006 AIME II Solutions 1-15<br />
***2006 USAMO Solutions 1-6<br />
***2006 USA TST Solutions 1-6<br />
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Thanks! [[User:Ignite168|Ignite168]] 20:06, 7 July 2006 (EDT)<br />
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Just adding a note to please strike out something by using <nowiki><s> to start the strike out and </s> to finish it</nowiki> when it is completed like so <s>example</s>. Also, you can work on 2005, 2004, 2003, etc. but I just put 2006 here to start with. Oh and to joml88: Thanks for all your work on problems in past years so far. [[User:Ignite168|Ignite168]] 01:25, 9 July 2006 (EDT)<br />
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== Find Articles about AoPS Members ==<br />
<br />
Please help find articles about Art of Problem Solving Members and place [[Template:AoPSMember]] on the talk page of that article. Before you use this template though, please first read the usage instructions [[Template:AoPSMember#How_to_use_this_template|here]]. [[User:Ignite168|Ignite168]] 00:36, 1 July 2006 (EDT)<br />
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== Convention for naming articles ==<br />
It's important that we set this standard now, otherwise, there's going to be a lot of cleaning up to do, not only in terms of admins moving pages, but also in terms of cleaning up links to those articles. Please see the stick post in the AoPSWiki forum about this! Chime in with your opinion. See [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=97741 this forum post] for details.<br />
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== Other ==<br />
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Patrons:Don't edit other's wiki profiles!<br />
Admins:Please change the access restrictions on user's pages<br />
==General Topics==<br />
*[[Combinatorics]] and [[Probability]] Topics Techiniques<br />
*[[Logic]] and [[Game Theory]] Topics<br />
*[[Functions]] and [[Functional Equations]] Topics<br />
*[[Number Theory]] Techinques and Topics -- well, we have a Number theory page...<br />
*[[Algebra]] Topics and Techniques<br />
*[[Inequalities]] and solving techniques<br />
*[[Geometry]] Topics<br />
*[[Arithmetic sequence]] needs work<br />
*Other sciences<br />
*Linking to ready made content, (Sato's NT packet, the geometry packet by Kedlaya or some name like that, mildorf and other's equality packets, Joe's factoring topic, the formulary, the inequality learning marathon in the forum, the mathematical idea's blog, etc)<br />
*Study plans and Problem sets<br />
*Especially problem sets<br />
*Instructive problem sets<br />
*A topic on why doing problems is the fastest way to learn<br />
* [[LaTeX]] page (very incomplete, could do with some explaining of latex, origins, and codes for useful things like \boxed or something)<br />
* Problem solving Strategies(chapter 2 of Zeitz)<br />
* Advanced techniques (Invariants, monovariants, symmetry, things like that)<br />
* ...<br />
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===Techiniques===<br />
Adding techniques frequently used in each discipline would be nice, like PIE, substituion for a new variable, solving equations by substituing in trigonometric expressions, etc.<br />
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===General Usage===<br />
*Adding contest problems to illustrate techniques<br />
*Learning to use the signature button in the editor<br />
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== 2006 Canadian MO ==<br />
<!--Please place comments below this line--><br />
'''Hi there''' people, but we really need some solutions for the [[2006_Canadian_MO]].--[[User:Anirudh|Anirudh]] 12:16, 6 February 2007 (EST)<br />
:Unfortunately, that's not the only contest we need to write solutions for: about <math>\lim_{x \to 0+} (100 - x)%</math> of the problem articles on this wiki need solutions :(wow, I guess I am a pessimist). On a slightly irrelevant note, I think (for organizational purposes) that it would be better to start adding new posts to the bottom. It's virtually impossible to trace a reply like "I agree" in such a long discussion. [[User:Azjps|Azjps]] 19:38, 7 February 2007 (EST)<br />
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= Wiki-wide discussion board =<br />
<br />
'''Add your message to THE BOTTOM'''<br />
== categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated ==<br />
I agree. --[[User:Chess64|Chess64]] 16:24, 24 December 2006 (EST)<br />
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I propose that the categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated, for the following reasons :<br />
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* They are indistinguishable for olympiad problems.<br />
* All of them can be classified as either algebra or geometry problems.<br />
* The IMO uses only the other four categories for olympiad problems currently in existance.<br />
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Does anybody agree or disagree? I also mentioned this on the discussion page for [[Contest Problems Standards]]. &mdash;[[User:Boy Soprano II|Boy Soprano II]] 17:21, 25 August 2006 (EDT)<br />
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== Math on the page is horribly garbled ==<br />
Does anyone here get this problem? What happens is that on some pages (notably those with centered math), the math on the page is horribly garbled. See [[Talk:Fallacious proof]] for a picture. I use IE6, Windows XP. --[[User:IntrepidMath|IntrepidMath]] 15:38, 4 August 2006 (EDT)<br />
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Sean, you can use <nowiki> <pre> ... </pre> </nowiki> to make the box:<br />
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<pre> Testing to make sure. </pre><br />
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--[[User:Joml88|Joe]] 09:43, 1 August 2006 (EDT)<br />
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If you're typing an olympiad problem (or indeed, any problem for which you think alternate solutions could be enlightening), you can use the <nowiki>{{alternate solutions}}</nowiki> template I made. It currently prints the text right after this message. Sean, I'm not sure, but you may find your answer [http://meta.wikimedia.org/wiki/Help:Wiki_markup_examples#Disabling_wikitext_interpretation_and.2For_reformatting here]. --[[User:Boy Soprano II|Boy Soprano II]] 19:55, 25 July 2006 (EDT) {{alternate solutions}}<br />
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To answer my own question, see [[templates & categories]]. Now I have a new question: how do you box something in AoPSWiki? I have a long code that needs to be in a box, because the article would look much cleaner. Thanks! --[[User:Mysmartmouth|Sean]] 13:32, 27 June 2006 (EDT)<br />
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How do you create a template? Is this something only admins can do? --[[User:Mysmartmouth|Sean]] 23:57, 23 June 2006 (EDT)<br />
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OK, for definitions,should there be a category or a template or nothing?--[[User:Solafidefarms|solafidefarms]] 22:26, 23 June 2006 (EDT)<br />
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you can add any problems you want, just give credit to the source. like <br />
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* ([[The Art and Craft of Problem Solving]]) Problem text here.<br />
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Solution<br />
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--[[User:Chess64|Chess64]] 10:28, 22 June 2006 (EDT)<br />
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are we allowed to add problems from problem books to the wiki? I notice people are adding AIME problems, whose books can we add problems from? I don't mean the whole thing or anything, just one or two problems at a time. --[[User:Agolsme|Agolsme]] 17:09, 21 June 2006 (EDT)<br />
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Err, my bad. That was a typo... now I have to fix it in the article too... --[[User:Chess64|Chess64]] 10:15, 19 June 2006 (EDT)<br />
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@alvaro I linked up the general topics area, ok?<br />
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where are the pages of the general topics? must we create them? --[[User:alvaro|alvaro]] 11:25, 18 June 2006 (EDT)<br />
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Yes, the formula is now right. Joe changed it. It was off a bit before. --[[User:Mysmartmouth|Mysmartmouth]] 19:02, 18 June 2006 (EDT)<br />
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I like it, PenguinIntegral. Mysmartmouth, the formula is definitely right. --[[User:Chess64|Chess64]] 18:20, 18 June 2006 (EDT)<br />
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I added some structure to this page. Feel free to comment.<br />
--[[User:PenguinIntegral|PenguinIntegral]] 18:08, 18 June 2006 (EDT)<br />
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Millenium problems would be a good topic; people are always asking about those problems. Also, can someone take a look at [[Vieta's formulas]]? I think the formula given is wrong. <br />
--[[User:Mysmartmouth|Mysmartmouth]] 14:32, 18 June 2006 (EDT)<br />
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I just want to make a note that there is a better way to create a signature. If you look at the Wiki toolbar above, you see the second button from the right. It looks like a signature. Just hit that button at the end of your comment, and a signature, with timestamp, will be added. That is the widely accepted way to sign comments on Wikipedia, and it would be nice to have some kind of standard here as well. Just a suggestion. --[[User:Mysmartmouth|Mysmartmouth]] 11:09, 18 June 2006 (EDT)<br />
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I added a lot of info to the [[MathCounts]] page in my bid to become a moderator...<br />
--[[User:Treething|Treething]] 15:57, 18 June 2006 (EDT)<br />
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The Inequalities need skeleton pages set up. Can someone help my math parsing on the [[Power mean inequality]]? It is really messing up.<br />
-PenguinIntegral<br />
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The [[Polynomials]] page needs a skeleton too...<br />
-chess64<br />
What does everyone think of me using AIME problems to illistrate mathematical concepts like completing the square?<br />
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See [[Completing the square]]<br />
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Hey, I'm not sure exactly how to format this page...but I edited the completing the square page somewhat (btw there are some Latex problems that someone (not me) needs to fix), anyone else have feedback?<br />
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I like your idea of using sample problems, but I don't really understand what the sample problem you placed in the [[Completing the square]] page has to do with the topic...<br />
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-eryaman<br />
Yeah, it probably would have been nice if I explained how the solution uses adding/subtracting to factor, of which completing the square is a special case.<br />
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Someone smart should fix that.<br />
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Does anyone have ideas for new topics? I think we should split up the wiki like the USAMO problem subjects: Combo and Probability, Algebra and Polynomials, Functions, Inequalities, Geometry, and Number Theory. I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it, so I'll look into starting a page on counting strategies.<br />
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Always use example problems; they really reinforce the material and prepare the reader for using them in a contest setting.<br />
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(Ok, I just made that up. But it feels good to start a fad)<br />
-PenguinIntegral<br />
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"I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it..." uh actually no i'm not but i guess i'll work on it<br />
-chess64<br />
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Idea: Should the Wiki turn into an "example emporium"? We should wait for an Admin's go-ahead before starting... Also-Should we link to the [[Needed Pages]] on the home page?<br />
-IntrepidMath<br />
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Insanity is only exceptable within reason. We shouldn't put problems on every page, but as the AoPS books show, examples really help learning.<br />
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-PenguinIntegral<br />
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I'll start some Combinatorics pages/links, but how do you start a page?<br />
-quantum leap<br />
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search for the name of the article that you want to write [-chess64]<br />
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uh guys this is the "community portal" so i think these discussions should be in the "discussion" page of this (see the blue button at the top) and this page should be used for things like links to [[needed pages]]... should i go ahead and fix this?<br />
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-chess64<br />
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Um, there are two cauchy-schwarz inequality pages (depending on whether or not the "s" in schwarz is capitalized) :/ I guess they should be combined... -quantum leap<br />
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==monobook.js==<br />
Would it be possible for an administrator to somehow activate the usage of the personal javascript file - [[Special:Mypage/monobook.js]]? It would certainly help to expedite the process of building this wiki. [[User:Azjps|Azjps]] 19:43, 6 February 2007 (EST)<br />
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I remember a Firefox and IE bug recently where I could deviously steal your AoPS password. Thus I think that's a bad idea. --[[User:Solafidefarms|solafidefarms]] 15:38, 15 February 2007 (EST)<br />
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:Oh, never mind then. I certainly wasn't aware of that. Thanks, [[User:Azjps|Azjps]] ([[User talk:Azjps|<font color="green">talk</font>]]) 16:32, 15 February 2007 (EST)<br />
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== Dollar signs ==<br />
How do you indicate <math>15000 without the wiki doing latex? </math>\<math></math> doesn't work. --[[User:Solafidefarms|solafidefarms]] 10:02, 30 August 2006 (EDT)<br />
We need a lot more amc 10s--[[User:Anirudh|Anirudh]] 19:47, 31 December 2006 (EST)<br />
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Try using the nowiki tags:<nowiki>$</nowiki> formatting.--[[User:IntrepidMath|IntrepidMath]] 10:49, 30 August 2006 (EDT)<br />
Thanks!--[[User:Solafidefarms|solafidefarms]] 17:33, 30 August 2006 (EDT)<br />
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== Serious bug in login ==<br />
When I logged into AOPS Wiki a second time, I typed my username in lowercase, and it logged in as a new user. [[User:AMC37.5|AMC37.5]] 19:46, 24 February 2007 (EST)</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Discussion&diff=13357AoPS Wiki:Discussion2007-02-25T00:44:48Z<p>AMC37.5: /* Wiki-wide discussion board */ e</p>
<hr />
<div>{{shortcut|[[AoPS:CP]]<br />[[AoPS:HELP]]}}<br />
<br />
<br />
=Pages to start off with=<br />
<Advertise your wikipage here><br />
<br />
[[Function]] really needs work. It's about 1/3rd written, and about 1/3rd of that is properly latexed. --[[User:Solafidefarms|solafidefarms]] 16:46, 22 June 2006 (EDT)<br />
[[Function]] is i think looks latexed--[[User:Anirudh|Anirudh]] 19:54, 30 December 2006 (EST)<br />
<br />
Look at [[Special:Wantedpages]] to find interesting pages to work on. Or look at the list of stubs (visit the page Category:Stubs) to find pages in need of more content. Or, look at the list of [[Special:Newpages]] and look for the pages I've created, since most of them are just 2 sentences long. --[[User_talk:JBL|JBL]] 11:07, 12 July 2006 (EDT)<br />
<br />
=Things to do=<br />
Please add more to the list below<br />
<br />
== Suggestion - maybe add PDF's of contests ==<br />
Maybe we should add pdfs of the contests so people can download and print them?--[[User:Anirudh|Anirudh]] 22:00, 31 December 2006 (EST)<br />
:Just add them as TeX which can be rendered as a printable image. Acrobat is slow. [[User:AMC37.5|AMC37.5]] 01:32, 24 February 2007 (EST)<br />
<br />
== Adding AMC Problems and Solutions! ==<br />
you should let awupu hve images too. --[[User:Anirudh|Anirudh]] 20:04, 27 November 2006 (EST)<br />
'''awupu2''': the AoPSWiki Unofficial Problem Uploader was just updated, and now automatically links to other wiki articles for you! See [http://mathideas.org/code/awupu/ awupu].<br />
--[[User:Chess64|Chess64]] 22:39, 5 November 2006 (EST)<br />
<br />
Please see the [http://mathideas.org/code/awupu AoPSWiki Problem Uploader], which can help you save a lot of time when you are uploading MO problems. --[[User:Chess64|Chess64]] 20:27, 28 July 2006 (EDT)<br />
<br />
Every member can contribute to this no matter what kind of math knowledge they have. This is also very important to the amount of information on the Wiki. Please go to the Contests Page and copy problems from the competitions to the pages they are missing from. (see below) If you have more time, please add a solution to the pages that are missing solutions. (also see below)<br />
<br />
*2006<br />
**Missing Problems<br />
***2001 AMC 10 Problems 1-25<br />
***<s>2006 AMC 10B Problems 1-25</s><br />
***<s>2006 AMC 12A Problems 1-25</s><br />
***2006 AMC 12B Problems 1-25<br />
***2006 USAMO Problems 1-6<br />
***2006 USA TST Problems 1-6<br />
**Missing Solutions<br />
***2006 AMC 10A Solutions 7-25<br />
***<s>2006 AMC 10B Solutions 1-25</s><br />
***2006 AMC 12A Solutions 1-25<br />
***2006 AMC 12B Solutions 1-25<br />
***2006 AIME I Solutions 4, 7-11, 13-15<br />
***2006 AIME II Solutions 1-15<br />
***2006 USAMO Solutions 1-6<br />
***2006 USA TST Solutions 1-6<br />
<br />
Thanks! [[User:Ignite168|Ignite168]] 20:06, 7 July 2006 (EDT)<br />
<br />
Just adding a note to please strike out something by using <nowiki><s> to start the strike out and </s> to finish it</nowiki> when it is completed like so <s>example</s>. Also, you can work on 2005, 2004, 2003, etc. but I just put 2006 here to start with. Oh and to joml88: Thanks for all your work on problems in past years so far. [[User:Ignite168|Ignite168]] 01:25, 9 July 2006 (EDT)<br />
<br />
== Find Articles about AoPS Members ==<br />
<br />
Please help find articles about Art of Problem Solving Members and place [[Template:AoPSMember]] on the talk page of that article. Before you use this template though, please first read the usage instructions [[Template:AoPSMember#How_to_use_this_template|here]]. [[User:Ignite168|Ignite168]] 00:36, 1 July 2006 (EDT)<br />
<br />
== Convention for naming articles ==<br />
It's important that we set this standard now, otherwise, there's going to be a lot of cleaning up to do, not only in terms of admins moving pages, but also in terms of cleaning up links to those articles. Please see the stick post in the AoPSWiki forum about this! Chime in with your opinion. See [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=97741 this forum post] for details.<br />
<br />
== Other ==<br />
<br />
Patrons:Don't edit other's wiki profiles!<br />
Admins:Please change the access restrictions on user's pages<br />
==General Topics==<br />
*[[Combinatorics]] and [[Probability]] Topics Techiniques<br />
*[[Logic]] and [[Game Theory]] Topics<br />
*[[Functions]] and [[Functional Equations]] Topics<br />
*[[Number Theory]] Techinques and Topics -- well, we have a Number theory page...<br />
*[[Algebra]] Topics and Techniques<br />
*[[Inequalities]] and solving techniques<br />
*[[Geometry]] Topics<br />
*[[Arithmetic sequence]] needs work<br />
*Other sciences<br />
*Linking to ready made content, (Sato's NT packet, the geometry packet by Kedlaya or some name like that, mildorf and other's equality packets, Joe's factoring topic, the formulary, the inequality learning marathon in the forum, the mathematical idea's blog, etc)<br />
*Study plans and Problem sets<br />
*Especially problem sets<br />
*Instructive problem sets<br />
*A topic on why doing problems is the fastest way to learn<br />
* [[LaTeX]] page (very incomplete, could do with some explaining of latex, origins, and codes for useful things like \boxed or something)<br />
* Problem solving Strategies(chapter 2 of Zeitz)<br />
* Advanced techniques (Invariants, monovariants, symmetry, things like that)<br />
* ...<br />
<br />
===Techiniques===<br />
Adding techniques frequently used in each discipline would be nice, like PIE, substituion for a new variable, solving equations by substituing in trigonometric expressions, etc.<br />
<br />
===General Usage===<br />
*Adding contest problems to illustrate techniques<br />
*Learning to use the signature button in the editor<br />
<br />
== 2006 Canadian MO ==<br />
<!--Please place comments below this line--><br />
'''Hi there''' people, but we really need some solutions for the [[2006_Canadian_MO]].--[[User:Anirudh|Anirudh]] 12:16, 6 February 2007 (EST)<br />
:Unfortunately, that's not the only contest we need to write solutions for: about <math>\lim_{x \to 0+} (100 - x)%</math> of the problem articles on this wiki need solutions :(wow, I guess I am a pessimist). On a slightly irrelevant note, I think (for organizational purposes) that it would be better to start adding new posts to the bottom. It's virtually impossible to trace a reply like "I agree" in such a long discussion. [[User:Azjps|Azjps]] 19:38, 7 February 2007 (EST)<br />
<br />
= Wiki-wide discussion board =<br />
<br />
'''Add your message to THE BOTTOM'''<br />
== categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated ==<br />
I agree. --[[User:Chess64|Chess64]] 16:24, 24 December 2006 (EST)<br />
<br />
I propose that the categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated, for the following reasons :<br />
<br />
* They are indistinguishable for olympiad problems.<br />
* All of them can be classified as either algebra or geometry problems.<br />
* The IMO uses only the other four categories for olympiad problems currently in existance.<br />
<br />
Does anybody agree or disagree? I also mentioned this on the discussion page for [[Contest Problems Standards]]. &mdash;[[User:Boy Soprano II|Boy Soprano II]] 17:21, 25 August 2006 (EDT)<br />
<br />
== Math on the page is horribly garbled ==<br />
Does anyone here get this problem? What happens is that on some pages (notably those with centered math), the math on the page is horribly garbled. See [[Talk:Fallacious proof]] for a picture. I use IE6, Windows XP. --[[User:IntrepidMath|IntrepidMath]] 15:38, 4 August 2006 (EDT)<br />
<br />
<br />
Sean, you can use <nowiki> <pre> ... </pre> </nowiki> to make the box:<br />
<br />
<pre> Testing to make sure. </pre><br />
<br />
--[[User:Joml88|Joe]] 09:43, 1 August 2006 (EDT)<br />
<br />
<br />
If you're typing an olympiad problem (or indeed, any problem for which you think alternate solutions could be enlightening), you can use the <nowiki>{{alternate solutions}}</nowiki> template I made. It currently prints the text right after this message. Sean, I'm not sure, but you may find your answer [http://meta.wikimedia.org/wiki/Help:Wiki_markup_examples#Disabling_wikitext_interpretation_and.2For_reformatting here]. --[[User:Boy Soprano II|Boy Soprano II]] 19:55, 25 July 2006 (EDT) {{alternate solutions}}<br />
<br />
To answer my own question, see [[templates & categories]]. Now I have a new question: how do you box something in AoPSWiki? I have a long code that needs to be in a box, because the article would look much cleaner. Thanks! --[[User:Mysmartmouth|Sean]] 13:32, 27 June 2006 (EDT)<br />
<br />
How do you create a template? Is this something only admins can do? --[[User:Mysmartmouth|Sean]] 23:57, 23 June 2006 (EDT)<br />
<br />
OK, for definitions,should there be a category or a template or nothing?--[[User:Solafidefarms|solafidefarms]] 22:26, 23 June 2006 (EDT)<br />
<br />
you can add any problems you want, just give credit to the source. like <br />
<br />
* ([[The Art and Craft of Problem Solving]]) Problem text here.<br />
<br />
Solution<br />
<br />
--[[User:Chess64|Chess64]] 10:28, 22 June 2006 (EDT)<br />
<br />
are we allowed to add problems from problem books to the wiki? I notice people are adding AIME problems, whose books can we add problems from? I don't mean the whole thing or anything, just one or two problems at a time. --[[User:Agolsme|Agolsme]] 17:09, 21 June 2006 (EDT)<br />
<br />
Err, my bad. That was a typo... now I have to fix it in the article too... --[[User:Chess64|Chess64]] 10:15, 19 June 2006 (EDT)<br />
<br />
@alvaro I linked up the general topics area, ok?<br />
<br />
where are the pages of the general topics? must we create them? --[[User:alvaro|alvaro]] 11:25, 18 June 2006 (EDT)<br />
<br />
Yes, the formula is now right. Joe changed it. It was off a bit before. --[[User:Mysmartmouth|Mysmartmouth]] 19:02, 18 June 2006 (EDT)<br />
<br />
I like it, PenguinIntegral. Mysmartmouth, the formula is definitely right. --[[User:Chess64|Chess64]] 18:20, 18 June 2006 (EDT)<br />
<br />
I added some structure to this page. Feel free to comment.<br />
--[[User:PenguinIntegral|PenguinIntegral]] 18:08, 18 June 2006 (EDT)<br />
<br />
Millenium problems would be a good topic; people are always asking about those problems. Also, can someone take a look at [[Vieta's formulas]]? I think the formula given is wrong. <br />
--[[User:Mysmartmouth|Mysmartmouth]] 14:32, 18 June 2006 (EDT)<br />
<br />
I just want to make a note that there is a better way to create a signature. If you look at the Wiki toolbar above, you see the second button from the right. It looks like a signature. Just hit that button at the end of your comment, and a signature, with timestamp, will be added. That is the widely accepted way to sign comments on Wikipedia, and it would be nice to have some kind of standard here as well. Just a suggestion. --[[User:Mysmartmouth|Mysmartmouth]] 11:09, 18 June 2006 (EDT)<br />
<br />
<br />
I added a lot of info to the [[MathCounts]] page in my bid to become a moderator...<br />
--[[User:Treething|Treething]] 15:57, 18 June 2006 (EDT)<br />
<br />
<br />
The Inequalities need skeleton pages set up. Can someone help my math parsing on the [[Power mean inequality]]? It is really messing up.<br />
-PenguinIntegral<br />
<br />
The [[Polynomials]] page needs a skeleton too...<br />
-chess64<br />
What does everyone think of me using AIME problems to illistrate mathematical concepts like completing the square?<br />
<br />
See [[Completing the square]]<br />
<br />
Hey, I'm not sure exactly how to format this page...but I edited the completing the square page somewhat (btw there are some Latex problems that someone (not me) needs to fix), anyone else have feedback?<br />
<br />
<br />
I like your idea of using sample problems, but I don't really understand what the sample problem you placed in the [[Completing the square]] page has to do with the topic...<br />
<br />
-eryaman<br />
Yeah, it probably would have been nice if I explained how the solution uses adding/subtracting to factor, of which completing the square is a special case.<br />
<br />
Someone smart should fix that.<br />
<br />
Does anyone have ideas for new topics? I think we should split up the wiki like the USAMO problem subjects: Combo and Probability, Algebra and Polynomials, Functions, Inequalities, Geometry, and Number Theory. I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it, so I'll look into starting a page on counting strategies.<br />
<br />
Always use example problems; they really reinforce the material and prepare the reader for using them in a contest setting.<br />
<br />
(Ok, I just made that up. But it feels good to start a fad)<br />
-PenguinIntegral<br />
<br />
"I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it..." uh actually no i'm not but i guess i'll work on it<br />
-chess64<br />
<br />
<br />
Idea: Should the Wiki turn into an "example emporium"? We should wait for an Admin's go-ahead before starting... Also-Should we link to the [[Needed Pages]] on the home page?<br />
-IntrepidMath<br />
<br />
Insanity is only exceptable within reason. We shouldn't put problems on every page, but as the AoPS books show, examples really help learning.<br />
<br />
<br />
-PenguinIntegral<br />
<br />
I'll start some Combinatorics pages/links, but how do you start a page?<br />
-quantum leap<br />
<br />
search for the name of the article that you want to write [-chess64]<br />
<br />
uh guys this is the "community portal" so i think these discussions should be in the "discussion" page of this (see the blue button at the top) and this page should be used for things like links to [[needed pages]]... should i go ahead and fix this?<br />
<br />
-chess64<br />
<br />
Um, there are two cauchy-schwarz inequality pages (depending on whether or not the "s" in schwarz is capitalized) :/ I guess they should be combined... -quantum leap<br />
<br />
==monobook.js==<br />
Would it be possible for an administrator to somehow activate the usage of the personal javascript file - [[Special:Mypage/monobook.js]]? It would certainly help to expedite the process of building this wiki. [[User:Azjps|Azjps]] 19:43, 6 February 2007 (EST)<br />
<br />
I remember a Firefox and IE bug recently where I could deviously steal your AoPS password. Thus I think that's a bad idea. --[[User:Solafidefarms|solafidefarms]] 15:38, 15 February 2007 (EST)<br />
<br />
:Oh, never mind then. I certainly wasn't aware of that. Thanks, [[User:Azjps|Azjps]] ([[User talk:Azjps|<font color="green">talk</font>]]) 16:32, 15 February 2007 (EST)<br />
<br />
== Dollar signs ==<br />
How do you indicate <math>15000 without the wiki doing latex? </math>\<math></math> doesn't work. --[[User:Solafidefarms|solafidefarms]] 10:02, 30 August 2006 (EDT)<br />
We need a lot more amc 10s--[[User:Anirudh|Anirudh]] 19:47, 31 December 2006 (EST)<br />
<br />
Try using the nowiki tags:<nowiki>$</nowiki> formatting.--[[User:IntrepidMath|IntrepidMath]] 10:49, 30 August 2006 (EDT)<br />
Thanks!--[[User:Solafidefarms|solafidefarms]] 17:33, 30 August 2006 (EDT)</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Discussion&diff=13356AoPS Wiki:Discussion2007-02-25T00:40:58Z<p>AMC37.5: move discussion at top to appropriate section</p>
<hr />
<div>{{shortcut|[[AoPS:CP]]<br />[[AoPS:HELP]]}}<br />
<br />
<br />
=Pages to start off with=<br />
<Advertise your wikipage here><br />
<br />
[[Function]] really needs work. It's about 1/3rd written, and about 1/3rd of that is properly latexed. --[[User:Solafidefarms|solafidefarms]] 16:46, 22 June 2006 (EDT)<br />
[[Function]] is i think looks latexed--[[User:Anirudh|Anirudh]] 19:54, 30 December 2006 (EST)<br />
<br />
Look at [[Special:Wantedpages]] to find interesting pages to work on. Or look at the list of stubs (visit the page Category:Stubs) to find pages in need of more content. Or, look at the list of [[Special:Newpages]] and look for the pages I've created, since most of them are just 2 sentences long. --[[User_talk:JBL|JBL]] 11:07, 12 July 2006 (EDT)<br />
<br />
=Things to do=<br />
Please add more to the list below<br />
<br />
== Suggestion - maybe add PDF's of contests ==<br />
Maybe we should add pdfs of the contests so people can download and print them?--[[User:Anirudh|Anirudh]] 22:00, 31 December 2006 (EST)<br />
:Just add them as TeX which can be rendered as a printable image. Acrobat is slow. [[User:AMC37.5|AMC37.5]] 01:32, 24 February 2007 (EST)<br />
<br />
== Adding AMC Problems and Solutions! ==<br />
you should let awupu hve images too. --[[User:Anirudh|Anirudh]] 20:04, 27 November 2006 (EST)<br />
'''awupu2''': the AoPSWiki Unofficial Problem Uploader was just updated, and now automatically links to other wiki articles for you! See [http://mathideas.org/code/awupu/ awupu].<br />
--[[User:Chess64|Chess64]] 22:39, 5 November 2006 (EST)<br />
<br />
Please see the [http://mathideas.org/code/awupu AoPSWiki Problem Uploader], which can help you save a lot of time when you are uploading MO problems. --[[User:Chess64|Chess64]] 20:27, 28 July 2006 (EDT)<br />
<br />
Every member can contribute to this no matter what kind of math knowledge they have. This is also very important to the amount of information on the Wiki. Please go to the Contests Page and copy problems from the competitions to the pages they are missing from. (see below) If you have more time, please add a solution to the pages that are missing solutions. (also see below)<br />
<br />
*2006<br />
**Missing Problems<br />
***2001 AMC 10 Problems 1-25<br />
***<s>2006 AMC 10B Problems 1-25</s><br />
***<s>2006 AMC 12A Problems 1-25</s><br />
***2006 AMC 12B Problems 1-25<br />
***2006 USAMO Problems 1-6<br />
***2006 USA TST Problems 1-6<br />
**Missing Solutions<br />
***2006 AMC 10A Solutions 7-25<br />
***<s>2006 AMC 10B Solutions 1-25</s><br />
***2006 AMC 12A Solutions 1-25<br />
***2006 AMC 12B Solutions 1-25<br />
***2006 AIME I Solutions 4, 7-11, 13-15<br />
***2006 AIME II Solutions 1-15<br />
***2006 USAMO Solutions 1-6<br />
***2006 USA TST Solutions 1-6<br />
<br />
Thanks! [[User:Ignite168|Ignite168]] 20:06, 7 July 2006 (EDT)<br />
<br />
Just adding a note to please strike out something by using <nowiki><s> to start the strike out and </s> to finish it</nowiki> when it is completed like so <s>example</s>. Also, you can work on 2005, 2004, 2003, etc. but I just put 2006 here to start with. Oh and to joml88: Thanks for all your work on problems in past years so far. [[User:Ignite168|Ignite168]] 01:25, 9 July 2006 (EDT)<br />
<br />
== Find Articles about AoPS Members ==<br />
<br />
Please help find articles about Art of Problem Solving Members and place [[Template:AoPSMember]] on the talk page of that article. Before you use this template though, please first read the usage instructions [[Template:AoPSMember#How_to_use_this_template|here]]. [[User:Ignite168|Ignite168]] 00:36, 1 July 2006 (EDT)<br />
<br />
== Convention for naming articles ==<br />
It's important that we set this standard now, otherwise, there's going to be a lot of cleaning up to do, not only in terms of admins moving pages, but also in terms of cleaning up links to those articles. Please see the stick post in the AoPSWiki forum about this! Chime in with your opinion. See [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=97741 this forum post] for details.<br />
<br />
== Other ==<br />
<br />
Patrons:Don't edit other's wiki profiles!<br />
Admins:Please change the access restrictions on user's pages<br />
==General Topics==<br />
*[[Combinatorics]] and [[Probability]] Topics Techiniques<br />
*[[Logic]] and [[Game Theory]] Topics<br />
*[[Functions]] and [[Functional Equations]] Topics<br />
*[[Number Theory]] Techinques and Topics -- well, we have a Number theory page...<br />
*[[Algebra]] Topics and Techniques<br />
*[[Inequalities]] and solving techniques<br />
*[[Geometry]] Topics<br />
*[[Arithmetic sequence]] needs work<br />
*Other sciences<br />
*Linking to ready made content, (Sato's NT packet, the geometry packet by Kedlaya or some name like that, mildorf and other's equality packets, Joe's factoring topic, the formulary, the inequality learning marathon in the forum, the mathematical idea's blog, etc)<br />
*Study plans and Problem sets<br />
*Especially problem sets<br />
*Instructive problem sets<br />
*A topic on why doing problems is the fastest way to learn<br />
* [[LaTeX]] page (very incomplete, could do with some explaining of latex, origins, and codes for useful things like \boxed or something)<br />
* Problem solving Strategies(chapter 2 of Zeitz)<br />
* Advanced techniques (Invariants, monovariants, symmetry, things like that)<br />
* ...<br />
<br />
===Techiniques===<br />
Adding techniques frequently used in each discipline would be nice, like PIE, substituion for a new variable, solving equations by substituing in trigonometric expressions, etc.<br />
<br />
===General Usage===<br />
*Adding contest problems to illustrate techniques<br />
*Learning to use the signature button in the editor<br />
<br />
== 2006 Canadian MO ==<br />
<!--Please place comments below this line--><br />
'''Hi there''' people, but we really need some solutions for the [[2006_Canadian_MO]].--[[User:Anirudh|Anirudh]] 12:16, 6 February 2007 (EST)<br />
:Unfortunately, that's not the only contest we need to write solutions for: about <math>\lim_{x \to 0+} (100 - x)%</math> of the problem articles on this wiki need solutions :(wow, I guess I am a pessimist). On a slightly irrelevant note, I think (for organizational purposes) that it would be better to start adding new posts to the bottom. It's virtually impossible to trace a reply like "I agree" in such a long discussion. [[User:Azjps|Azjps]] 19:38, 7 February 2007 (EST)<br />
<br />
= Wiki-wide discussion board =<br />
<br />
'''Add your message to THE BOTTOM'''<br />
<br />
I agree. --[[User:Chess64|Chess64]] 16:24, 24 December 2006 (EST)<br />
<br />
I propose that the categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated, for the following reasons :<br />
<br />
* They are indistinguishable for olympiad problems.<br />
* All of them can be classified as either algebra or geometry problems.<br />
* The IMO uses only the other four categories for olympiad problems currently in existance.<br />
<br />
Does anybody agree or disagree? I also mentioned this on the discussion page for [[Contest Problems Standards]]. &mdash;[[User:Boy Soprano II|Boy Soprano II]] 17:21, 25 August 2006 (EDT)<br />
<br />
Does anyone here get this problem? What happens is that on some pages (notably those with centered math), the math on the page is horribly garbled. See [[Talk:Fallacious proof]] for a picture. I use IE6, Windows XP. --[[User:IntrepidMath|IntrepidMath]] 15:38, 4 August 2006 (EDT)<br />
<br />
<br />
Sean, you can use <nowiki> <pre> ... </pre> </nowiki> to make the box:<br />
<br />
<pre> Testing to make sure. </pre><br />
<br />
--[[User:Joml88|Joe]] 09:43, 1 August 2006 (EDT)<br />
<br />
<br />
If you're typing an olympiad problem (or indeed, any problem for which you think alternate solutions could be enlightening), you can use the <nowiki>{{alternate solutions}}</nowiki> template I made. It currently prints the text right after this message. Sean, I'm not sure, but you may find your answer [http://meta.wikimedia.org/wiki/Help:Wiki_markup_examples#Disabling_wikitext_interpretation_and.2For_reformatting here]. --[[User:Boy Soprano II|Boy Soprano II]] 19:55, 25 July 2006 (EDT) {{alternate solutions}}<br />
<br />
To answer my own question, see [[templates & categories]]. Now I have a new question: how do you box something in AoPSWiki? I have a long code that needs to be in a box, because the article would look much cleaner. Thanks! --[[User:Mysmartmouth|Sean]] 13:32, 27 June 2006 (EDT)<br />
<br />
How do you create a template? Is this something only admins can do? --[[User:Mysmartmouth|Sean]] 23:57, 23 June 2006 (EDT)<br />
<br />
OK, for definitions,should there be a category or a template or nothing?--[[User:Solafidefarms|solafidefarms]] 22:26, 23 June 2006 (EDT)<br />
<br />
you can add any problems you want, just give credit to the source. like <br />
<br />
* ([[The Art and Craft of Problem Solving]]) Problem text here.<br />
<br />
Solution<br />
<br />
--[[User:Chess64|Chess64]] 10:28, 22 June 2006 (EDT)<br />
<br />
are we allowed to add problems from problem books to the wiki? I notice people are adding AIME problems, whose books can we add problems from? I don't mean the whole thing or anything, just one or two problems at a time. --[[User:Agolsme|Agolsme]] 17:09, 21 June 2006 (EDT)<br />
<br />
Err, my bad. That was a typo... now I have to fix it in the article too... --[[User:Chess64|Chess64]] 10:15, 19 June 2006 (EDT)<br />
<br />
@alvaro I linked up the general topics area, ok?<br />
<br />
where are the pages of the general topics? must we create them? --[[User:alvaro|alvaro]] 11:25, 18 June 2006 (EDT)<br />
<br />
Yes, the formula is now right. Joe changed it. It was off a bit before. --[[User:Mysmartmouth|Mysmartmouth]] 19:02, 18 June 2006 (EDT)<br />
<br />
I like it, PenguinIntegral. Mysmartmouth, the formula is definitely right. --[[User:Chess64|Chess64]] 18:20, 18 June 2006 (EDT)<br />
<br />
I added some structure to this page. Feel free to comment.<br />
--[[User:PenguinIntegral|PenguinIntegral]] 18:08, 18 June 2006 (EDT)<br />
<br />
Millenium problems would be a good topic; people are always asking about those problems. Also, can someone take a look at [[Vieta's formulas]]? I think the formula given is wrong. <br />
--[[User:Mysmartmouth|Mysmartmouth]] 14:32, 18 June 2006 (EDT)<br />
<br />
I just want to make a note that there is a better way to create a signature. If you look at the Wiki toolbar above, you see the second button from the right. It looks like a signature. Just hit that button at the end of your comment, and a signature, with timestamp, will be added. That is the widely accepted way to sign comments on Wikipedia, and it would be nice to have some kind of standard here as well. Just a suggestion. --[[User:Mysmartmouth|Mysmartmouth]] 11:09, 18 June 2006 (EDT)<br />
<br />
<br />
I added a lot of info to the [[MathCounts]] page in my bid to become a moderator...<br />
--[[User:Treething|Treething]] 15:57, 18 June 2006 (EDT)<br />
<br />
<br />
The Inequalities need skeleton pages set up. Can someone help my math parsing on the [[Power mean inequality]]? It is really messing up.<br />
-PenguinIntegral<br />
<br />
The [[Polynomials]] page needs a skeleton too...<br />
-chess64<br />
What does everyone think of me using AIME problems to illistrate mathematical concepts like completing the square?<br />
<br />
See [[Completing the square]]<br />
<br />
Hey, I'm not sure exactly how to format this page...but I edited the completing the square page somewhat (btw there are some Latex problems that someone (not me) needs to fix), anyone else have feedback?<br />
<br />
<br />
I like your idea of using sample problems, but I don't really understand what the sample problem you placed in the [[Completing the square]] page has to do with the topic...<br />
<br />
-eryaman<br />
Yeah, it probably would have been nice if I explained how the solution uses adding/subtracting to factor, of which completing the square is a special case.<br />
<br />
Someone smart should fix that.<br />
<br />
Does anyone have ideas for new topics? I think we should split up the wiki like the USAMO problem subjects: Combo and Probability, Algebra and Polynomials, Functions, Inequalities, Geometry, and Number Theory. I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it, so I'll look into starting a page on counting strategies.<br />
<br />
Always use example problems; they really reinforce the material and prepare the reader for using them in a contest setting.<br />
<br />
(Ok, I just made that up. But it feels good to start a fad)<br />
-PenguinIntegral<br />
<br />
"I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it..." uh actually no i'm not but i guess i'll work on it<br />
-chess64<br />
<br />
<br />
Idea: Should the Wiki turn into an "example emporium"? We should wait for an Admin's go-ahead before starting... Also-Should we link to the [[Needed Pages]] on the home page?<br />
-IntrepidMath<br />
<br />
Insanity is only exceptable within reason. We shouldn't put problems on every page, but as the AoPS books show, examples really help learning.<br />
<br />
<br />
-PenguinIntegral<br />
<br />
I'll start some Combinatorics pages/links, but how do you start a page?<br />
-quantum leap<br />
<br />
search for the name of the article that you want to write [-chess64]<br />
<br />
uh guys this is the "community portal" so i think these discussions should be in the "discussion" page of this (see the blue button at the top) and this page should be used for things like links to [[needed pages]]... should i go ahead and fix this?<br />
<br />
-chess64<br />
<br />
Um, there are two cauchy-schwarz inequality pages (depending on whether or not the "s" in schwarz is capitalized) :/ I guess they should be combined... -quantum leap<br />
<br />
==monobook.js==<br />
Would it be possible for an administrator to somehow activate the usage of the personal javascript file - [[Special:Mypage/monobook.js]]? It would certainly help to expedite the process of building this wiki. [[User:Azjps|Azjps]] 19:43, 6 February 2007 (EST)<br />
<br />
I remember a Firefox and IE bug recently where I could deviously steal your AoPS password. Thus I think that's a bad idea. --[[User:Solafidefarms|solafidefarms]] 15:38, 15 February 2007 (EST)<br />
<br />
:Oh, never mind then. I certainly wasn't aware of that. Thanks, [[User:Azjps|Azjps]] ([[User talk:Azjps|<font color="green">talk</font>]]) 16:32, 15 February 2007 (EST)<br />
<br />
== Dollar signs ==<br />
How do you indicate <math>15000 without the wiki doing latex? </math>\<math></math> doesn't work. --[[User:Solafidefarms|solafidefarms]] 10:02, 30 August 2006 (EDT)<br />
We need a lot more amc 10s--[[User:Anirudh|Anirudh]] 19:47, 31 December 2006 (EST)<br />
<br />
Try using the nowiki tags:<nowiki>$</nowiki> formatting.--[[User:IntrepidMath|IntrepidMath]] 10:49, 30 August 2006 (EDT)<br />
Thanks!--[[User:Solafidefarms|solafidefarms]] 17:33, 30 August 2006 (EDT)</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Discussion&diff=13355AoPS Wiki:Discussion2007-02-25T00:37:46Z<p>AMC37.5: /* General Topics */ fix level</p>
<hr />
<div>{{shortcut|[[AoPS:CP]]<br />[[AoPS:HELP]]}}<br />
<!--Please place comments below this line--><br />
'''Hi there''' people, but we really need some solutions for the [[2006_Canadian_MO]].--[[User:Anirudh|Anirudh]] 12:16, 6 February 2007 (EST)<br />
:Unfortunately, that's not the only contest we need to write solutions for: about <math>\lim_{x \to 0+} (100 - x)%</math> of the problem articles on this wiki need solutions :(wow, I guess I am a pessimist). On a slightly irrelevant note, I think (for organizational purposes) that it would be better to start adding new posts to the bottom. It's virtually impossible to trace a reply like "I agree" in such a long discussion. [[User:Azjps|Azjps]] 19:38, 7 February 2007 (EST)<br />
<br />
Dollar signs: How do you indicate <math>15000 without the wiki doing latex? </math>\<math></math> doesn't work. --[[User:Solafidefarms|solafidefarms]] 10:02, 30 August 2006 (EDT)<br />
We need a lot more amc 10s--[[User:Anirudh|Anirudh]] 19:47, 31 December 2006 (EST)<br />
<br />
Try using the nowiki tags:<nowiki>$</nowiki> formatting.--[[User:IntrepidMath|IntrepidMath]] 10:49, 30 August 2006 (EDT)<br />
Thanks!--[[User:Solafidefarms|solafidefarms]] 17:33, 30 August 2006 (EDT)<br />
<br />
=Pages to start off with=<br />
<Advertise your wikipage here><br />
<br />
[[Function]] really needs work. It's about 1/3rd written, and about 1/3rd of that is properly latexed. --[[User:Solafidefarms|solafidefarms]] 16:46, 22 June 2006 (EDT)<br />
[[Function]] is i think looks latexed--[[User:Anirudh|Anirudh]] 19:54, 30 December 2006 (EST)<br />
<br />
Look at [[Special:Wantedpages]] to find interesting pages to work on. Or look at the list of stubs (visit the page Category:Stubs) to find pages in need of more content. Or, look at the list of [[Special:Newpages]] and look for the pages I've created, since most of them are just 2 sentences long. --[[User_talk:JBL|JBL]] 11:07, 12 July 2006 (EDT)<br />
<br />
=Things to do=<br />
Please add more to the list below<br />
<br />
== Suggestion - maybe add PDF's of contests ==<br />
Maybe we should add pdfs of the contests so people can download and print them?--[[User:Anirudh|Anirudh]] 22:00, 31 December 2006 (EST)<br />
:Just add them as TeX which can be rendered as a printable image. Acrobat is slow. [[User:AMC37.5|AMC37.5]] 01:32, 24 February 2007 (EST)<br />
<br />
== Adding AMC Problems and Solutions! ==<br />
you should let awupu hve images too. --[[User:Anirudh|Anirudh]] 20:04, 27 November 2006 (EST)<br />
'''awupu2''': the AoPSWiki Unofficial Problem Uploader was just updated, and now automatically links to other wiki articles for you! See [http://mathideas.org/code/awupu/ awupu].<br />
--[[User:Chess64|Chess64]] 22:39, 5 November 2006 (EST)<br />
<br />
Please see the [http://mathideas.org/code/awupu AoPSWiki Problem Uploader], which can help you save a lot of time when you are uploading MO problems. --[[User:Chess64|Chess64]] 20:27, 28 July 2006 (EDT)<br />
<br />
Every member can contribute to this no matter what kind of math knowledge they have. This is also very important to the amount of information on the Wiki. Please go to the Contests Page and copy problems from the competitions to the pages they are missing from. (see below) If you have more time, please add a solution to the pages that are missing solutions. (also see below)<br />
<br />
*2006<br />
**Missing Problems<br />
***2001 AMC 10 Problems 1-25<br />
***<s>2006 AMC 10B Problems 1-25</s><br />
***<s>2006 AMC 12A Problems 1-25</s><br />
***2006 AMC 12B Problems 1-25<br />
***2006 USAMO Problems 1-6<br />
***2006 USA TST Problems 1-6<br />
**Missing Solutions<br />
***2006 AMC 10A Solutions 7-25<br />
***<s>2006 AMC 10B Solutions 1-25</s><br />
***2006 AMC 12A Solutions 1-25<br />
***2006 AMC 12B Solutions 1-25<br />
***2006 AIME I Solutions 4, 7-11, 13-15<br />
***2006 AIME II Solutions 1-15<br />
***2006 USAMO Solutions 1-6<br />
***2006 USA TST Solutions 1-6<br />
<br />
Thanks! [[User:Ignite168|Ignite168]] 20:06, 7 July 2006 (EDT)<br />
<br />
Just adding a note to please strike out something by using <nowiki><s> to start the strike out and </s> to finish it</nowiki> when it is completed like so <s>example</s>. Also, you can work on 2005, 2004, 2003, etc. but I just put 2006 here to start with. Oh and to joml88: Thanks for all your work on problems in past years so far. [[User:Ignite168|Ignite168]] 01:25, 9 July 2006 (EDT)<br />
<br />
== Find Articles about AoPS Members ==<br />
<br />
Please help find articles about Art of Problem Solving Members and place [[Template:AoPSMember]] on the talk page of that article. Before you use this template though, please first read the usage instructions [[Template:AoPSMember#How_to_use_this_template|here]]. [[User:Ignite168|Ignite168]] 00:36, 1 July 2006 (EDT)<br />
<br />
== Convention for naming articles ==<br />
It's important that we set this standard now, otherwise, there's going to be a lot of cleaning up to do, not only in terms of admins moving pages, but also in terms of cleaning up links to those articles. Please see the stick post in the AoPSWiki forum about this! Chime in with your opinion. See [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=97741 this forum post] for details.<br />
<br />
== Other ==<br />
<br />
Patrons:Don't edit other's wiki profiles!<br />
Admins:Please change the access restrictions on user's pages<br />
==General Topics==<br />
*[[Combinatorics]] and [[Probability]] Topics Techiniques<br />
*[[Logic]] and [[Game Theory]] Topics<br />
*[[Functions]] and [[Functional Equations]] Topics<br />
*[[Number Theory]] Techinques and Topics -- well, we have a Number theory page...<br />
*[[Algebra]] Topics and Techniques<br />
*[[Inequalities]] and solving techniques<br />
*[[Geometry]] Topics<br />
*[[Arithmetic sequence]] needs work<br />
*Other sciences<br />
*Linking to ready made content, (Sato's NT packet, the geometry packet by Kedlaya or some name like that, mildorf and other's equality packets, Joe's factoring topic, the formulary, the inequality learning marathon in the forum, the mathematical idea's blog, etc)<br />
*Study plans and Problem sets<br />
*Especially problem sets<br />
*Instructive problem sets<br />
*A topic on why doing problems is the fastest way to learn<br />
* [[LaTeX]] page (very incomplete, could do with some explaining of latex, origins, and codes for useful things like \boxed or something)<br />
* Problem solving Strategies(chapter 2 of Zeitz)<br />
* Advanced techniques (Invariants, monovariants, symmetry, things like that)<br />
* ...<br />
<br />
===Techiniques===<br />
Adding techniques frequently used in each discipline would be nice, like PIE, substituion for a new variable, solving equations by substituing in trigonometric expressions, etc.<br />
<br />
===General Usage===<br />
*Adding contest problems to illustrate techniques<br />
*Learning to use the signature button in the editor<br />
<br />
=Wiki-wide discussion board=<br />
<br />
'''Add your message to THE BOTTOM'''<br />
<br />
I agree. --[[User:Chess64|Chess64]] 16:24, 24 December 2006 (EST)<br />
<br />
I propose that the categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated, for the following reasons :<br />
<br />
* They are indistinguishable for olympiad problems.<br />
* All of them can be classified as either algebra or geometry problems.<br />
* The IMO uses only the other four categories for olympiad problems currently in existance.<br />
<br />
Does anybody agree or disagree? I also mentioned this on the discussion page for [[Contest Problems Standards]]. &mdash;[[User:Boy Soprano II|Boy Soprano II]] 17:21, 25 August 2006 (EDT)<br />
<br />
Does anyone here get this problem? What happens is that on some pages (notably those with centered math), the math on the page is horribly garbled. See [[Talk:Fallacious proof]] for a picture. I use IE6, Windows XP. --[[User:IntrepidMath|IntrepidMath]] 15:38, 4 August 2006 (EDT)<br />
<br />
<br />
Sean, you can use <nowiki> <pre> ... </pre> </nowiki> to make the box:<br />
<br />
<pre> Testing to make sure. </pre><br />
<br />
--[[User:Joml88|Joe]] 09:43, 1 August 2006 (EDT)<br />
<br />
<br />
If you're typing an olympiad problem (or indeed, any problem for which you think alternate solutions could be enlightening), you can use the <nowiki>{{alternate solutions}}</nowiki> template I made. It currently prints the text right after this message. Sean, I'm not sure, but you may find your answer [http://meta.wikimedia.org/wiki/Help:Wiki_markup_examples#Disabling_wikitext_interpretation_and.2For_reformatting here]. --[[User:Boy Soprano II|Boy Soprano II]] 19:55, 25 July 2006 (EDT) {{alternate solutions}}<br />
<br />
To answer my own question, see [[templates & categories]]. Now I have a new question: how do you box something in AoPSWiki? I have a long code that needs to be in a box, because the article would look much cleaner. Thanks! --[[User:Mysmartmouth|Sean]] 13:32, 27 June 2006 (EDT)<br />
<br />
How do you create a template? Is this something only admins can do? --[[User:Mysmartmouth|Sean]] 23:57, 23 June 2006 (EDT)<br />
<br />
OK, for definitions,should there be a category or a template or nothing?--[[User:Solafidefarms|solafidefarms]] 22:26, 23 June 2006 (EDT)<br />
<br />
you can add any problems you want, just give credit to the source. like <br />
<br />
* ([[The Art and Craft of Problem Solving]]) Problem text here.<br />
<br />
Solution<br />
<br />
--[[User:Chess64|Chess64]] 10:28, 22 June 2006 (EDT)<br />
<br />
are we allowed to add problems from problem books to the wiki? I notice people are adding AIME problems, whose books can we add problems from? I don't mean the whole thing or anything, just one or two problems at a time. --[[User:Agolsme|Agolsme]] 17:09, 21 June 2006 (EDT)<br />
<br />
Err, my bad. That was a typo... now I have to fix it in the article too... --[[User:Chess64|Chess64]] 10:15, 19 June 2006 (EDT)<br />
<br />
@alvaro I linked up the general topics area, ok?<br />
<br />
where are the pages of the general topics? must we create them? --[[User:alvaro|alvaro]] 11:25, 18 June 2006 (EDT)<br />
<br />
Yes, the formula is now right. Joe changed it. It was off a bit before. --[[User:Mysmartmouth|Mysmartmouth]] 19:02, 18 June 2006 (EDT)<br />
<br />
I like it, PenguinIntegral. Mysmartmouth, the formula is definitely right. --[[User:Chess64|Chess64]] 18:20, 18 June 2006 (EDT)<br />
<br />
I added some structure to this page. Feel free to comment.<br />
--[[User:PenguinIntegral|PenguinIntegral]] 18:08, 18 June 2006 (EDT)<br />
<br />
Millenium problems would be a good topic; people are always asking about those problems. Also, can someone take a look at [[Vieta's formulas]]? I think the formula given is wrong. <br />
--[[User:Mysmartmouth|Mysmartmouth]] 14:32, 18 June 2006 (EDT)<br />
<br />
I just want to make a note that there is a better way to create a signature. If you look at the Wiki toolbar above, you see the second button from the right. It looks like a signature. Just hit that button at the end of your comment, and a signature, with timestamp, will be added. That is the widely accepted way to sign comments on Wikipedia, and it would be nice to have some kind of standard here as well. Just a suggestion. --[[User:Mysmartmouth|Mysmartmouth]] 11:09, 18 June 2006 (EDT)<br />
<br />
<br />
I added a lot of info to the [[MathCounts]] page in my bid to become a moderator...<br />
--[[User:Treething|Treething]] 15:57, 18 June 2006 (EDT)<br />
<br />
<br />
The Inequalities need skeleton pages set up. Can someone help my math parsing on the [[Power mean inequality]]? It is really messing up.<br />
-PenguinIntegral<br />
<br />
The [[Polynomials]] page needs a skeleton too...<br />
-chess64<br />
What does everyone think of me using AIME problems to illistrate mathematical concepts like completing the square?<br />
<br />
See [[Completing the square]]<br />
<br />
Hey, I'm not sure exactly how to format this page...but I edited the completing the square page somewhat (btw there are some Latex problems that someone (not me) needs to fix), anyone else have feedback?<br />
<br />
<br />
I like your idea of using sample problems, but I don't really understand what the sample problem you placed in the [[Completing the square]] page has to do with the topic...<br />
<br />
-eryaman<br />
Yeah, it probably would have been nice if I explained how the solution uses adding/subtracting to factor, of which completing the square is a special case.<br />
<br />
Someone smart should fix that.<br />
<br />
Does anyone have ideas for new topics? I think we should split up the wiki like the USAMO problem subjects: Combo and Probability, Algebra and Polynomials, Functions, Inequalities, Geometry, and Number Theory. I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it, so I'll look into starting a page on counting strategies.<br />
<br />
Always use example problems; they really reinforce the material and prepare the reader for using them in a contest setting.<br />
<br />
(Ok, I just made that up. But it feels good to start a fad)<br />
-PenguinIntegral<br />
<br />
"I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it..." uh actually no i'm not but i guess i'll work on it<br />
-chess64<br />
<br />
<br />
Idea: Should the Wiki turn into an "example emporium"? We should wait for an Admin's go-ahead before starting... Also-Should we link to the [[Needed Pages]] on the home page?<br />
-IntrepidMath<br />
<br />
Insanity is only exceptable within reason. We shouldn't put problems on every page, but as the AoPS books show, examples really help learning.<br />
<br />
<br />
-PenguinIntegral<br />
<br />
I'll start some Combinatorics pages/links, but how do you start a page?<br />
-quantum leap<br />
<br />
search for the name of the article that you want to write [-chess64]<br />
<br />
uh guys this is the "community portal" so i think these discussions should be in the "discussion" page of this (see the blue button at the top) and this page should be used for things like links to [[needed pages]]... should i go ahead and fix this?<br />
<br />
-chess64<br />
<br />
Um, there are two cauchy-schwarz inequality pages (depending on whether or not the "s" in schwarz is capitalized) :/ I guess they should be combined... -quantum leap<br />
<br />
===monobook.js===<br />
Would it be possible for an administrator to somehow activate the usage of the personal javascript file - [[Special:Mypage/monobook.js]]? It would certainly help to expedite the process of building this wiki. [[User:Azjps|Azjps]] 19:43, 6 February 2007 (EST)<br />
<br />
I remember a Firefox and IE bug recently where I could deviously steal your AoPS password. Thus I think that's a bad idea. --[[User:Solafidefarms|solafidefarms]] 15:38, 15 February 2007 (EST)<br />
<br />
:Oh, never mind then. I certainly wasn't aware of that. Thanks, [[User:Azjps|Azjps]] ([[User talk:Azjps|<font color="green">talk</font>]]) 16:32, 15 February 2007 (EST)</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Discussion&diff=13354AoPS Wiki:Discussion2007-02-25T00:37:04Z<p>AMC37.5: /* Wiki-wide discussion board */ convert to bigger section</p>
<hr />
<div>{{shortcut|[[AoPS:CP]]<br />[[AoPS:HELP]]}}<br />
<!--Please place comments below this line--><br />
'''Hi there''' people, but we really need some solutions for the [[2006_Canadian_MO]].--[[User:Anirudh|Anirudh]] 12:16, 6 February 2007 (EST)<br />
:Unfortunately, that's not the only contest we need to write solutions for: about <math>\lim_{x \to 0+} (100 - x)%</math> of the problem articles on this wiki need solutions :(wow, I guess I am a pessimist). On a slightly irrelevant note, I think (for organizational purposes) that it would be better to start adding new posts to the bottom. It's virtually impossible to trace a reply like "I agree" in such a long discussion. [[User:Azjps|Azjps]] 19:38, 7 February 2007 (EST)<br />
<br />
Dollar signs: How do you indicate <math>15000 without the wiki doing latex? </math>\<math></math> doesn't work. --[[User:Solafidefarms|solafidefarms]] 10:02, 30 August 2006 (EDT)<br />
We need a lot more amc 10s--[[User:Anirudh|Anirudh]] 19:47, 31 December 2006 (EST)<br />
<br />
Try using the nowiki tags:<nowiki>$</nowiki> formatting.--[[User:IntrepidMath|IntrepidMath]] 10:49, 30 August 2006 (EDT)<br />
Thanks!--[[User:Solafidefarms|solafidefarms]] 17:33, 30 August 2006 (EDT)<br />
<br />
=Pages to start off with=<br />
<Advertise your wikipage here><br />
<br />
[[Function]] really needs work. It's about 1/3rd written, and about 1/3rd of that is properly latexed. --[[User:Solafidefarms|solafidefarms]] 16:46, 22 June 2006 (EDT)<br />
[[Function]] is i think looks latexed--[[User:Anirudh|Anirudh]] 19:54, 30 December 2006 (EST)<br />
<br />
Look at [[Special:Wantedpages]] to find interesting pages to work on. Or look at the list of stubs (visit the page Category:Stubs) to find pages in need of more content. Or, look at the list of [[Special:Newpages]] and look for the pages I've created, since most of them are just 2 sentences long. --[[User_talk:JBL|JBL]] 11:07, 12 July 2006 (EDT)<br />
<br />
=Things to do=<br />
Please add more to the list below<br />
<br />
== Suggestion - maybe add PDF's of contests ==<br />
Maybe we should add pdfs of the contests so people can download and print them?--[[User:Anirudh|Anirudh]] 22:00, 31 December 2006 (EST)<br />
:Just add them as TeX which can be rendered as a printable image. Acrobat is slow. [[User:AMC37.5|AMC37.5]] 01:32, 24 February 2007 (EST)<br />
<br />
== Adding AMC Problems and Solutions! ==<br />
you should let awupu hve images too. --[[User:Anirudh|Anirudh]] 20:04, 27 November 2006 (EST)<br />
'''awupu2''': the AoPSWiki Unofficial Problem Uploader was just updated, and now automatically links to other wiki articles for you! See [http://mathideas.org/code/awupu/ awupu].<br />
--[[User:Chess64|Chess64]] 22:39, 5 November 2006 (EST)<br />
<br />
Please see the [http://mathideas.org/code/awupu AoPSWiki Problem Uploader], which can help you save a lot of time when you are uploading MO problems. --[[User:Chess64|Chess64]] 20:27, 28 July 2006 (EDT)<br />
<br />
Every member can contribute to this no matter what kind of math knowledge they have. This is also very important to the amount of information on the Wiki. Please go to the Contests Page and copy problems from the competitions to the pages they are missing from. (see below) If you have more time, please add a solution to the pages that are missing solutions. (also see below)<br />
<br />
*2006<br />
**Missing Problems<br />
***2001 AMC 10 Problems 1-25<br />
***<s>2006 AMC 10B Problems 1-25</s><br />
***<s>2006 AMC 12A Problems 1-25</s><br />
***2006 AMC 12B Problems 1-25<br />
***2006 USAMO Problems 1-6<br />
***2006 USA TST Problems 1-6<br />
**Missing Solutions<br />
***2006 AMC 10A Solutions 7-25<br />
***<s>2006 AMC 10B Solutions 1-25</s><br />
***2006 AMC 12A Solutions 1-25<br />
***2006 AMC 12B Solutions 1-25<br />
***2006 AIME I Solutions 4, 7-11, 13-15<br />
***2006 AIME II Solutions 1-15<br />
***2006 USAMO Solutions 1-6<br />
***2006 USA TST Solutions 1-6<br />
<br />
Thanks! [[User:Ignite168|Ignite168]] 20:06, 7 July 2006 (EDT)<br />
<br />
Just adding a note to please strike out something by using <nowiki><s> to start the strike out and </s> to finish it</nowiki> when it is completed like so <s>example</s>. Also, you can work on 2005, 2004, 2003, etc. but I just put 2006 here to start with. Oh and to joml88: Thanks for all your work on problems in past years so far. [[User:Ignite168|Ignite168]] 01:25, 9 July 2006 (EDT)<br />
<br />
== Find Articles about AoPS Members ==<br />
<br />
Please help find articles about Art of Problem Solving Members and place [[Template:AoPSMember]] on the talk page of that article. Before you use this template though, please first read the usage instructions [[Template:AoPSMember#How_to_use_this_template|here]]. [[User:Ignite168|Ignite168]] 00:36, 1 July 2006 (EDT)<br />
<br />
== Convention for naming articles ==<br />
It's important that we set this standard now, otherwise, there's going to be a lot of cleaning up to do, not only in terms of admins moving pages, but also in terms of cleaning up links to those articles. Please see the stick post in the AoPSWiki forum about this! Chime in with your opinion. See [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=97741 this forum post] for details.<br />
<br />
== Other ==<br />
<br />
Patrons:Don't edit other's wiki profiles!<br />
Admins:Please change the access restrictions on user's pages<br />
===General Topics===<br />
*[[Combinatorics]] and [[Probability]] Topics Techiniques<br />
*[[Logic]] and [[Game Theory]] Topics<br />
*[[Functions]] and [[Functional Equations]] Topics<br />
*[[Number Theory]] Techinques and Topics -- well, we have a Number theory page...<br />
*[[Algebra]] Topics and Techniques<br />
*[[Inequalities]] and solving techniques<br />
*[[Geometry]] Topics<br />
*[[Arithmetic sequence]] needs work<br />
*Other sciences<br />
*Linking to ready made content, (Sato's NT packet, the geometry packet by Kedlaya or some name like that, mildorf and other's equality packets, Joe's factoring topic, the formulary, the inequality learning marathon in the forum, the mathematical idea's blog, etc)<br />
*Study plans and Problem sets<br />
*Especially problem sets<br />
*Instructive problem sets<br />
*A topic on why doing problems is the fastest way to learn<br />
* [[LaTeX]] page (very incomplete, could do with some explaining of latex, origins, and codes for useful things like \boxed or something)<br />
* Problem solving Strategies(chapter 2 of Zeitz)<br />
* Advanced techniques (Invariants, monovariants, symmetry, things like that)<br />
* ...<br />
<br />
===Techiniques===<br />
Adding techniques frequently used in each discipline would be nice, like PIE, substituion for a new variable, solving equations by substituing in trigonometric expressions, etc.<br />
<br />
===General Usage===<br />
*Adding contest problems to illustrate techniques<br />
*Learning to use the signature button in the editor<br />
<br />
=Wiki-wide discussion board=<br />
<br />
'''Add your message to THE BOTTOM'''<br />
<br />
I agree. --[[User:Chess64|Chess64]] 16:24, 24 December 2006 (EST)<br />
<br />
I propose that the categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated, for the following reasons :<br />
<br />
* They are indistinguishable for olympiad problems.<br />
* All of them can be classified as either algebra or geometry problems.<br />
* The IMO uses only the other four categories for olympiad problems currently in existance.<br />
<br />
Does anybody agree or disagree? I also mentioned this on the discussion page for [[Contest Problems Standards]]. &mdash;[[User:Boy Soprano II|Boy Soprano II]] 17:21, 25 August 2006 (EDT)<br />
<br />
Does anyone here get this problem? What happens is that on some pages (notably those with centered math), the math on the page is horribly garbled. See [[Talk:Fallacious proof]] for a picture. I use IE6, Windows XP. --[[User:IntrepidMath|IntrepidMath]] 15:38, 4 August 2006 (EDT)<br />
<br />
<br />
Sean, you can use <nowiki> <pre> ... </pre> </nowiki> to make the box:<br />
<br />
<pre> Testing to make sure. </pre><br />
<br />
--[[User:Joml88|Joe]] 09:43, 1 August 2006 (EDT)<br />
<br />
<br />
If you're typing an olympiad problem (or indeed, any problem for which you think alternate solutions could be enlightening), you can use the <nowiki>{{alternate solutions}}</nowiki> template I made. It currently prints the text right after this message. Sean, I'm not sure, but you may find your answer [http://meta.wikimedia.org/wiki/Help:Wiki_markup_examples#Disabling_wikitext_interpretation_and.2For_reformatting here]. --[[User:Boy Soprano II|Boy Soprano II]] 19:55, 25 July 2006 (EDT) {{alternate solutions}}<br />
<br />
To answer my own question, see [[templates & categories]]. Now I have a new question: how do you box something in AoPSWiki? I have a long code that needs to be in a box, because the article would look much cleaner. Thanks! --[[User:Mysmartmouth|Sean]] 13:32, 27 June 2006 (EDT)<br />
<br />
How do you create a template? Is this something only admins can do? --[[User:Mysmartmouth|Sean]] 23:57, 23 June 2006 (EDT)<br />
<br />
OK, for definitions,should there be a category or a template or nothing?--[[User:Solafidefarms|solafidefarms]] 22:26, 23 June 2006 (EDT)<br />
<br />
you can add any problems you want, just give credit to the source. like <br />
<br />
* ([[The Art and Craft of Problem Solving]]) Problem text here.<br />
<br />
Solution<br />
<br />
--[[User:Chess64|Chess64]] 10:28, 22 June 2006 (EDT)<br />
<br />
are we allowed to add problems from problem books to the wiki? I notice people are adding AIME problems, whose books can we add problems from? I don't mean the whole thing or anything, just one or two problems at a time. --[[User:Agolsme|Agolsme]] 17:09, 21 June 2006 (EDT)<br />
<br />
Err, my bad. That was a typo... now I have to fix it in the article too... --[[User:Chess64|Chess64]] 10:15, 19 June 2006 (EDT)<br />
<br />
@alvaro I linked up the general topics area, ok?<br />
<br />
where are the pages of the general topics? must we create them? --[[User:alvaro|alvaro]] 11:25, 18 June 2006 (EDT)<br />
<br />
Yes, the formula is now right. Joe changed it. It was off a bit before. --[[User:Mysmartmouth|Mysmartmouth]] 19:02, 18 June 2006 (EDT)<br />
<br />
I like it, PenguinIntegral. Mysmartmouth, the formula is definitely right. --[[User:Chess64|Chess64]] 18:20, 18 June 2006 (EDT)<br />
<br />
I added some structure to this page. Feel free to comment.<br />
--[[User:PenguinIntegral|PenguinIntegral]] 18:08, 18 June 2006 (EDT)<br />
<br />
Millenium problems would be a good topic; people are always asking about those problems. Also, can someone take a look at [[Vieta's formulas]]? I think the formula given is wrong. <br />
--[[User:Mysmartmouth|Mysmartmouth]] 14:32, 18 June 2006 (EDT)<br />
<br />
I just want to make a note that there is a better way to create a signature. If you look at the Wiki toolbar above, you see the second button from the right. It looks like a signature. Just hit that button at the end of your comment, and a signature, with timestamp, will be added. That is the widely accepted way to sign comments on Wikipedia, and it would be nice to have some kind of standard here as well. Just a suggestion. --[[User:Mysmartmouth|Mysmartmouth]] 11:09, 18 June 2006 (EDT)<br />
<br />
<br />
I added a lot of info to the [[MathCounts]] page in my bid to become a moderator...<br />
--[[User:Treething|Treething]] 15:57, 18 June 2006 (EDT)<br />
<br />
<br />
The Inequalities need skeleton pages set up. Can someone help my math parsing on the [[Power mean inequality]]? It is really messing up.<br />
-PenguinIntegral<br />
<br />
The [[Polynomials]] page needs a skeleton too...<br />
-chess64<br />
What does everyone think of me using AIME problems to illistrate mathematical concepts like completing the square?<br />
<br />
See [[Completing the square]]<br />
<br />
Hey, I'm not sure exactly how to format this page...but I edited the completing the square page somewhat (btw there are some Latex problems that someone (not me) needs to fix), anyone else have feedback?<br />
<br />
<br />
I like your idea of using sample problems, but I don't really understand what the sample problem you placed in the [[Completing the square]] page has to do with the topic...<br />
<br />
-eryaman<br />
Yeah, it probably would have been nice if I explained how the solution uses adding/subtracting to factor, of which completing the square is a special case.<br />
<br />
Someone smart should fix that.<br />
<br />
Does anyone have ideas for new topics? I think we should split up the wiki like the USAMO problem subjects: Combo and Probability, Algebra and Polynomials, Functions, Inequalities, Geometry, and Number Theory. I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it, so I'll look into starting a page on counting strategies.<br />
<br />
Always use example problems; they really reinforce the material and prepare the reader for using them in a contest setting.<br />
<br />
(Ok, I just made that up. But it feels good to start a fad)<br />
-PenguinIntegral<br />
<br />
"I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it..." uh actually no i'm not but i guess i'll work on it<br />
-chess64<br />
<br />
<br />
Idea: Should the Wiki turn into an "example emporium"? We should wait for an Admin's go-ahead before starting... Also-Should we link to the [[Needed Pages]] on the home page?<br />
-IntrepidMath<br />
<br />
Insanity is only exceptable within reason. We shouldn't put problems on every page, but as the AoPS books show, examples really help learning.<br />
<br />
<br />
-PenguinIntegral<br />
<br />
I'll start some Combinatorics pages/links, but how do you start a page?<br />
-quantum leap<br />
<br />
search for the name of the article that you want to write [-chess64]<br />
<br />
uh guys this is the "community portal" so i think these discussions should be in the "discussion" page of this (see the blue button at the top) and this page should be used for things like links to [[needed pages]]... should i go ahead and fix this?<br />
<br />
-chess64<br />
<br />
Um, there are two cauchy-schwarz inequality pages (depending on whether or not the "s" in schwarz is capitalized) :/ I guess they should be combined... -quantum leap<br />
<br />
===monobook.js===<br />
Would it be possible for an administrator to somehow activate the usage of the personal javascript file - [[Special:Mypage/monobook.js]]? It would certainly help to expedite the process of building this wiki. [[User:Azjps|Azjps]] 19:43, 6 February 2007 (EST)<br />
<br />
I remember a Firefox and IE bug recently where I could deviously steal your AoPS password. Thus I think that's a bad idea. --[[User:Solafidefarms|solafidefarms]] 15:38, 15 February 2007 (EST)<br />
<br />
:Oh, never mind then. I certainly wasn't aware of that. Thanks, [[User:Azjps|Azjps]] ([[User talk:Azjps|<font color="green">talk</font>]]) 16:32, 15 February 2007 (EST)</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=User:AMC37.5&diff=13350User:AMC37.52007-02-24T06:35:44Z<p>AMC37.5: fix</p>
<hr />
<div><pre><br />
^<br />
--------------|<br />
</pre><br />
That is not my score.<br />
<br />
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=User:AMC37.5&diff=13349User:AMC37.52007-02-24T06:35:29Z<p>AMC37.5: q</p>
<hr />
<div><pre><br />
^<br />
-----------|<br />
</pre><br />
That is not my score.<br />
<br />
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Discussion&diff=13348AoPS Wiki:Discussion2007-02-24T06:32:03Z<p>AMC37.5: /* Suggestion - maybe add PDF's of contests */ tex</p>
<hr />
<div>{{shortcut|[[AoPS:CP]]<br />[[AoPS:HELP]]}}<br />
<!--Please place comments below this line--><br />
'''Hi there''' people, but we really need some solutions for the [[2006_Canadian_MO]].--[[User:Anirudh|Anirudh]] 12:16, 6 February 2007 (EST)<br />
:Unfortunately, that's not the only contest we need to write solutions for: about <math>\lim_{x \to 0+} (100 - x)%</math> of the problem articles on this wiki need solutions :(wow, I guess I am a pessimist). On a slightly irrelevant note, I think (for organizational purposes) that it would be better to start adding new posts to the bottom. It's virtually impossible to trace a reply like "I agree" in such a long discussion. [[User:Azjps|Azjps]] 19:38, 7 February 2007 (EST)<br />
<br />
Dollar signs: How do you indicate <math>15000 without the wiki doing latex? </math>\<math></math> doesn't work. --[[User:Solafidefarms|solafidefarms]] 10:02, 30 August 2006 (EDT)<br />
We need a lot more amc 10s--[[User:Anirudh|Anirudh]] 19:47, 31 December 2006 (EST)<br />
<br />
Try using the nowiki tags:<nowiki>$</nowiki> formatting.--[[User:IntrepidMath|IntrepidMath]] 10:49, 30 August 2006 (EDT)<br />
Thanks!--[[User:Solafidefarms|solafidefarms]] 17:33, 30 August 2006 (EDT)<br />
<br />
=Pages to start off with=<br />
<Advertise your wikipage here><br />
<br />
[[Function]] really needs work. It's about 1/3rd written, and about 1/3rd of that is properly latexed. --[[User:Solafidefarms|solafidefarms]] 16:46, 22 June 2006 (EDT)<br />
[[Function]] is i think looks latexed--[[User:Anirudh|Anirudh]] 19:54, 30 December 2006 (EST)<br />
<br />
Look at [[Special:Wantedpages]] to find interesting pages to work on. Or look at the list of stubs (visit the page Category:Stubs) to find pages in need of more content. Or, look at the list of [[Special:Newpages]] and look for the pages I've created, since most of them are just 2 sentences long. --[[User_talk:JBL|JBL]] 11:07, 12 July 2006 (EDT)<br />
<br />
=Things to do=<br />
Please add more to the list below<br />
<br />
== Suggestion - maybe add PDF's of contests ==<br />
Maybe we should add pdfs of the contests so people can download and print them?--[[User:Anirudh|Anirudh]] 22:00, 31 December 2006 (EST)<br />
:Just add them as TeX which can be rendered as a printable image. Acrobat is slow. [[User:AMC37.5|AMC37.5]] 01:32, 24 February 2007 (EST)<br />
<br />
== Adding AMC Problems and Solutions! ==<br />
you should let awupu hve images too. --[[User:Anirudh|Anirudh]] 20:04, 27 November 2006 (EST)<br />
'''awupu2''': the AoPSWiki Unofficial Problem Uploader was just updated, and now automatically links to other wiki articles for you! See [http://mathideas.org/code/awupu/ awupu].<br />
--[[User:Chess64|Chess64]] 22:39, 5 November 2006 (EST)<br />
<br />
Please see the [http://mathideas.org/code/awupu AoPSWiki Problem Uploader], which can help you save a lot of time when you are uploading MO problems. --[[User:Chess64|Chess64]] 20:27, 28 July 2006 (EDT)<br />
<br />
Every member can contribute to this no matter what kind of math knowledge they have. This is also very important to the amount of information on the Wiki. Please go to the Contests Page and copy problems from the competitions to the pages they are missing from. (see below) If you have more time, please add a solution to the pages that are missing solutions. (also see below)<br />
<br />
*2006<br />
**Missing Problems<br />
***2001 AMC 10 Problems 1-25<br />
***<s>2006 AMC 10B Problems 1-25</s><br />
***<s>2006 AMC 12A Problems 1-25</s><br />
***2006 AMC 12B Problems 1-25<br />
***2006 USAMO Problems 1-6<br />
***2006 USA TST Problems 1-6<br />
**Missing Solutions<br />
***2006 AMC 10A Solutions 7-25<br />
***<s>2006 AMC 10B Solutions 1-25</s><br />
***2006 AMC 12A Solutions 1-25<br />
***2006 AMC 12B Solutions 1-25<br />
***2006 AIME I Solutions 4, 7-11, 13-15<br />
***2006 AIME II Solutions 1-15<br />
***2006 USAMO Solutions 1-6<br />
***2006 USA TST Solutions 1-6<br />
<br />
Thanks! [[User:Ignite168|Ignite168]] 20:06, 7 July 2006 (EDT)<br />
<br />
Just adding a note to please strike out something by using <nowiki><s> to start the strike out and </s> to finish it</nowiki> when it is completed like so <s>example</s>. Also, you can work on 2005, 2004, 2003, etc. but I just put 2006 here to start with. Oh and to joml88: Thanks for all your work on problems in past years so far. [[User:Ignite168|Ignite168]] 01:25, 9 July 2006 (EDT)<br />
<br />
== Find Articles about AoPS Members ==<br />
<br />
Please help find articles about Art of Problem Solving Members and place [[Template:AoPSMember]] on the talk page of that article. Before you use this template though, please first read the usage instructions [[Template:AoPSMember#How_to_use_this_template|here]]. [[User:Ignite168|Ignite168]] 00:36, 1 July 2006 (EDT)<br />
<br />
== Convention for naming articles ==<br />
It's important that we set this standard now, otherwise, there's going to be a lot of cleaning up to do, not only in terms of admins moving pages, but also in terms of cleaning up links to those articles. Please see the stick post in the AoPSWiki forum about this! Chime in with your opinion. See [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=97741 this forum post] for details.<br />
<br />
== Other ==<br />
<br />
Patrons:Don't edit other's wiki profiles!<br />
Admins:Please change the access restrictions on user's pages<br />
===General Topics===<br />
*[[Combinatorics]] and [[Probability]] Topics Techiniques<br />
*[[Logic]] and [[Game Theory]] Topics<br />
*[[Functions]] and [[Functional Equations]] Topics<br />
*[[Number Theory]] Techinques and Topics -- well, we have a Number theory page...<br />
*[[Algebra]] Topics and Techniques<br />
*[[Inequalities]] and solving techniques<br />
*[[Geometry]] Topics<br />
*[[Arithmetic sequence]] needs work<br />
*Other sciences<br />
*Linking to ready made content, (Sato's NT packet, the geometry packet by Kedlaya or some name like that, mildorf and other's equality packets, Joe's factoring topic, the formulary, the inequality learning marathon in the forum, the mathematical idea's blog, etc)<br />
*Study plans and Problem sets<br />
*Especially problem sets<br />
*Instructive problem sets<br />
*A topic on why doing problems is the fastest way to learn<br />
* [[LaTeX]] page (very incomplete, could do with some explaining of latex, origins, and codes for useful things like \boxed or something)<br />
* Problem solving Strategies(chapter 2 of Zeitz)<br />
* Advanced techniques (Invariants, monovariants, symmetry, things like that)<br />
* ...<br />
<br />
===Techiniques===<br />
Adding techniques frequently used in each discipline would be nice, like PIE, substituion for a new variable, solving equations by substituing in trigonometric expressions, etc.<br />
<br />
===General Usage===<br />
*Adding contest problems to illustrate techniques<br />
*Learning to use the signature button in the editor<br />
<br />
==Wiki-wide discussion board==<br />
<br />
'''Add your message to THE BOTTOM'''<br />
<br />
I agree. --[[User:Chess64|Chess64]] 16:24, 24 December 2006 (EST)<br />
<br />
I propose that the categories Olympiad Trigonometry Problems and Olympiad Complex Numbers problems be eliminated, for the following reasons :<br />
<br />
* They are indistinguishable for olympiad problems.<br />
* All of them can be classified as either algebra or geometry problems.<br />
* The IMO uses only the other four categories for olympiad problems currently in existance.<br />
<br />
Does anybody agree or disagree? I also mentioned this on the discussion page for [[Contest Problems Standards]]. &mdash;[[User:Boy Soprano II|Boy Soprano II]] 17:21, 25 August 2006 (EDT)<br />
<br />
Does anyone here get this problem? What happens is that on some pages (notably those with centered math), the math on the page is horribly garbled. See [[Talk:Fallacious proof]] for a picture. I use IE6, Windows XP. --[[User:IntrepidMath|IntrepidMath]] 15:38, 4 August 2006 (EDT)<br />
<br />
<br />
Sean, you can use <nowiki> <pre> ... </pre> </nowiki> to make the box:<br />
<br />
<pre> Testing to make sure. </pre><br />
<br />
--[[User:Joml88|Joe]] 09:43, 1 August 2006 (EDT)<br />
<br />
<br />
If you're typing an olympiad problem (or indeed, any problem for which you think alternate solutions could be enlightening), you can use the <nowiki>{{alternate solutions}}</nowiki> template I made. It currently prints the text right after this message. Sean, I'm not sure, but you may find your answer [http://meta.wikimedia.org/wiki/Help:Wiki_markup_examples#Disabling_wikitext_interpretation_and.2For_reformatting here]. --[[User:Boy Soprano II|Boy Soprano II]] 19:55, 25 July 2006 (EDT) {{alternate solutions}}<br />
<br />
To answer my own question, see [[templates & categories]]. Now I have a new question: how do you box something in AoPSWiki? I have a long code that needs to be in a box, because the article would look much cleaner. Thanks! --[[User:Mysmartmouth|Sean]] 13:32, 27 June 2006 (EDT)<br />
<br />
How do you create a template? Is this something only admins can do? --[[User:Mysmartmouth|Sean]] 23:57, 23 June 2006 (EDT)<br />
<br />
OK, for definitions,should there be a category or a template or nothing?--[[User:Solafidefarms|solafidefarms]] 22:26, 23 June 2006 (EDT)<br />
<br />
you can add any problems you want, just give credit to the source. like <br />
<br />
* ([[The Art and Craft of Problem Solving]]) Problem text here.<br />
<br />
Solution<br />
<br />
--[[User:Chess64|Chess64]] 10:28, 22 June 2006 (EDT)<br />
<br />
are we allowed to add problems from problem books to the wiki? I notice people are adding AIME problems, whose books can we add problems from? I don't mean the whole thing or anything, just one or two problems at a time. --[[User:Agolsme|Agolsme]] 17:09, 21 June 2006 (EDT)<br />
<br />
Err, my bad. That was a typo... now I have to fix it in the article too... --[[User:Chess64|Chess64]] 10:15, 19 June 2006 (EDT)<br />
<br />
@alvaro I linked up the general topics area, ok?<br />
<br />
where are the pages of the general topics? must we create them? --[[User:alvaro|alvaro]] 11:25, 18 June 2006 (EDT)<br />
<br />
Yes, the formula is now right. Joe changed it. It was off a bit before. --[[User:Mysmartmouth|Mysmartmouth]] 19:02, 18 June 2006 (EDT)<br />
<br />
I like it, PenguinIntegral. Mysmartmouth, the formula is definitely right. --[[User:Chess64|Chess64]] 18:20, 18 June 2006 (EDT)<br />
<br />
I added some structure to this page. Feel free to comment.<br />
--[[User:PenguinIntegral|PenguinIntegral]] 18:08, 18 June 2006 (EDT)<br />
<br />
Millenium problems would be a good topic; people are always asking about those problems. Also, can someone take a look at [[Vieta's formulas]]? I think the formula given is wrong. <br />
--[[User:Mysmartmouth|Mysmartmouth]] 14:32, 18 June 2006 (EDT)<br />
<br />
I just want to make a note that there is a better way to create a signature. If you look at the Wiki toolbar above, you see the second button from the right. It looks like a signature. Just hit that button at the end of your comment, and a signature, with timestamp, will be added. That is the widely accepted way to sign comments on Wikipedia, and it would be nice to have some kind of standard here as well. Just a suggestion. --[[User:Mysmartmouth|Mysmartmouth]] 11:09, 18 June 2006 (EDT)<br />
<br />
<br />
I added a lot of info to the [[MathCounts]] page in my bid to become a moderator...<br />
--[[User:Treething|Treething]] 15:57, 18 June 2006 (EDT)<br />
<br />
<br />
The Inequalities need skeleton pages set up. Can someone help my math parsing on the [[Power mean inequality]]? It is really messing up.<br />
-PenguinIntegral<br />
<br />
The [[Polynomials]] page needs a skeleton too...<br />
-chess64<br />
What does everyone think of me using AIME problems to illistrate mathematical concepts like completing the square?<br />
<br />
See [[Completing the square]]<br />
<br />
Hey, I'm not sure exactly how to format this page...but I edited the completing the square page somewhat (btw there are some Latex problems that someone (not me) needs to fix), anyone else have feedback?<br />
<br />
<br />
I like your idea of using sample problems, but I don't really understand what the sample problem you placed in the [[Completing the square]] page has to do with the topic...<br />
<br />
-eryaman<br />
Yeah, it probably would have been nice if I explained how the solution uses adding/subtracting to factor, of which completing the square is a special case.<br />
<br />
Someone smart should fix that.<br />
<br />
Does anyone have ideas for new topics? I think we should split up the wiki like the USAMO problem subjects: Combo and Probability, Algebra and Polynomials, Functions, Inequalities, Geometry, and Number Theory. I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it, so I'll look into starting a page on counting strategies.<br />
<br />
Always use example problems; they really reinforce the material and prepare the reader for using them in a contest setting.<br />
<br />
(Ok, I just made that up. But it feels good to start a fad)<br />
-PenguinIntegral<br />
<br />
"I think Adeel will basically write up the entire Algebra and NT sections in 5 nanoseconds, because he so good at it..." uh actually no i'm not but i guess i'll work on it<br />
-chess64<br />
<br />
<br />
Idea: Should the Wiki turn into an "example emporium"? We should wait for an Admin's go-ahead before starting... Also-Should we link to the [[Needed Pages]] on the home page?<br />
-IntrepidMath<br />
<br />
Insanity is only exceptable within reason. We shouldn't put problems on every page, but as the AoPS books show, examples really help learning.<br />
<br />
<br />
-PenguinIntegral<br />
<br />
I'll start some Combinatorics pages/links, but how do you start a page?<br />
-quantum leap<br />
<br />
search for the name of the article that you want to write [-chess64]<br />
<br />
uh guys this is the "community portal" so i think these discussions should be in the "discussion" page of this (see the blue button at the top) and this page should be used for things like links to [[needed pages]]... should i go ahead and fix this?<br />
<br />
-chess64<br />
<br />
Um, there are two cauchy-schwarz inequality pages (depending on whether or not the "s" in schwarz is capitalized) :/ I guess they should be combined... -quantum leap<br />
<br />
===monobook.js===<br />
Would it be possible for an administrator to somehow activate the usage of the personal javascript file - [[Special:Mypage/monobook.js]]? It would certainly help to expedite the process of building this wiki. [[User:Azjps|Azjps]] 19:43, 6 February 2007 (EST)<br />
<br />
I remember a Firefox and IE bug recently where I could deviously steal your AoPS password. Thus I think that's a bad idea. --[[User:Solafidefarms|solafidefarms]] 15:38, 15 February 2007 (EST)<br />
<br />
:Oh, never mind then. I certainly wasn't aware of that. Thanks, [[User:Azjps|Azjps]] ([[User talk:Azjps|<font color="green">talk</font>]]) 16:32, 15 February 2007 (EST)</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Geometry&diff=13347Geometry2007-02-24T06:28:15Z<p>AMC37.5: fix link</p>
<hr />
<div>'''Geometry''' is the field of [[mathematics]] dealing with figures in a given space.<br />
<br />
== Student Guides to Geometry ==<br />
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* [[Geometry/Introduction | Introductory Geometry]]<br />
* [[Geometry/Intermediate | Intermediate Geometry]]<br />
* [[Geometry/Olympiad | Olympiad Geometry]]<br />
* [[Geometry/Resources | Geometry Resources]]<br />
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== Other Topics of Interest ==<br />
* The notion of [[dimension]]s<br />
** [[n-space]]<br />
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== See also ==<br />
* [[Table of Contents]]<br />
* [[Mathematics news]]<br />
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[[Category:Geometry]]</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Geometry&diff=13346Geometry2007-02-24T06:27:41Z<p>AMC37.5: Category:Geometry</p>
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<div>'''Geometry''' is the field of [[mathematics]] dealing with figures in a given space.<br />
<br />
== Student Guides to Geometry ==<br />
<br />
* [[Geometry/Introduction | Introductory Geometry]]<br />
* [[Geometry/Intermediate | Intermediate Geometry]]<br />
* [[Geometry/Olympiad | Olympiad Geometry]]<br />
* [[Geometry/Resources | Geometry Resources]]<br />
<br />
== Other Topics of Interest ==<br />
* The notion of [[dimensions]]<br />
** [[n-space]]<br />
<br />
== See also ==<br />
* [[Table of Contents]]<br />
* [[Mathematics news]]<br />
<br />
[[Category:Geometry]]</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Abstract_algebra&diff=13345Abstract algebra2007-02-24T06:26:45Z<p>AMC37.5: describe it</p>
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<div>Abstract algebra is the study of algebras besides standard elementary [[algebra]].<br />
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== See also ==<br />
*[[ring]]<br />
*[[field]]<br />
*[[group]]<br />
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{{stub}}</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Linear_algebra&diff=13344Linear algebra2007-02-24T06:24:49Z<p>AMC37.5: create article with description</p>
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<div>Linear algebra is the study of systems of linear equations. [[matrix|Matrices]] are useful for solving such systems.</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Degenerate&diff=13343Degenerate2007-02-24T06:23:00Z<p>AMC37.5: describe degenerate cases</p>
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<div>Degenerate cases are special cases in which a problem reduces to a simple form. It is often used in [[geometry]] to describe simple [[conic section]]s such as [[point]]s and triangles which are actually line segments.</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Nondegenerate&diff=13342Nondegenerate2007-02-24T06:21:23Z<p>AMC37.5: redirect to general degenerate concept</p>
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<div>#REDIRECT [[degenerate]]</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Polyhedron&diff=13341Polyhedron2007-02-24T06:20:13Z<p>AMC37.5: create article as stub</p>
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<div>A polyhedron is a three-dimensional surface composed of at least four flat [[face]]s which encloses a region of [[space]]. These faces intersect in [[edge]]s and [[vertex|vertices]]. Polyhedra are 3-D analogues of [[polygon]]s. They can be thought of as sets of ordered triples.<br />
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== Classification ==<br />
===Concavity===<br />
Polyhedra can be [[convex]] or concave]].<br />
===Number of sides===<br />
===Regular polyhedra===<br />
They have congruent faces, angles, and edges. Only regular tetrahedra, hexahedra ([[cube]]s), octahedra, dodecahedra, and icosahedra exist. (In addition, a [[sphere]] could be thought of a polyhedron with an infinite number of faces.)<br />
== Common polyhedra ==<br />
The polyhedra most commonly encountered include:<br />
* [[tetrahedron]] - 4 faces<br />
* [[hexahedron]] - 6 faces<br />
etc.<br />
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[[Prism]]s and [[pyramid]]s can be polyhedra.<br />
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== Surface area ==<br />
The [[surface area]] of a polyhedron is the sum of its sides.<br />
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== Volume ==<br />
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== Angles ==<br />
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== Related figures ==<br />
* [[Polyhedral solid]]s are the union of a polyhedron and the space that it encloses.<br />
* [[Polygon]]s<br />
* [[Polytope]]s<br />
{{stub}}<br />
[[Category:geometry]]</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Polyhedra&diff=13340Polyhedra2007-02-24T06:09:17Z<p>AMC37.5: redirect polyhedron</p>
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<div>#REDIRECT [[polyhedron]]</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=User:AMC37.5&diff=13339User:AMC37.52007-02-24T06:06:27Z<p>AMC37.5: PI</p>
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<div>3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986</div>AMC37.5https://artofproblemsolving.com/wiki/index.php?title=Computer_programming&diff=13338Computer programming2007-02-24T06:05:35Z<p>AMC37.5: rephrase</p>
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<div>The phrase computer programming is quite self-explanatory. A computer programmer is someone who sends instructions to a computer using some language or the other. Even when you are typing out latex commands, you are essentially programming.<br />
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{{stub}}</div>AMC37.5