Difference between revisions of "User:Johnxyz1"

(Created page with "Below are some stuff I am doing to practice <math>\LaTeX</math> (that logo typeset by <code>\LaTeX</code> looks a bit off). <cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{...")
 
(Major Contributions)
 
(23 intermediate revisions by the same user not shown)
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Below are some stuff I am doing to practice <math>\LaTeX</math> (that logo typeset by <code>\LaTeX</code> looks a bit off).
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<math>\huge\mathcal{JOHN}</math>
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==Major Contributions==
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*''[[Tree (graph theory)]]''
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*''[[Reverse Polish notation]]''
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*''[[LaTeX:Packages]]''
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*''[[Basic Programming With Python]]''
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==Favorites==
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Favorite topic: <cmath>\text{Counting \& Probability}</cmath>for which I am reading AOPS intermediate book on
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Favorite color: <cmath>\text{\textcolor{green}{Green}}</cmath>
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Favorite software: <cmath>\mathit{Microsoft}\ \text{Excel}</cmath>
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Favorite Typesetting Software: <cmath>\text{\LaTeX}</cmath>
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<math>\textit{Remark.}</math>
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<cmath>\text\LaTeX>\text{Word}>\text{Canva}</cmath>
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<cmath>\text{\LaTeX}+\textsf{beamer}>\text{Powerpoint}>\text{Canva}</cmath>
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Favorite Operating System: Linux (although I am rarely on one)
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==<math>\Large\text{\bfseries\LaTeX}</math> typesetting==
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Below are some stuff I am doing to practice <math>\text{\LaTeX}</math>. That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the <math>e^{i\pi}</math> one)
  
 
<cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath>
 
<cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath>
 
<cmath>e^{i\pi}+1=0</cmath>
 
<cmath>e^{i\pi}+1=0</cmath>
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<cmath>\sum_{x=1}^{\infty} \frac{1}{x}=2</cmath>
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<cmath>\begin{align*}
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x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \
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& + \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \
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&\text{(I copied it from another website but I typeset it myself;}\
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&\text{I am pretty sure those are not copyrightable. I still need \textit{years} to even understand this.)}\
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&\text{This is the cubic formula, although it is \textit{rarely} actually used and memorized a lot. The equation is}\
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&ax^3+bx^2+cx+d=0
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\end{align*}
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</cmath>
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Source code for equations:
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https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm
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==Personal==
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Complementary casework example: https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_25
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===Representing Actions as Permutations===
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''The idea is that if you must do a fixed number of operations of multiple types, you can make those operations letters, and permutate them.'' For example, if you have a grid of 4×6 and you want to walk from one corner to the opposite one, WLOG you need to go up 4 times and right 6 times. You can do that in any order, so basically you are arranging
 +
    UUUURRRRRR
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which simplifies the problem.
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Example: 2024 AMC 8 Problems/Problem 13. In this problem you can treat going up as U and going down as D. Since you have to end up on the ground in 6 steps you have 3 U's and 3 D's; same as above. There are some special cases --- begin with U end with D and invalid stuff.

Latest revision as of 14:32, 21 September 2024

$\huge\mathcal{JOHN}$

Major Contributions

Favorites

Favorite topic: \[\text{Counting \& Probability}\]for which I am reading AOPS intermediate book on

Favorite color: \[\text{\textcolor{green}{Green}}\]

Favorite software: \[\mathit{Microsoft}\ \text{Excel}\]

Favorite Typesetting Software: \[\text{\LaTeX}\]

$\textit{Remark.}$ \[\text\LaTeX>\text{Word}>\text{Canva}\] \[\text{\LaTeX}+\textsf{beamer}>\text{Powerpoint}>\text{Canva}\]


Favorite Operating System: Linux (although I am rarely on one)

$\Large\text{\bfseries\LaTeX}$ typesetting

Below are some stuff I am doing to practice $\text{\LaTeX}$. That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the $e^{i\pi}$ one)

\[\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] \[e^{i\pi}+1=0\] \[\sum_{x=1}^{\infty} \frac{1}{x}=2\] \begin{align*} x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \\ & + \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \\ &\text{(I copied it from another website but I typeset it myself;}\\ &\text{I am pretty sure those are not copyrightable. I still need \textit{years} to even understand this.)}\\ &\text{This is the cubic formula, although it is \textit{rarely} actually used and memorized a lot. The equation is}\\ &ax^3+bx^2+cx+d=0 \end{align*}


Source code for equations:

https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm


Personal

Complementary casework example: https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_25

Representing Actions as Permutations

The idea is that if you must do a fixed number of operations of multiple types, you can make those operations letters, and permutate them. For example, if you have a grid of 4×6 and you want to walk from one corner to the opposite one, WLOG you need to go up 4 times and right 6 times. You can do that in any order, so basically you are arranging

   UUUURRRRRR

which simplifies the problem.

Example: 2024 AMC 8 Problems/Problem 13. In this problem you can treat going up as U and going down as D. Since you have to end up on the ground in 6 steps you have 3 U's and 3 D's; same as above. There are some special cases --- begin with U end with D and invalid stuff.