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AoPS Fall Classes Math Jam

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Art of Problem Solving instructors discuss upcoming AoPS online courses. We'll work through a few sample problems, discuss how the courses work, and answer questions about the courses.

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Facilitator: Deven Ware

devenware 2018-09-05 19:30:43
Hello, and welcome to an Art of Problem Solving Math Jam. Today we'll be discussing Art of Problem Solving classes. We'll start with a few sample problems, so you can get a little taste of what the classes are like. Then, I'll give an overview of how our courses work, and answer any questions you may have about the courses.
devenware 2018-09-05 19:30:52
Before we get started I would like to take a moment to explain our Virtual Classroom to those who have not previously participated in a Math Jam or one of our online classes.
devenware 2018-09-05 19:31:14
First. Everyone say "HELLO!!!"
devenware 2018-09-05 19:31:20
(That's three exclamation points)
devenware 2018-09-05 19:31:49
Can you see what you typed?
Rikri 2018-09-05 19:32:04
no
danielp 2018-09-05 19:32:04
no
Pi-dPiper 2018-09-05 19:32:04
NO
nhle72 2018-09-05 19:32:04
no
joanna418m 2018-09-05 19:32:04
no.
edgymemelord 2018-09-05 19:32:04
no
maxcaribou 2018-09-05 19:32:04
No
hole_in_1 2018-09-05 19:32:04
no
mathlogician 2018-09-05 19:32:04
NOOO!!!!
ShOhMd 2018-09-05 19:32:04
no
advancedjus 2018-09-05 19:32:04
no
devenware 2018-09-05 19:32:18
Hmm.. how about now:
Dseg123 2018-09-05 19:32:20
HELLO!!!
g1zq 2018-09-05 19:32:20
HELLO!!
lol777 2018-09-05 19:32:20
HELLO!!!
Mathlete99s 2018-09-05 19:32:20
"HELLO!!!"
advancedjus 2018-09-05 19:32:20
HELLO!!!
szelda64 2018-09-05 19:32:20
HELLO!!!
maxcaribou 2018-09-05 19:32:20
HELlO!!!
nhle72 2018-09-05 19:32:20
hiiiii
ak2003 2018-09-05 19:32:20
"HELLO!!!"
g1zq 2018-09-05 19:32:20
HELLO!!!
hole_in_1 2018-09-05 19:32:20
HELLO!!!
BearJere 2018-09-05 19:32:20
HELLO!!!
ShOhMd 2018-09-05 19:32:20
Hello!!!
srisan 2018-09-05 19:32:20
HELLO!!!
RZ2004 2018-09-05 19:32:20
HELLO!!!
Rikri 2018-09-05 19:32:20
HELLO™!!!
Idv 2018-09-05 19:32:20
HELLO!!!
Pi-dPiper 2018-09-05 19:32:20
HELLO!!!
Shonk 2018-09-05 19:32:20
HELLO!!!
srisan 2018-09-05 19:32:41
yes
Mathlete99s 2018-09-05 19:32:41
ya
ShOhMd 2018-09-05 19:32:41
yes
maxcaribou 2018-09-05 19:32:41
YES!!!
Logicoverlord 2018-09-05 19:32:41
yes!!lol
devenware 2018-09-05 19:32:44
Good!
devenware 2018-09-05 19:32:47
The classroom is moderated: students can type into the classroom, but only the moderators can choose a comment to drop into the classroom. So, when you send a message, it will not appear immediately, and may not appear at all. This helps keep the class organized and on track. Also, only moderators can enter into private chats with other people in the classroom.
devenware 2018-09-05 19:32:58
Communication in our classroom consists of text and images (no audio or video). You can read more here about why we structure the classroom this way.
devenware 2018-09-05 19:33:10
To give you a sense of how images appear in our classroom, here's a picture of Paul Ryu, the lead developer of much of the software that runs our Online School:
devenware 2018-09-05 19:33:12
http://data.artofproblemsolving.com/images/people/pryu309x309staff.png
g1zq 2018-09-05 19:33:30
KITTYY
devenware 2018-09-05 19:33:32
Oh, it looks like Paul has stepped out. That's Butters. If you're taking a class with Paul, you'll likely see more of Butters.
devenware 2018-09-05 19:33:47
We can also render math in the classroom.
devenware 2018-09-05 19:33:48
For example,
devenware 2018-09-05 19:33:50
\$\$\frac4\pi = 1+\frac{1^2}{2+\frac{3^2}{2+\frac{5^2}{2+\frac{7^2}{2+\frac{9^2}{2+\cdots}}}}}\$\$
devenware 2018-09-05 19:33:52
becomes
devenware 2018-09-05 19:33:54
\[\frac4\pi = 1+\frac{1^2}{2+\frac{3^2}{2+\frac{5^2}{2+\frac{7^2}{2+\frac{9^2}{2+\cdots}}}}}\]
advancedjus 2018-09-05 19:34:05
$$\frac4\pi = 1+\frac{1^2}{2+\frac{3^2}{2+\frac{5^2}{2+\frac{7^2}{2+\frac{9^2}{2+\cdots}}}}}$$
devenware 2018-09-05 19:34:14
And a little light programming in Asymptote becomes:
devenware 2018-09-05 19:34:15
advancedjus 2018-09-05 19:34:40
fractals!!
devenware 2018-09-05 19:34:43
You can adjust the sizing of the classroom to your liking; feel free to experiment with it! For example, most of the bars between sections of the room can be slid around. And you can change the text size with the A's at the top of the classroom.
devenware 2018-09-05 19:34:54
In general in our classes, we have assistant instructors in all of our classes, and all math questions get answered by the primary instructor of the assistants. Tonight, since there are so many of you, we might not be able to answer *every single math question*, but we get to them all in the classes.
devenware 2018-09-05 19:35:09
Kyle Guillet and Laura Zehender are joining me tonight to help field questions. They're part of our awesome team of curriculum developers and teachers here at AoPS.
devenware 2018-09-05 19:35:13
As for questions about the classes, we will try to answer all of those tonight. I will let you know when to start asking questions about specific classes.
kguillet 2018-09-05 19:35:14
Hello!
LauraZed 2018-09-05 19:35:22
HI!
BearJere 2018-09-05 19:35:31
hi!
lol777 2018-09-05 19:35:31
Hi
Kari04 2018-09-05 19:35:31
Hello
BearJere 2018-09-05 19:35:31
Hi!
maxcaribou 2018-09-05 19:35:31
HI!!!
henna 2018-09-05 19:35:31
hi
hole_in_1 2018-09-05 19:35:31
Hi!
ShOhMd 2018-09-05 19:35:36
hi!
Kari04 2018-09-05 19:35:36
hi
Rikri 2018-09-05 19:35:43
You need three exclamation marks or it doesn't count
devenware 2018-09-05 19:35:51
Oh man, they all broke the exclamation point rule!
Logicoverlord 2018-09-05 19:36:06
hi!!!
tango14 2018-09-05 19:36:06
Hi!!!
RZ2004 2018-09-05 19:36:06
Hi!!!
Mathgru 2018-09-05 19:36:06
Ello!!!
nhle72 2018-09-05 19:36:06
hello!!!
Reseacher 2018-09-05 19:36:06
HI!!!
LooF521 2018-09-05 19:36:06
HI!!!
Ponni 2018-09-05 19:36:06
Hi!!!
Sarky 2018-09-05 19:36:06
HELLO!!!
devenware 2018-09-05 19:36:07
In this Math Jam, we will start off by doing a few sample problems. These will be drawn from our Introduction to Counting & Probability course. We won't be doing problems from all of the courses tonight, since that would take too long. Instead, we'll just do a batch of problems at the beginning of the Math Jam, and discuss the courses for the remainder of the class.
devenware 2018-09-05 19:36:12
If you're just here to discuss the courses, you can tune out for 15-20 minutes while we do some math. You can also read more about how our courses work here:
devenware 2018-09-05 19:36:15
And you can read more about our online classroom here:
devenware 2018-09-05 19:36:27
Before we get started with the math, I'd like to note that the mathematics we will discuss today covers a wide range of difficulty. Moreover, I know that many of you are here just to check out the classroom before your classes start.
devenware 2018-09-05 19:36:34
Please understand that if you are enrolled in one of our introductory classes, or haven't much experience yet with advanced problem solving, then much of the material we cover tonight might be well beyond you right now. We won't be able to teach you all the math you need to understand this material in one night! So, don't be frustrated if you don't understand the problems we discuss for those classes -- your time will come!
devenware 2018-09-05 19:36:42
While the discussion tonight will be somewhat similar to that in our classes, there are a few differences between tonight and the typical class.
devenware 2018-09-05 19:36:55
There is a much wider range of students here tonight than in our typical classes. So, some of you will find tonight's material very, very easy, and others will find it very, very hard. Also, because there's such a wide spread of students, we typically end up going a bit faster in the Math Jam than we do in class.
devenware 2018-09-05 19:37:00
Furthermore, there are many more students here tonight than in a typical class. In our classes, we get to all the student questions, and everyone who is participating gets lots of "air time" in the classroom.
devenware 2018-09-05 19:37:08
So, tonight won't be as much fun as our classes usually are, and you won't be able to get all of your math questions answered. But in our courses, you'll get to interact a lot more with the teachers and assistants during class, and you'll get your math questions answered.
devenware 2018-09-05 19:37:12
Okay, ready for some math?
BearJere 2018-09-05 19:37:35
YES!!!
Logicoverlord 2018-09-05 19:37:35
lol yes
abdullahi 2018-09-05 19:37:35
yes
Sarky 2018-09-05 19:37:35
YES!!!!
lol777 2018-09-05 19:37:35
Ya!!!
Masrock9 2018-09-05 19:37:35
yes
joanna418m 2018-09-05 19:37:35
yaa dudeeee
AngelaG 2018-09-05 19:37:35
Ya!!!
advancedjus 2018-09-05 19:37:35
YES
Mathlete99s 2018-09-05 19:37:35
yes
g1zq 2018-09-05 19:37:35
YAZZZZ!!!
ak2003 2018-09-05 19:37:35
YES!!!
awesomealexovechkin 2018-09-05 19:37:35
YE
danielp 2018-09-05 19:37:35
yes!!!
hole_in_1 2018-09-05 19:37:35
Yes!!!
ShOhMd 2018-09-05 19:37:35
Yes!!!
devenware 2018-09-05 19:37:44
Suppose we have a group of 4 girls and 3 boys and we wish to seat them in a row of 7 chairs. In how many ways can the students be seated?
devenware 2018-09-05 19:37:52
Note that I can stick the problem to the top of the classroom, so it won't scroll away while we discuss it; you can adjust the bar between it and the rest of the room.
g1zq 2018-09-05 19:38:13
are the peeps distinguishable?
devenware 2018-09-05 19:38:22
They sure think so!
nashdawg55 2018-09-05 19:38:57
7!
Mathlete99s 2018-09-05 19:38:57
7!
Sarky 2018-09-05 19:38:57
7!
yolozchallengez 2018-09-05 19:38:57
7! ?
frogcoder 2018-09-05 19:38:57
$7!$
devenware 2018-09-05 19:39:06
You all seem very excited about the number 7....
manick 2018-09-05 19:39:31
7 factorial
yajingyang08 2018-09-05 19:39:31
factorials
Mathlete99s 2018-09-05 19:39:31
its a factorial
Sarky 2018-09-05 19:39:31
its a factorial
SparklyJeans 2018-09-05 19:39:31
its 7 factorial
advancedjus 2018-09-05 19:39:31
$!$ means factorial
devenware 2018-09-05 19:39:41
Factorial? What does that mean?
Rikri 2018-09-05 19:40:36
7*6*5*4*3*2*1
RZ2004 2018-09-05 19:40:36
7*6*5*4*3*2*1
szelda64 2018-09-05 19:40:36
7 * 6 * 5 * 4 * 3 * 2 * 1
knpnj 2018-09-05 19:40:36
7*6*5*4*3*2*1
AngelaG 2018-09-05 19:40:36
7*6*5*4*3*2*1
mathlovers2018 2018-09-05 19:40:36
7*6*5*4*3*2*1
ak2003 2018-09-05 19:40:36
7x6x5x4x3x2x1
Dseg123 2018-09-05 19:40:36
7 x 6 x 5 x 4 x 3 x 2
yajingyang08 2018-09-05 19:40:36
7!=1*2*3*4*5*6*7
knpnj 2018-09-05 19:40:36
7*6*5*4*3*2
BearJere 2018-09-05 19:40:36
for example, 4! is 4*3*2*1 and 5! is 5*4*3*2*1
Mathlete99s 2018-09-05 19:40:36
if we have n! n!= all the positive integers before n
nashdawg55 2018-09-05 19:40:36
7*6*5*4*3*2*1
DragonAlliance 2018-09-05 19:40:36
you multiply 1*2*3*4*5*6*7
abdullahi 2018-09-05 19:40:36
that number multiplied by everything before
sooper 2018-09-05 19:40:36
the product of all positive integers less than or equal to the number(x)
devenware 2018-09-05 19:40:39
Ah, you're saying this problem is just a multiplication problem! Why is this just a multiplication problem?
RZ2004 2018-09-05 19:41:35
7 ways for the first student, 6 ways for the second, and so on
frogcoder 2018-09-05 19:41:35
Seven ways to choose the student in the first seat, six for the second, five for the third, etc.
Sarky 2018-09-05 19:41:35
seven possibilities for the first seat, six for the next one, five for the next one...so on so on
abdullahi 2018-09-05 19:41:35
because there is 7 choices for the first seat, 6 for the next and so on
Mathlete99s 2018-09-05 19:41:35
7 ways to put a student in seat 1, 6 in seat 2 and so on so forth
advancedjus 2018-09-05 19:41:35
7 chairs for the first person, 6 chairs for the next, etc.
Dseg123 2018-09-05 19:41:35
7 options for the first seat x 6 options for the 2nd x 5 options for the 3rd and so on
devenware 2018-09-05 19:41:42
There are 7 students who could sit in the first seat. For each of these choices we make for the first seat, there are 6 ways to choose a student for the next seat, so there are 7 x 6 ways to seat the first two students.
devenware 2018-09-05 19:41:55
Continuing in this vein, for each of these 7 x 6 ways to seat the first two students, there are 5 ways to pick a student for the third seat. Thus, there are 7 x 6 x 5 ways to seat the first three students.
Predator007 2018-09-05 19:42:17
Continue it down to 1.
devenware 2018-09-05 19:42:18
We keep going like this: there are 4 ways to seat the fourth student, 3 ways to seat the fifth, 2 ways to seat the sixth, and one way to seat the last student. This gives us 7 x 6 x 5 x 4 x 3 x 2 x 1 ways to seat all the students.
devenware 2018-09-05 19:42:24
We run into products like 7 x 6 x 5 x 4 x 3 x 2 x 1 so much in mathematics that we have a symbol and a name for it. We write 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! and we call this 'seven factorial'.
devenware 2018-09-05 19:42:29
Similarly,
devenware 2018-09-05 19:42:30
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
devenware 2018-09-05 19:42:31
What does 7! equal?
LooF521 2018-09-05 19:42:53
5040
Dseg123 2018-09-05 19:42:53
5040
Mathlete99s 2018-09-05 19:42:53
5040
manick 2018-09-05 19:42:53
5040
abdullahi 2018-09-05 19:42:53
5040
RZ2004 2018-09-05 19:42:53
5040
advancedjus 2018-09-05 19:42:53
5,040
STEMathematics 2018-09-05 19:42:53
5040
AngelaG 2018-09-05 19:42:53
5040
mathlovers2018 2018-09-05 19:42:53
5040
Mathgru 2018-09-05 19:42:53
5040
devenware 2018-09-05 19:43:01
Hmm... how'd you multiply all those numbers so fast?
knpnj 2018-09-05 19:43:17
720*7
naby 2018-09-05 19:43:17
720 * 7 = 5040
User360702 2018-09-05 19:43:17
720*7
knpnj 2018-09-05 19:43:17
6!*7
RZ2004 2018-09-05 19:43:17
720*7
DragonAlliance 2018-09-05 19:43:17
we multiplied 720 by 7
STEMathematics 2018-09-05 19:43:17
Just do 6!*7
devenware 2018-09-05 19:43:21
Oh, that's clever!
devenware 2018-09-05 19:43:27
We have 7! = 7*6*5*4*3*2*1 = 7*(6!) = 7*(720) = 5040.
devenware 2018-09-05 19:43:45
Let's put a wrinkle in that problem. Suppose we must have a girl in the first chair and a girl in the last chair. Then how many seatings are there?
devenware 2018-09-05 19:44:01
Wait. I know how to do this one.
devenware 2018-09-05 19:44:04
There are 4 ways to choose the girl for the first chair. After that, we have 6 students left for the next chair, then 5 for the next, and so on, giving us a total of:
devenware 2018-09-05 19:44:06
4 x 6 x 5 x 4 x 3 x 2 x 1 seatings.
devenware 2018-09-05 19:44:30
Does my answer seem good to you?
Mathlete99s 2018-09-05 19:44:50
no
maxcaribou 2018-09-05 19:44:50
NO!!!
User360702 2018-09-05 19:44:50
nope
advancedjus 2018-09-05 19:44:50
no
RZ2004 2018-09-05 19:44:50
NO!!!
Mathlete99s 2018-09-05 19:44:50
not really
Predator007 2018-09-05 19:44:50
no
BearJere 2018-09-05 19:44:50
NO!
ak2003 2018-09-05 19:44:50
no!!!
SparklyJeans 2018-09-05 19:44:50
no
DragonAlliance 2018-09-05 19:44:50
no
Rikri 2018-09-05 19:44:50
NO
devenware 2018-09-05 19:44:56
What's wrong with my answer?
RZ2004 2018-09-05 19:45:33
No, you have to take care of the restrictions first
math2fun 2018-09-05 19:45:33
does not guarantee there is a girl in the last chair!!!
AngelaG 2018-09-05 19:45:33
No, you have to pick a girl for both ends
Eyed 2018-09-05 19:45:33
no, you didn't include the last girl
LooF521 2018-09-05 19:45:33
no because there is no guarentee that the one last is a girl
knpnj 2018-09-05 19:45:33
the last chair??
Mathlete99s 2018-09-05 19:45:33
There is a possibility that the last seat would have a boy and not a girl!
edgymemelord 2018-09-05 19:45:33
LAST CHAIR
Dseg123 2018-09-05 19:45:33
you didn't include the girl in the last chair
DragonAlliance 2018-09-05 19:45:33
You forgot the girl for the last chair
manick 2018-09-05 19:45:33
you need to count the girl in the last chair
lol777 2018-09-05 19:45:33
You didn't make sure there was a second girl at the end
edgymemelord 2018-09-05 19:45:33
there is one more requirement
LooF521 2018-09-05 19:45:33
because u dont guarantee a girl in the last one.
devenware 2018-09-05 19:45:52
The problem here is the last chair - we must have a girl in that last chair, but my approach definitely does not guarantee this. We might end up with a boy left at the end, which would violate the problem.
devenware 2018-09-05 19:46:04
Hmm... okay. How can we deal with this?
Ilikeapos 2018-09-05 19:46:51
Take care of the first chair and the last chair first
Mathlete99s 2018-09-05 19:46:51
Maybe pick two girls for the first and last seat
Predator007 2018-09-05 19:46:51
Start with the restriction
math2fun 2018-09-05 19:46:51
you choose the girl in the last seat before you choose the rest
Sarky 2018-09-05 19:46:51
eliminate restrictions first
RZ2004 2018-09-05 19:46:51
Take restrictions first
DLJ_03 2018-09-05 19:46:51
start with the first and last chairs
advancedjus 2018-09-05 19:46:51
take care of the restriction first
devenware 2018-09-05 19:47:14
Ah, that's smart. We can start with the restrictions.
devenware 2018-09-05 19:47:21
Okay, first the easy one. How many ways to put a girl in the first seat?
nashdawg55 2018-09-05 19:47:41
4
DragonAlliance 2018-09-05 19:47:41
4
szelda64 2018-09-05 19:47:41
4
ShOhMd 2018-09-05 19:47:41
4
Logicoverlord 2018-09-05 19:47:41
4
danielp 2018-09-05 19:47:41
4???
advancedjus 2018-09-05 19:47:41
4
devenware 2018-09-05 19:47:51
Cool. There are 4 girls we can put in the first seat.
devenware 2018-09-05 19:48:04
Okay, now we follow all of your advice and look at the last seat. How many ways to put a girl there?
edgymemelord 2018-09-05 19:48:17
3girls
Mathlete2017 2018-09-05 19:48:17
$3$
Predator007 2018-09-05 19:48:17
3
lol777 2018-09-05 19:48:17
3
ShOhMd 2018-09-05 19:48:17
3
maxcaribou 2018-09-05 19:48:17
3!!!
Dseg123 2018-09-05 19:48:17
3
ak2003 2018-09-05 19:48:17
3 ways to put the girl in the last seat.
RZ2004 2018-09-05 19:48:17
3
edgymemelord 2018-09-05 19:48:17
3
DragonAlliance 2018-09-05 19:48:17
3
henna 2018-09-05 19:48:17
3
devenware 2018-09-05 19:48:28
Good. There are 3 girls left, so there are 3 choices.
devenware 2018-09-05 19:48:36
Now we have the restriction taken care of. What do we do next?
yolozchallengez 2018-09-05 19:49:24
Then there is 5! ways to arrange the 5 chairs in between, making it 12*5! = 1440...?
edgymemelord 2018-09-05 19:49:24
start form the 2nd seat
AngelaG 2018-09-05 19:49:24
do 5! for therest
Mathgru 2018-09-05 19:49:24
5*4*3*2
Dseg123 2018-09-05 19:49:24
multiply by the remaining seats: 5!
Rikri 2018-09-05 19:49:24
multiply that by 5!
Calebtheawesome 2018-09-05 19:49:24
times 5!
Predator007 2018-09-05 19:49:24
Solve the rest with factorials.
ak2003 2018-09-05 19:49:24
5x4x3x2x1
danielp 2018-09-05 19:49:24
fill the 2nd,3rd,4th,5th,and 6th chair
devenware 2018-09-05 19:49:35
We can then seat the rest of the students as before. There are 5 students left to choose one for the second chair, then 4 students for the third chair, and so on.
devenware 2018-09-05 19:49:40
Thus, we have 4 x 3 ways to seat girls at each end, and for each of these seatings we have 5 x 4 x 3 x 2 x 1 ways to seat the rest of the students, for a total of:
Mathlete99s 2018-09-05 19:49:55
$4*3*5!$=1440
edgymemelord 2018-09-05 19:49:55
1440
maxcaribou 2018-09-05 19:49:55
1440!!!
Predator007 2018-09-05 19:49:55
1440
RZ2004 2018-09-05 19:49:55
5!*4*3=1440
Mathlete99s 2018-09-05 19:49:55
1440
advancedjus 2018-09-05 19:49:58
1440
lol777 2018-09-05 19:49:58
1440
devenware 2018-09-05 19:50:00
4 x 3 x 5 x 4 x 3 x 2 x 1 = 1440
devenware 2018-09-05 19:50:01
ways to seat the students such that there is a girl on either end.
devenware 2018-09-05 19:50:07
This example brings up two important counting concepts.
devenware 2018-09-05 19:50:09
First, when dealing with a counting problem that has restrictions, it often pays to think about how you would create one possible arrangement yourself. Here, we realize that if we seated the students ourselves, we'd start with the girls on the ends. This brings us to our second important counting concept:
devenware 2018-09-05 19:50:16
When dealing with restrictions, it usually helps to deal with the restrictions first. Here, we took care of the girls on the ends first since that was our restriction.
devenware 2018-09-05 19:50:40
By the way, don't forget, if you have questions about the material in class, just speak up and someone will help you!
devenware 2018-09-05 19:51:04
Okay, one more problem.
devenware 2018-09-05 19:51:07
We still have 7 students to seat in a row, but two of them, Ali and Brianna, refuse to sit next to each other. In how many ways can we seat the students now?
devenware 2018-09-05 19:51:41
What's wrong with this solution:
devenware 2018-09-05 19:51:45
There are 7 ways to seat Ali. We deal with the restriction first and realize that we can't seat Brianna in either of the seats next to Ali. Hence, Brianna has 4 choices. Then the next student has 5 choices, the one after that has 4 choices, and so on.
devenware 2018-09-05 19:51:49
What's wrong?
Mathlete99s 2018-09-05 19:52:39
Ali-a could possibly sit last
edgymemelord 2018-09-05 19:52:39
she can be on the edge
Dseg123 2018-09-05 19:52:39
didn't include if ali is on the side
panda2018 2018-09-05 19:52:39
we don't know where ali sits
e513131 2018-09-05 19:52:39
What is Ali is in the edge?
RZ2004 2018-09-05 19:52:39
Ail could be sitting on a side
Leon2000 2018-09-05 19:52:39
Ali might be on the edge, sir
devenware 2018-09-05 19:52:47
Wait... what goes wrong if Ali is on the edge?
Sarky 2018-09-05 19:53:19
brianna has one more seat option
ShOhMd 2018-09-05 19:53:19
there are 5 choices
Dseg123 2018-09-05 19:53:19
5 spots for brianna
edgymemelord 2018-09-05 19:53:19
5 seats for brianna
Sarky 2018-09-05 19:53:19
so 5 instead of 4
RZ2004 2018-09-05 19:53:19
Then Brianna could sit in 5 seats
advancedjus 2018-09-05 19:53:19
brianna will have 5 choices
Mathlete99s 2018-09-05 19:53:19
Brianna will have 5 choices?
abdullahi 2018-09-05 19:53:19
oh so this applies to any problem?
DLJ_03 2018-09-05 19:53:19
brianna would have 5 choices
DragonAlliance 2018-09-05 19:53:19
there is more choices for brianna
devenware 2018-09-05 19:53:38
Right, when Ali is at the end, there are 5 places Briana can sit.
devenware 2018-09-05 19:53:45
We could deal with this by using casework (and we'll discuss very important casework strategies in the course - these tricky casework problems are often the difference in proceeding to the next level in MATHCOUNTS/AMC), but there is a slicker approach. What else could we do?
joanna418m 2018-09-05 19:54:39
count the numbers of ways where Ali and Brianna do sit next to eachother, and then subtract that from the total number of ways (aka $7!$).
Predator007 2018-09-05 19:54:39
Find the total number of possibilities then subtract of the restricted possibilities.
RZ2004 2018-09-05 19:54:39
Complementary Counting
advancedjus 2018-09-05 19:54:39
complementary counting
BearJere 2018-09-05 19:54:39
complimetary counting
TheMagician 2018-09-05 19:54:39
so we can use complementary counting
math2fun 2018-09-05 19:54:39
combine them as one person and complimentary count
maxcaribou 2018-09-05 19:54:39
reverse
Sarky 2018-09-05 19:54:39
complementary counting
Kagebaka 2018-09-05 19:54:39
complementary counting
devenware 2018-09-05 19:54:47
Ooh! That's a cool idea.
devenware 2018-09-05 19:54:53
Instead of counting our desired seatings directly, we count what we don't want and subtract.
devenware 2018-09-05 19:55:01
We know there are 7! ways without restrictions, so we will try to count those that violate our restriction that Ali and Brianna are separate. We'll then subtract these violators from our total.
devenware 2018-09-05 19:55:12
In how many ways can we do the seating if Ali and Brianna are together?
math2fun 2018-09-05 19:56:06
2*6!
WANGR 2018-09-05 19:56:06
2*6!
LooF521 2018-09-05 19:56:06
6!
e513131 2018-09-05 19:56:06
6!
Sarky 2018-09-05 19:56:06
6!
maxcaribou 2018-09-05 19:56:06
6!*2 or 1440
Sarky 2018-09-05 19:56:06
or 2*6!
devenware 2018-09-05 19:56:08
I see some of you saying 6! and some of you saying 2*6! (and some of you saying both!). Hmmm... First, where does the 6! come from? I thought there were 7 students?!?
Dseg123 2018-09-05 19:56:54
if ali and bri are combined, it becomes 6
TheMagician 2018-09-05 19:56:54
We combine A and B to one person
RZ2004 2018-09-05 19:56:54
Treat Ali and Brianna as one person
maxcaribou 2018-09-05 19:56:54
combine the two people
harrypotterfan 2018-09-05 19:56:54
make brianna and ali one student
Predator007 2018-09-05 19:56:54
Group Ali and Brianna together.
edgymemelord 2018-09-05 19:56:54
but you can reverse their order
DLJ_03 2018-09-05 19:56:54
we can combine them as one student since they must sit together, therefore 6!
Sarky 2018-09-05 19:56:54
ali and brianna are one unit
franchester 2018-09-05 19:56:54
make ali and brianna "one person" and then order the six "people"
Logicoverlord 2018-09-05 19:56:54
ali and brianna can't sit next to each other
BearJere 2018-09-05 19:56:54
beause you put ali and brianna together
advancedjus 2018-09-05 19:56:54
we group ali and brianna together, then multiply the ways that we can arrange them
joanna418m 2018-09-05 19:56:54
cuz we're kinda counting ali and brianna as one
devenware 2018-09-05 19:57:10
We can pretend Ali and Brianna are one person: AliBrianna. Then, we have 6 students and we have no restrictions. Thus, we have 6! ways to seat these students. But what do we have to remember?
LooF521 2018-09-05 19:57:54
2x6! because u can switch Ali and briana
e513131 2018-09-05 19:57:54
they can switch!
edgymemelord 2018-09-05 19:57:54
reverse their order
franchester 2018-09-05 19:57:54
multiply by two for ordering ali and brianna within their group
Dseg123 2018-09-05 19:57:54
ali and brianna can be ordered in 2 different ways!
Robabob1 2018-09-05 19:57:54
Switched
WANGR 2018-09-05 19:57:54
Ali & Brianna can be seated 2! ways
Robabob1 2018-09-05 19:57:54
Around
Predator007 2018-09-05 19:57:54
we can switch the order of Ali and Brianna.
RZ2004 2018-09-05 19:57:54
It could also be BriannaAli or AliBrianna
TheMagician 2018-09-05 19:57:54
we can orientate them in 2 ways
maxcaribou 2018-09-05 19:57:54
we can switch their order so multiply by 2
TheMagician 2018-09-05 19:57:54
we have to multiply by 2 because they can switch
ShOhMd 2018-09-05 19:57:54
ali and brianna can switch
Kagebaka 2018-09-05 19:57:54
there are two ways to order alibrianna
devenware 2018-09-05 19:57:58
Ali and Brianna are not the same person. They could be AliBrianna or BriannaAli. Thus, for each of our 6! seatings, there are 2 orders in which we can seat Ali and Brianna in their slot. Hence, there are 2 x 6! ways to seat the students such that Ali and Brianna are together.
devenware 2018-09-05 19:58:07
So, in how many ways can we seat the students so that Ali and Brianna are apart?
Kagebaka 2018-09-05 19:59:04
3600
Dseg123 2018-09-05 19:59:04
5040 - 1440 = 3600
Mathphy2005 2018-09-05 19:59:04
7!-2*6!
Calebtheawesome 2018-09-05 19:59:04
7!-2*6!
TheMagician 2018-09-05 19:59:04
5040-1440=3600
RZ2004 2018-09-05 19:59:04
7!-6!*2=3600
edgymemelord 2018-09-05 19:59:04
3600
Robabob1 2018-09-05 19:59:04
3600 ways
edgymemelord 2018-09-05 19:59:04
5040-1440=3600
lol777 2018-09-05 19:59:04
3600
szelda64 2018-09-05 19:59:04
3600 ways
devenware 2018-09-05 19:59:07
There are 7! ways without restrictions, and 2 x 6! ways for them to be together. This leaves 7! - 2 x 6! ways for them to be apart.
devenware 2018-09-05 19:59:10
Computing this gives 7! - 2 x 6! = 7 x 6! - 2 x 6! = 5 x 6! = 5 x 720 = 3600.
devenware 2018-09-05 19:59:20
This example brings up a couple more important tactics.
devenware 2018-09-05 19:59:21
First, when it looks hard to count something directly, try counting the opposite of what you're asked for. We call this approach complementary counting, since 'complement' in dealing with groups of objects in mathematics roughly means 'opposite'. I also call this 'counting what you don't want'.
devenware 2018-09-05 19:59:27
Second, when your restriction is that some of your items must remain together when putting them in a row, a useful tactic is to consider the items all together as a single item, as we did AliBrianna above. Then you separately consider how many ways you can order the items within the group.
devenware 2018-09-05 19:59:30
These three basic examples show why it is pointless to memorize your way through counting - I can ask zillions of variations of the above questions. Instead of memorizing your way through each variation, you should learn when to add, when to subtract, when to multiply, and when to divide. Since you already know how to perform these operations, once you know when to do them, you know how to count!
devenware 2018-09-05 19:59:36
The first of these three problems was considerably easier than most of the problems we will do in the Introduction to Counting & Probability course. The second and third are a little closer to the middle in difficulty, though they are still a good bit easier than the average problem.
devenware 2018-09-05 19:59:43
In general in the course we will go through the ideas more gradually than we did here - each idea will be explored with gradually more difficult examples. Thus, the pace at which new ideas are introduced is a little slower than we did here (in which we introduced 4 general tactics in two problems!)
devenware 2018-09-05 19:59:48
While the discussion tonight was similar to that in our classes, there are a few BIG differences between tonight and the typical class.
devenware 2018-09-05 19:59:54
Anyone want to venture a guess about what they are?
BearJere 2018-09-05 20:00:24
there's a lot of people
lol777 2018-09-05 20:00:24
Not as many people?
ShOhMd 2018-09-05 20:00:24
There are a lot more people tonight
LooF521 2018-09-05 20:00:24
much less people
nhle72 2018-09-05 20:00:24
there are less people
maxcaribou 2018-09-05 20:00:24
A lot more people!!!
a28546 2018-09-05 20:00:24
more people here
nhle72 2018-09-05 20:00:24
not as many people in each class
ancientwarrior 2018-09-05 20:00:24
smaller class?
devenware 2018-09-05 20:00:33
There are way more students here tonight than in a typical class. In our classes, we get to all of the student questions, and everyone who is participating gets lots of "air time" in the classroom. We also often have an extra assistant in our usual classes. So, students get a lot more individual attention in the classes than we can give in these free Math Jams.
devenware 2018-09-05 20:01:02
Another one is that there is a much wider range of students here tonight than in our typical classes. So, some of you will find tonight's material very, very easy, and others will find it very, very hard. Also, because there's such a wide spread of students, we typically end up going a bit faster in the Math Jam than we do in class.
Sarky 2018-09-05 20:01:09
how are you typing so fast devenware
devenware 2018-09-05 20:01:16
I have several keyboards.
Sarky 2018-09-05 20:01:29
Thats so cool!
Dseg123 2018-09-05 20:01:29
efficient
maxcaribou 2018-09-05 20:01:29
whoa cool!
devenware 2018-09-05 20:01:37
That's it for the math tonight. We will now discuss the courses.
devenware 2018-09-05 20:01:41
I'll go through a quick overview of the classes, and then we'll answer your questions. Please hold your questions until I tell you to start asking them.
devenware 2018-09-05 20:01:44
Here are all the courses we offer in the coming months. Unless otherwise noted, each course meets once a week, 7:30 PM - 9 PM ET (4:30 PM - 6 PM PT).
devenware 2018-09-05 20:01:48
For each course, you can click on the corresponding course name to see what days we offer the course. You can also visit the schedule page to see the whole course schedule in one place.
Introductory level: Grades 5-10
Prealgebra 1 (1.25 hours; 7:30 - 8:45 PM ET)
Prealgebra 2 (1.25 hours; 7:30 - 8:45 PM ET)
Introduction to Algebra A
Introduction to Counting & Probability
Introduction to Number Theory
Introduction to Algebra B
Introduction to Geometry
MATHCOUNTS/AMC 8 Basics
MATHCOUNTS/AMC 8 Advanced
devenware 2018-09-05 20:01:55
Computer Science/Programming
Introduction to Programming with Python
devenware 2018-09-05 20:02:15
Many of these classes will fill, so please don't wait until the last minute to enroll.
devenware 2018-09-05 20:02:20
Classes that have reached capacity are marked as full on the schedule, but we do have several sections available for many of these courses. Each full class has a waitlist, which you can join by clicking the WAITLIST button on the schedule page. Joining the waitlist does not commit you to enrolling in the course, and does not ensure you a place in the course. Once on the waitlist, you will be emailed if a space becomes available for you. You will also be notified if the drop deadline passes without a space becoming available.
devenware 2018-09-05 20:02:29
More details about each course can be found by clicking the appropriate course name above or on this page:
devenware 2018-09-05 20:02:44
Broadly speaking, we have two types of classes: our core curriculum and specialty courses for contest-preparation.
devenware 2018-09-05 20:02:47
Classes meet weekly. Students also have a variety of resources outside of class time, which we'll discuss shortly. Chief among those resources are the weekly homework assignments and the course message board through which they can receive more support from AoPS personnel outside of class time.
devenware 2018-09-05 20:02:56
Students should expect to spend 5-7 hours per week in our curriculum courses and 3-4 hours/week in our contest prep classes, including time in class. That's a very rough estimate; there's a lot of variance from student to student and from course to course.
devenware 2018-09-05 20:03:04
Our courses are specifically designed for high-performing math students who might attend top-tier colleges and who might enter internationally-competitive intellectual careers.
devenware 2018-09-05 20:03:27
For example, the 6 members of the US team that won the International Math Olympiad in 2015 collectively enrolled in over 40 courses with AoPS, and the 6 members of the 2016 team that repeated as champions enrolled in nearly 40 AoPS courses as well.
devenware 2018-09-05 20:03:30
But you don't have to be a math contest champion to succeed in AoPS courses!
advancedjus 2018-09-05 20:03:45
wow
devenware 2018-09-05 20:03:46
We have thousands of students work through our courses each year. Qualities that are shared by most of our successful students include:
devenware 2018-09-05 20:03:49
** Willingness to ask questions when they need help. We are here to help the students, but they need to speak up when they need help.
devenware 2018-09-05 20:03:54
** Ability to work independently. Students learn by struggling through difficulties. This means sitting in a corner and failing at something until it clicks. We provide structure for planning and approaching classes, and we love to help when students are stuck, but we also expect them to be responsible for keeping up with their work and reaching out to us when they need support.
devenware 2018-09-05 20:04:00
** Desire to take on challenges. Our goal is to teach students how to solve problems they've never seen before. They only learn that skill by routinely encountering novel problems. This is a lot more difficult than simply regurgitating a mastered algorithm over and over. It's also a lot more fun and a lot more rewarding. Students who agree with that sentiment find a home at AoPS quickly.
devenware 2018-09-05 20:04:10
Having strong, eager students in our classes provides an outstanding peer group. It also gives AoPS an excellent recruiting tool for finding brilliant instructors.
devenware 2018-09-05 20:04:19
You can read more about our instructors here. You'll see that many have undergraduate and/or graduate degrees from schools like MIT, Harvard, Stanford, Princeton, CalTech, Carnegie Mellon, University of Chicago, and so on. Many of them have also won major national or international math contests, too.
devenware 2018-09-05 20:04:28
We have a couple special tips for first-time students who aren't used to working online, or who aren't used to being highly challenged in a math class.
devenware 2018-09-05 20:04:34
First, new students sometimes need a little time to adjust to not always getting 95% or more of the problems correctly.
devenware 2018-09-05 20:04:42
Second, students also sometimes need some encouragement to ask for help because they're not used to needing help. For this reason, students are able to ask for help anonymously on the course message board. Teachers will still know who the questioner is, but other students will not.
devenware 2018-09-05 20:04:48
Our main advice to parents is to encourage your children to ask questions and to understand that the yardstick of success is very different in our courses than in a typical math class. "70% correct" is doing just fine in many of our classes, just like it is in math and science classes at top universities.
devenware 2018-09-05 20:05:12
Different students take different avenues to success, so we deliver our instruction through multiple media. In addition to the live class sessions, courses include many other components from which students can learn, including each other! We'll now take a tour of these components.
devenware 2018-09-05 20:05:15
For students who miss class or need to review class material, we publish transcripts that contain all of the public discussions in class.
devenware 2018-09-05 20:05:17
http://data.artofproblemsolving.com/images/school/learning_ave_carousel/Transcript.png
devenware 2018-09-05 20:05:29
(Those usernames are pretty bland, I know.)
devenware 2018-09-05 20:05:35
Students can easily ask questions about the class material outside the classroom by clicking a symbol right next to the line about which they have a question.
devenware 2018-09-05 20:05:48
For students who would like suggestions about how to structure their studies during the week, we offer a My Goals tab on which they can create a customized approach to the assignments for each week.
devenware 2018-09-05 20:05:53
http://data.artofproblemsolving.com/images/school/learning_ave_carousel/GoalsTab.PNG
devenware 2018-09-05 20:05:57
Most AoPS curriculum classes are aligned to AoPS Textbooks, which you can read about here.
devenware 2018-09-05 20:05:59
http://data.artofproblemsolving.com/images/school/learning_ave_carousel/Ebook.png
devenware 2018-09-05 20:06:04
Students who have purchased the online version of a textbook will find the textbook embedded in their course homepage.
devenware 2018-09-05 20:06:26
A few of our courses include supplementary videos that a younger (and in some cases, much younger) version of Richard made.
devenware 2018-09-05 20:06:31
devenware 2018-09-05 20:06:59
OK, enough of that. You can catch the rest later.
devenware 2018-09-05 20:07:02
Most of learning math comes from tackling problems yourself. So, courses have weekly homework assignments.
devenware 2018-09-05 20:07:04
http://data.artofproblemsolving.com/images/school/learning_ave_carousel/HWTab.png
devenware 2018-09-05 20:07:10
Most of the problems are short-answer, so students receive immediate feedback on the accuracy of their work. They have access to a full solution to the problem as soon as they finish the problem, which is when a detailed solution can have the most impact on a student's understanding.
devenware 2018-09-05 20:07:14
Students are given as many tries as they like to solve a problem. While they get a little more credit for getting it right the first time, they still get plenty of credit for solving the problem on the second or third or tenth try.
devenware 2018-09-05 20:07:21
Our Introduction-level courses (Prealgebra courses and anything with "Introduction" in the title) have assignments from our Alcumus adaptive learning system:
devenware 2018-09-05 20:07:22
http://data.artofproblemsolving.com/images/school/learning_ave_carousel/Alcumus_grid.png
devenware 2018-09-05 20:07:35
Because Alcumus is adaptive, students who need more practice will work through more problems on Alcumus than those who don't need as much practice.
devenware 2018-09-05 20:07:40
Finally, most weeks of our curriculum classes (but not our contest prep classes) include one or two Writing Problems on which students are expected to write full solutions to problems.
devenware 2018-09-05 20:07:41
http://data.artofproblemsolving.com/images/school/learning_ave_carousel/Writing_problem.png
devenware 2018-09-05 20:07:51
Students receive feedback on both the accuracy and the presentation of their solutions. Through Writing Problems students learn how to communicate math and get some experience writing proofs.
devenware 2018-09-05 20:07:56
You might have noticed the little V and t symbols in the homework problem bars. These allow students to ask questions about problems outside the class time by posting messages that will appear on the course message board (and be attached to specific problems and class transcripts if students so choose).
devenware 2018-09-05 20:07:57
http://data.artofproblemsolving.com/images/school/learning_ave_carousel/MessageBoard1.png
devenware 2018-09-05 20:08:14
Course instructors and other AoPS personnel regularly monitor all class forums to address student questions.
devenware 2018-09-05 20:08:17
For many students, the course message board is not only the place to receive mathematical support outside class time, but it is also a social outlet through which they form friendships with other math-loving students. Over the years, a great many close friendships have been first forged on our course message boards.
devenware 2018-09-05 20:08:34
Students and parents have access to a wide range of reporting for tracking student progress.
devenware 2018-09-05 20:08:36
http://data.artofproblemsolving.com/images/school/reporting_carousel/ReportTab-closed.png
devenware 2018-09-05 20:08:41
The Report tab gives students a quick overview of their progress.
devenware 2018-09-05 20:08:51
Clicking on the thick bars of the Report page reveals a lot more information:
devenware 2018-09-05 20:08:53
http://data.artofproblemsolving.com/images/school/reporting_carousel/ReportTab-expanded-hover.png
Kavon 2018-09-05 20:09:03
wow bland
BearJere 2018-09-05 20:09:03
nice username
devenware 2018-09-05 20:09:08
I warned you the usernames were bland!
devenware 2018-09-05 20:09:15
We help students keep up with weekly reminders.
devenware 2018-09-05 20:09:17
http://data.artofproblemsolving.com/images/school/reporting_carousel/Email.png
devenware 2018-09-05 20:09:24
Parents who want to keep tabs on their children's progress have some tools at their disposal.
devenware 2018-09-05 20:09:26
They can subscribe to their students' class-related emails.
devenware 2018-09-05 20:09:28
http://data.artofproblemsolving.com/images/school/reporting_carousel/ProgReportPDF.png
devenware 2018-09-05 20:09:33
They can choose to receive printable progress reports.
devenware 2018-09-05 20:09:34
http://data.artofproblemsolving.com/images/school/reporting_carousel/ParentProgReport.png
devenware 2018-09-05 20:09:37
They can access more detailed reporting online.
devenware 2018-09-05 20:09:38
http://data.artofproblemsolving.com/images/school/reporting_carousel/ParentProbReport_Wk.png
devenware 2018-09-05 20:09:52
They can also access student work and feedback on writing problems.
devenware 2018-09-05 20:09:58
Finally, when the course is over, we can provide detailed grade reports upon request:
devenware 2018-09-05 20:10:01
http://data.artofproblemsolving.com/images/school/reporting_carousel/GReport_TwoPage.png
lol777 2018-09-05 20:10:20
can I meet your_username (000000)
devenware 2018-09-05 20:10:26
I think that's one of the AoPS ninjas.
devenware 2018-09-05 20:10:29
One use many students have for these grade report forms is to receive school credit for AoPS courses.
devenware 2018-09-05 20:10:33
The method for obtaining school credit for AoPS courses varies from school to school. You will have to talk with your school administrators about how to do so at your school. We are happy to provide further documentation to schools about our school as needed.
devenware 2018-09-05 20:10:37
Art of Problem Solving operates as a service vendor for a number of homeschool charter school networks. Charter school service vendor status gives some AoPS homeschool students the opportunity to spend institutional funds on their course enrollments. You can find a full list of the schools for which we have service vendor status here.
devenware 2018-09-05 20:10:41
Most of our students are not homeschooled, but some have still found ways to get school credit for AoPS courses. There are some schools that have been even more proactive, enrolling students in our classes themselves.
devenware 2018-09-05 20:10:45
For the most part, each school is a snowflake -- the process varies from school to school. We're happy to work with schools to help them understand our courses and provide the appropriate reporting.
devenware 2018-09-05 20:10:50
For parents who are trying to work with schools to get their children course credit for AoPS classes, we mostly recommend persistence. It also helps to have a teacher on your side who knows your child when talking with school administrators. Many parents who have succeeded in securing credit for their children's work tell us that they've needed a "don't take no for an answer" attitude to overcome some schools' initial resistance to making special arrangements for their children.
devenware 2018-09-05 20:10:57
Here are a few strategies that we've heard are helpful:
devenware 2018-09-05 20:11:01
Make the school tell you the rules before you start playing the game. It's usually best to be the second person to talk.
devenware 2018-09-05 20:11:06
Search the internet for your state's name and the word "gifted". There are a lot of really cool laws out there that say schools are required to break their own rules to help students out when the word "gifted" gets invoked.
devenware 2018-09-05 20:11:14
Try to keep your school focused on the goal: doing what's right for the student. This is where having a teacher on your side in these conversations can help a great deal -- the teacher can push this argument a lot more effectively than you can.
devenware 2018-09-05 20:11:33
Okay... whew. That was a lot of information.
devenware 2018-09-05 20:11:39
We'll take questions from you now.
devenware 2018-09-05 20:11:42
Click here for the schedule page.
devenware 2018-09-05 20:11:44
We've anticipated some of your questions in our explanation of how our classes work and in our FAQ page.
devenware 2018-09-05 20:11:50
Please note that we'll probably have a *lot* of questions tonight, so it might take us a little while to get to yours. But we will try to get to all of them!
devenware 2018-09-05 20:12:03
1) The most recent question we see is the one we will answer. Of course, while we're answering that, more will come in. We'll then move to the most recent.
devenware 2018-09-05 20:12:07
2) Please don't spam us: Don't ask the same question over and over in a short amount of time; we'll just ignore those. If we haven't answered your question in 10 minutes, then you can re-post it.
devenware 2018-09-05 20:12:12
3) If you don't feel like waiting for your question to be answered, you can email us at info@aops.com and we will answer your question by the end of tomorrow. If you are asking for a course recommendation, please include the student's math background, and we will make recommendations.
devenware 2018-09-05 20:12:21
Shortly after we're finished tonight, we'll post a complete transcript of this Math Jam here: http://www.artofproblemsolving.com/school/mathjams-transcripts
devenware 2018-09-05 20:12:25
Again, there are a lot of you here tonight, so it will take us a long time to get to all of the questions, and we're bound to miss a few. But if you email us at info@aops.com, we will answer your questions by email by the end of tomorrow, and you won't have to wait here for your question to get answered.
devenware 2018-09-05 20:13:13
Kyle Guillet (kguillet) and Laura Zehender (LauraZed) will be helping me answer questions tonight. They are instructors in our online school and manage a variety of aspects of the school. Kyle also works on our aforementioned Beast Academy (http://www.beastacademy.com) project.
devenware 2018-09-05 20:13:38
Okay! Floor is open for questions!
lol777 2018-09-05 20:14:46
If you're a taking the class at school, should I take the Intermediate or Introduction
kguillet 2018-09-05 20:14:46
That depends on your background. The Intermediate courses are some of our most difficult. If you haven't taken a rigorous algebra or geometry course yet, then you will want to get started with the Introductory courses. We provide pre- and post-assessments for each of our courses so that you can see if you are ready for them.
BearJere 2018-09-05 20:15:06
when is the next math jam
devenware 2018-09-05 20:15:06
You can find our schedule of Math Jams here: https://artofproblemsolving.com/school/mathjams
mathchampion1 2018-09-05 20:16:28
Hey, Deven! What are the plans for an Intermediate Alcumus?
devenware 2018-09-05 20:16:29
Don't tell anyone, but it's in the works.
KimmyT 2018-09-05 20:17:16
how much homework is there
devenware 2018-09-05 20:17:16
Depends on the class. Generally, classes will have Alcumus assignments which adapt to the student, several short-answer questions, and a writing problem which requires a full solution.
Mathlete99s 2018-09-05 20:18:10
b). If i covered probability in Volume 1 would could I skip to Intermediate Counting and Probability if I fit the other requirements or do I still need to do AoPS intro to counting and probability? c). I've seen people say that the AMC 10 problem series is useless because you basically just get old problems. Is this true, or would it truly be useful.
kguillet 2018-09-05 20:18:11
b) You might get the counting skills you need from Volume 1. Intro to Counting goes into more detail than Volume 1, so if your skills aren't quite up to par, I'd take that first. You can use the Intermediate Counting pre-test to see if you are ready.



c) The AMC 10 course does use old problems, but doing old problems is an excellent way to prepare for the upcoming test. What's more important though is the discussion and strategy behind the problems we do in class.
lol777 2018-09-05 20:18:22
where are the pre assessments?
devenware 2018-09-05 20:18:22
You can find those on the course catalog page for whatever course you're interested in. For example, if you wanted to take the pretest for Prealgebra 1, you can click "Are you ready?" on this page: https://artofproblemsolving.com/school/course/catalog/prealgebra1
Pi-dPiper 2018-09-05 20:18:46
Do we get to talk each other during the course?
devenware 2018-09-05 20:18:47
Of course! You can talk in the classroom, and you have the course message board.
Mathlete99s 2018-09-05 20:18:48
Okay so I have the following questions and that's it. . I've asked this question of forums and I would sincerly appreciate admins answering. a). Many people have relpied depends on you, but I'd like an estimate. Assuming that I wanted to finish the Geometry and Probability sections in Volume 1 how long would it take me on average.(pls give me an actual number) My previous post was too long so I will break it into parts
LauraZed 2018-09-05 20:18:48
Unfortunately, it's just not possible to give an accurate estimate. How long it'll take you to finish any math textbook (or a particular part of a math textbook) can vary so much depending on your mathematical background, and how easy/difficult you generally find the subject(s) covered in that text. My rule of thumb for how quickly to go through a math text: just go at whatever speed you need to in order to thoroughly learn the material it covers.
szelda64 2018-09-05 20:19:18
Im taking an integrated math class currently, which course should I enroll in?
kguillet 2018-09-05 20:19:19
That depends a lot on the course you are taking and those you have previously taken. I would recommend looking at an AoPS course that covers similar content, and checking out the pre-assessment for that AoPS course to see if you know the material well enough to move on.
nyu_parent 2018-09-05 20:19:40
is there a sibling discount if we register twins
devenware 2018-09-05 20:19:41
No, there is no discount for enrolling two students in our courses.
KimmyT 2018-09-05 20:20:17
Can I still sign up late if there's room?
devenware 2018-09-05 20:20:17
Yes, if there's room, you can still sign up. But be warned, many of these classes will fill up!
joanna418m 2018-09-05 20:20:37
why are there no videos for number theory? (at leats for intro to number theory)... or are there gonna be incoming videos?
LauraZed 2018-09-05 20:20:37
We do hope to make videos corresponding to our Introduction to Number Theory text in the coming years, but it probably won't happen in the near future as Richard unfortunately hasn't had time to get to the studio to make these supplementary videos lately.
advancedjus 2018-09-05 20:21:21
will there be an intermediate geo/number theory textbook?
devenware 2018-09-05 20:21:21
We don't have any current plans for one.
BruceTheSpruce 2018-09-05 20:22:24
I've been through many high school math classes with the same names and content as the ones AoPS offers, but I know the rigor and teaching methods for high school math classes is not very good. I enjoy solving math problems in my free time, but I struggle with the easiest of problems featured on this website. Would I fare well in one of your courses or would it be overwhelming?
kguillet 2018-09-05 20:22:25
It may just be a matter of finding the right course. Many of our courses are *very* difficult, especially if you do not have the requisite background knowledge. I'd start by looking at the earlier courses in our curriculum. Students who are eager and enjoy a good challenge tend to fare well with our curriculum. And just as a reminder: a little bit of struggle is good!
lol777 2018-09-05 20:22:28
If I already did the book, should I still take the class or go on to the next class
devenware 2018-09-05 20:22:29
That's really hard to say! The best thing to do is take the post-test for the class and see how you do.
rikhilranjit 2018-09-05 20:22:58
are there going to be any new classes?
devenware 2018-09-05 20:22:59
Physics WOOT is new this fall!
Pi-dPiper 2018-09-05 20:23:25
What if there are no videos for a specific topic?
Pi-dPiper 2018-09-05 20:23:25
Do we outsource for info?
LauraZed 2018-09-05 20:23:26
Each class has a dedicated message board, so you can post questions about material covered in class there if needed!p
danielp 2018-09-05 20:23:30
are the classes fun???
devenware 2018-09-05 20:23:31
I sure think so!
Pi-dPiper 2018-09-05 20:23:35
Do you recommend any specific instructor?
kguillet 2018-09-05 20:23:36
We go to great lengths to ensure that all of our instructions are incredibly well-qualified. You can't go wrong!
henna 2018-09-05 20:24:08
How many students are usually in one class
devenware 2018-09-05 20:24:08
Generally there are around 60 students in a class.
KimmyT 2018-09-05 20:24:31
why dose AoPs not serve younger kids?
kguillet 2018-09-05 20:24:32
We do! Beast Academy is part of AoPS and provides a complete, rigorous math curriculum for students in Grades 2-5. Learn more at beastacademy.com.
szelda64 2018-09-05 20:24:51
I have done some introductory Geometry in my Integrated Math class, and taken a summer course for Geometry at CTD, would I still benefit from an AoPS class?
devenware 2018-09-05 20:24:52
Probably, but it's really hard to say! The best thing to do is to look at the posttest for the course your considering to see if you already know the material or not.
giacomorizzo 2018-09-05 20:24:54
is aops making an intermediate geometry book?
kguillet 2018-09-05 20:24:55
We do not currently have plans for an Intermediate Geometry text, but I won't rule it out for the future!
danielp 2018-09-05 20:25:15
so,questions are hard???or easy
devenware 2018-09-05 20:25:15
In our classes? Usually pretty hard. You learn the most when you struggle.
Benjamin12 2018-09-05 20:25:21
Is it worth it to take precalculus or calculus from AoPS even if you have already taken it?
LauraZed 2018-09-05 20:25:22
Our classes cover material at a deeper and more challenging level than most other math programs, so it could be worth it! To see, I'd recommend taking the post-tests for our Intermediate Algebra (which covers the algebra material often included in precalc classes elsewhere), Precalculus, and Calculus courses:
https://artofproblemsolving.com/school/handbook/prospective/choosing#tests
Spakian 2018-09-05 20:25:51
Will AOPS do an advanced calculus textbook?
LauraZed 2018-09-05 20:25:52
We don't have plans for that currently.
abcb1030 2018-09-05 20:26:02
How long will it take me to learn all the intros book if i SPENT 30 minutes a day?
kguillet 2018-09-05 20:26:02
We expect each of our intro courses to take about as many weeks as the online class lasts (some last 12 weeks, some last up to 24). That's true even if you're working independently with just the textbook.
rikhilranjit 2018-09-05 20:26:51
What aops courses help with mathcounts?
devenware 2018-09-05 20:26:51
I would recommend any of the courses in the Intro series. Pick whichever subject sounds funnest and go with that. Additionally, you can take the MATHCOUNTS courses which are specifically designed for contest prep.
Spakian 2018-09-05 20:27:23
Are there any alternatives you can recommend for intermediate geometry?
LauraZed 2018-09-05 20:27:24
I would recommend UKMT Plane Euclidean Geometry (https://artofproblemsolving.com/store/item/ukmt-plane) or Euclidean Geometry in Mathematical Olympiads (https://www.maa.org/press/books/euclidean-geometry-in-mathematical-olympiads) ? the latter was actually written by an AoPS alum!
kittenwarrior 2018-09-05 20:27:47
what is the grading system like (blue, green, orange) in terms of A's, B's, C's?
kguillet 2018-09-05 20:27:48
There's no metric that converts the colors to specific letter grades. If you ask for a letter grade at the end of the course, your instructor will take your entire body of work into consideration and use his or her best judgment in assigning a grade. Generally speaking though, students who are able to consistently get green and blue on their report receive A's.
WANGR 2018-09-05 20:28:58
If i take the amc 10 series will it help me make aime
kguillet 2018-09-05 20:28:59
Absolutely. Top performers on the AMC 10 will qualify for the AIME, and our AMC 10 Problem Series course is specifically geared to improve students' performance on the AMC 10, providing strategy and skills for solving the toughest problems on the exam.
KimmyT 2018-09-05 20:29:01
Do high schools (Elinor Rosevelt) execpt AoPs credits to prove you know the class
LauraZed 2018-09-05 20:29:07
To make a long story short, it's up to each individual high school to decide whether or not they want to give credit for AoPS courses completed. You can find more info here: https://artofproblemsolving.com/school/handbook/prospective/school
Mathlete99s 2018-09-05 20:29:27
d). I've completed Intermediate Algebra, I've heard people talk about a Famous book called Dummit and Foote. Would Intermediate Algebra help prepare me for that as my next step in Algebra?
devenware 2018-09-05 20:29:28
I guess. Dummit and Foote is a book about abstract algebra, which is generally a topic you would see in college. You'll be prepared to go through that book, but the material won't really be relevant to anything you see in Intermediate Algebra.
Mason3090 2018-09-05 20:30:13
Can one take Intro Algebra A and Intro Algebra B, then take Counting and Number theory?
devenware 2018-09-05 20:30:14
Yeah, that order would be fine. Generally we suggest taking counting in between Algebra A and B, but it's all good either way.
o99999 2018-09-05 20:30:19
If you are in 8th grade are the advanced courses appropriate?
kguillet 2018-09-05 20:30:19
It really depends on your background. We don't really correlate between grade level and courses you should take. For some students in 8th grade, our Intermediate courses will be much too difficult, but others may find it to be the right fit. I would suggest using our pre-assessments to find where you should jump into the AoPS curriculum. Pre-assessments can be found by clicking on any course you are interested in here: https://artofproblemsolving.com/school/schedule?season=2018-2
Pi-dPiper 2018-09-05 20:31:27
Do these courses count toward college credit?
LauraZed 2018-09-05 20:31:28
That would also be up to the individual college to decide. You can learn more about getting credit from other institutions for AoPS courses here: https://artofproblemsolving.com/school/handbook/prospective/school
kittenwarrior 2018-09-05 20:31:51
do you have an Algebra 2 class?
kguillet 2018-09-05 20:31:51
We offer Algebra A and Algebra B, which don't always correlate perfectly with what most schools call Algebra 1 and 2. There is a fair amount of overlap, but we tend to go into topics much more deeply, and also cover material that doesn't get discussed at all in most schools. We also offer Intermediate Algebra, which does contain some material (though not a ton) that is often covered in Algebra 2 courses.
BruceTheSpruce 2018-09-05 20:32:40
If one doesn't have time to take a course, are there any self-study methods that could provide similar a education? If not, what should they do?
LauraZed 2018-09-05 20:32:41
If you can't commit to a course, you could work through a textbook independently instead ? while you won't have a live instructor, our textbooks are designed so that they can be used independently, and include full solutions for every problem: https://artofproblemsolving.com/store
rikhilranjit 2018-09-05 20:33:16
What happens if you get an orange average on a course?
kguillet 2018-09-05 20:33:17
Generally speaking, red on your report means that you have made insufficient progress, orange means you're getting there but could still use some improvement, green means you have passed and understood the material, and blue indicates mastery of the material. Students should aim for green and blue. There are no consequences for orange or red -- these are merely indicators of performance.
ancientwarrior 2018-09-05 20:33:51
is intro to nt good for amc 10?
kguillet 2018-09-05 20:33:51
Absolutely. All of our Introduction courses are great for preparing for the AMC 10.
Mason3090 2018-09-05 20:34:49
When the Spring 2019 schedule will be published? Thanks!
kguillet 2018-09-05 20:34:50
We should have the Spring 2019 schedule out sometime in the next couple of months.
lol777 2018-09-05 20:35:05
Is there any part of the Aops website to help with Mathcounts?
devenware 2018-09-05 20:35:05
Sure! Check out the Mathcounts Trainer! https://artofproblemsolving.com/mathcounts_trainer
Eth007 2018-09-05 20:35:41
Will AoPS make a way you can automatically save all class materials to a file?
devenware 2018-09-05 20:35:41
We don't have any current plans for that feature.
KimmyT 2018-09-05 20:35:44
what happends if you can't make a class
LauraZed 2018-09-05 20:35:45
Our courses offer full transcripts for each class session, so even if you're going to miss some classes, you'll still have access to everything that happened in them. Moreover, you'll be able to use the class message board to ask any questions you have outside of class time.
KimmyT 2018-09-05 20:36:32
If I do this I have to quit swim team do you think its worth it?
kguillet 2018-09-05 20:36:33
We strongly believe in having a good life balance! We can't make that decision for you, but keep in mind that math isn't the *only* important thing in life (though sometimes we may wish it were )
abdullahi 2018-09-05 20:36:46
im taking the contest math is it harder than the regular algebra?
devenware 2018-09-05 20:36:46
Not really. The contest courses don't teach everything as in-depth as the subject courses and focus more on doing contest problems with the material.
joanna418m 2018-09-05 20:37:22
HEY DEVEN U COULD MAKE THEM LIKE HOW U MADE SOME OF THE AMC VIDS
devenware 2018-09-05 20:37:22
Maybe one day...
Skupp3 2018-09-05 20:37:52
Sorry, I just joined. When will Calculus be?
kguillet 2018-09-05 20:37:53
You can view our Calculus offerings on our Schedule page here: https://artofproblemsolving.com/school/schedule?season=2018-2
henna 2018-09-05 20:39:48
are there videos to go with the classes
devenware 2018-09-05 20:39:48
There are videos for some of our courses in the intro series.
KimmyT 2018-09-05 20:39:57
Is the program lideraly just math or is there like ice breaker, team bulilding things or whatever
kguillet 2018-09-05 20:39:57
We tend to stay pretty focused on the math during class. Time is short, and we want to make it count!
devenware 2018-09-05 20:40:37
Alright. Last call for questions! If you have questions, ask them now.
Pi-dPiper 2018-09-05 20:41:10
What if you have to quit in the middle of a class?
LauraZed 2018-09-05 20:41:11
Students can withdraw from an AoPS course at any point before the beginning of the third class session for a full refund of the enrollment fee, so they have two weeks to make sure the course is a good fit for them.
skar02 2018-09-05 20:41:12
Is regular pre cal covered the Intermediate Algerba class
kguillet 2018-09-05 20:41:13
No. Precalculus is a separate course that should be taken after Intermediate Algebra.
ShOhMd 2018-09-05 20:41:51
if I purchase an online textbook, will it allow me to download and save the textbook in my hard drive?
devenware 2018-09-05 20:41:52
No. The online book will be accessed through the AoPS webpage.
Pi-dPiper 2018-09-05 20:42:05
Can I get a refund before the class starts?
LauraZed 2018-09-05 20:42:05
If you enroll in a class and then withdraw before it starts, you'll get a refund.
Pi-dPiper 2018-09-05 20:42:12
What difficulty level should albums be set to?
devenware 2018-09-05 20:42:12
It'll be automatically set, but you can make it whatever feels right to you.
Kavon 2018-09-05 20:42:20
how long is a class?
kguillet 2018-09-05 20:42:21
Almost all classes are 90 minutes long. The exceptions are Prealgebra 1 and 2, which are 75 minutes, and Calculus and WOOT courses, which are 120 minutes.
Kavon 2018-09-05 20:42:37
What if you have to leave or miss a class, how do u catch up?
LauraZed 2018-09-05 20:42:38
Review the transcript! More info here: https://artofproblemsolving.com/school/handbook/current/missclass
ShOhMd 2018-09-05 20:43:03
Are there any courses before pre-algebra?
kguillet 2018-09-05 20:43:03
Yes! The Beast Academy curriculum (part of AoPS) provides instruction for students in Grades 2-5. Learn more at beastacademy.com.
Mathlete99s 2018-09-05 20:43:05
can the first two or three problems on the AIME be solved if you only do volume 1
devenware 2018-09-05 20:43:05
Yeah; I'd expect so.
ShOhMd 2018-09-05 20:43:46
What are WOOT courses?
LauraZed 2018-09-05 20:43:47
They're our high school olympiad training programs. You can learn more about math WOOT, PhysicsWOOT, and ChemWOOT on the following pages:
https://artofproblemsolving.com/school/woot
https://artofproblemsolving.com/school/woot-chem
https://artofproblemsolving.com/school/woot-physics
andrewyung 2018-09-05 20:43:49
How much homework is there?
devenware 2018-09-05 20:43:50
Depends on the class. Generally, classes will have Alcumus assignments which adapt to the student, several short-answer questions, and a writing problem which requires a full solution.
Pi-dPiper 2018-09-05 20:44:15
Do some of these courses cover previous material?
kguillet 2018-09-05 20:44:15
We typically expect students to have the necessary background knowledge for any given course, though we do occasionally review concepts briefly if they are important to the lesson at hand.
math4anv 2018-09-05 20:44:22
I am a few questions away for making aime. What course would you recommend that I should take?
LauraZed 2018-09-05 20:44:24
Something in this section, probably: https://artofproblemsolving.com/school/recommendations#amc-12
Kavon 2018-09-05 20:45:37
If I need to reach a teacher how do I do that?
LauraZed 2018-09-05 20:45:37
If you're enrolled in an AoPS class, post on the dedicated course message board! AoPS instructional staff are on the class message boards every weekday from 7:30-8:30pm ET for 'office hours' – students can either post their questions during those office hours to receive help in real time, or they can make a post at any other time and it'll receive an answer during the next office hours at the latest.
a28546 2018-09-05 20:45:48
How many problems does a class like Algebra have?
devenware 2018-09-05 20:45:48
About 10 short-answer per week, plus a writing problem. Then there's Alcumus which really depends on the student.
ShOhMd 2018-09-05 20:46:06
how do you submit the homework?
KimmyT 2018-09-05 20:46:06
Is there a presentation at the end to show our parents or somthing
kguillet 2018-09-05 20:46:07
All homework is submitted online on your course homepage. Most problems will give you instantaneous feedback on how you did. If you are taking a subject course, you will also submit a written solution to a problem and receive detailed feedback from a human grader.
LauraZed 2018-09-05 20:46:07
You can request documentation after completing an AoPS course: https://artofproblemsolving.com/school/handbook/current/documentation
Pi-dPiper 2018-09-05 20:46:29
Can you ask the teachers any questions?
devenware 2018-09-05 20:46:30
Yeah; definitely! You should feel free to ask questions at any time during class. And outside of class time you can post your questions to the class message board.
September31st 2018-09-05 20:47:11
should I take number theory if I'm already in AMC 10 PROBLEM SERIES and studying algebra 2 in school?
TheDifferentialPenguin 2018-09-05 20:48:14
What do you recommend for going from 8 to 15 on AIME?
devenware 2018-09-05 20:48:17
It's really hard to get 15 on the AIME! But anyway, I would recommend WOOT.
niranjan_ng 2018-09-05 20:48:29
Do you guys know any tips for improving my mathcounts scores?
kguillet 2018-09-05 20:48:29
Our Mathcounts Basics and Mathcounts Advanced courses are fantastic resources. You can also work on old Mathcounts problems. The AMC 8 often has similar questions, so working on old AMC 8 exams can be helpful too. Find the area you are weakest in, and study hard in that subject.
lol777 2018-09-05 20:48:47
If we are going to be out, should we contact the teachers?
devenware 2018-09-05 20:48:49
No, you don't need to. However, you should set up extensions if you're going to need extra time on the homework!
o99999 2018-09-05 20:49:01
I'm taking precalc and finishing of Algebra 2 in 3 weeks. Do you have any suggestions for the next course I should take?
LauraZed 2018-09-05 20:49:04
After finishing Algebra 2 or our Algebra B course, we actually generally reccommmend taking Introduction to Geometry ? you can find our recommended course progression in our Course Map:
https://artofproblemsolving.com/school/recommendations
ASnerd 2018-09-05 20:49:21
Why is there no olympiad geometry this year
kguillet 2018-09-05 20:49:21
Olympiad Geometry will be offered again, just not this Fall, as there was not sufficient demand.
Mathlete99s 2018-09-05 20:50:19
for the AMC 10 problem series is it just solving problems or is there some theory?
kguillet 2018-09-05 20:50:20
The course is structured around solving problems, but in doing so we discuss a lot of strategy and introduce problem solving techniques that apply to wide variety of problems.
Wolfy2005 2018-09-05 20:50:47
What do you recommend to place in Mathcounts state??
devenware 2018-09-05 20:50:48
I'd recommend that you start with the AoPS Intro Series for Mathcounts prep.
KimmyT 2018-09-05 20:52:46
What happends if we do a class but the high school we go to dosn't take AoPs credits so we have to do the whole thing over
LauraZed 2018-09-05 20:52:52
If you want to avoid that, I'd recommend talking to your school's academic advisor/counselor before taking an AoPS course, to see if they'd give you credit for that (or at least allow you to skip the corresponding class at school!) I'd recommend bringing along the syllabus of the class you're interested in taking when you go to talk to your school about this:
https://artofproblemsolving.com/school/handbook/prospective/choosing#syllabi
devenware 2018-09-05 20:52:59
Thank you for attending the Math Jam! If you have any questions later, you can email us at info@aops.com. If you need specific course recommendations, please include the student's math background and we will make recommendations.
kguillet 2018-09-05 20:53:29
Bye everyone!
LauraZed 2018-09-05 20:53:32
bye!
devenware 2018-09-05 20:54:11
Bye!
lol777 2018-09-05 20:54:21
Thanks!
ancientwarrior 2018-09-05 20:54:21
bye!
ancientwarrior 2018-09-05 20:54:21
Thanks!
September31st 2018-09-05 20:54:21
thank you!!!!
carzland 2018-09-05 20:54:21
Bye!
Mathlete99s 2018-09-05 20:54:21
bye
Pi-dPiper 2018-09-05 20:54:21
Goodbye
Pi-dPiper 2018-09-05 20:54:21
THANKS DEVEN

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