Math Jams

rrusczyk 2011-08-22 19:21:24
This is not the classroom for the AoPS Introduction to Geometry, Mathematical Tapas, Introduction to Programming, or AIME Problem Series class. This is the AoPS Classes Math Jam. If you are enrolled in a course and trying to attend it, then you should leave the classroom now, click Classroom, and then choose the appropriate link on the next page.

rrusczyk 2011-08-22 19:21:30
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.

rrusczyk 2011-08-22 19:29:14
We'll get started in a couple minutes.

rrusczyk 2011-08-22 19:29:40
We'll start with a description of how this Math Jam works, then do a couple sample problems, and then talk about all of the fall classes.

rrusczyk 2011-08-22 19:30:10
The math will last about 20 minutes. The discussion afterwards, which will mostly be question-and-answer, will go on as long as my hands can bear it.

rrusczyk 2011-08-22 19:30:24
A couple of you have asked about sound. There is no sound in the classroom. This webpage explains why:

rrusczyk 2011-08-22 19:30:27
http://www.artofproblemsolving.com/School/index.php?page=howclassroomworks

rrusczyk 2011-08-22 19:31:26
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.

rrusczyk 2011-08-22 19:31:36
My name is Richard Rusczyk. I founded Art of Problem Solving and have written several Art of Problem Solving textbooks.

rrusczyk 2011-08-22 19:31:44
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.

rrusczyk 2011-08-22 19:32:01
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.

rrusczyk 2011-08-22 19:32:28
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.

rrusczyk 2011-08-22 19:32:37
Our assistant tonight is Shannon Rogers, a curriculum developer here at Art of Problem Solving working on a top secret project.

srogers 2011-08-22 19:32:43
Hi!

ChipDale 2011-08-22 19:33:12
You are either copying or a fast typer.

rrusczyk 2011-08-22 19:33:14
I have 25 fingers. My last name gives me trouble.

rrusczyk 2011-08-22 19:33:47
For those of you asking, here's a hint about the top secret project: http://www.beastacademy.com

thinker88 2011-08-22 19:33:56
How do you have 25 fingers???:-o

rrusczyk 2011-08-22 19:34:00
Um, 5 hands.

rrusczyk 2011-08-22 19:34:15
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.

rrusczyk 2011-08-22 19:34:30
Also, note that 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 little box with the number on it (it's right above the box where you type).

rrusczyk 2011-08-22 19:35:37
A couple of you have asked about sound. There is no sound in the classroom. This webpage explains why:

rrusczyk 2011-08-22 19:35:41
http://www.artofproblemsolving.com/School/index.php?page=howclassroomworks

rrusczyk 2011-08-22 19:35:45
You can read that later; you don't have to check it out now. There will be a full transcript of this class available on the Math Jam pages about an hour after we finish.

rrusczyk 2011-08-22 19:36:30
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.

rrusczyk 2011-08-22 19:36:55
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:

rrusczyk 2011-08-22 19:36:58
http://www.artofproblemsolving.com/School/index.php?page=classinformation

rrusczyk 2011-08-22 19:37:13
And you can read more about our online classroom here:

rrusczyk 2011-08-22 19:37:17
http://www.artofproblemsolving.com/School/index.php?page=howclassroomworks

rrusczyk 2011-08-22 19:37:33
Before we get started, 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.

rrusczyk 2011-08-22 19:37:43
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!

rrusczyk 2011-08-22 19:38:06
One quick note before we start on the math. While the discussion tonight will be similar to that in our classes, there are a few differences between tonight and the typical class.

rrusczyk 2011-08-22 19:38:15
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.

rrusczyk 2011-08-22 19:38:35
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. We also often have an extra assistant in our usual classes.

rrusczyk 2011-08-22 19:39:13
Now, let's do a few problems, and then we'll discuss the courses. Then, I'll take questions about the courses (please hold your questions about the courses until then).

rrusczyk 2011-08-22 19:39:28
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?

rrusczyk 2011-08-22 19:39:35
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.

knittingfrenzy18 2011-08-22 19:40:24
Are the girls distiguishable?

rrusczyk 2011-08-22 19:40:30
They sure think they are!

dbug660 2011-08-22 19:40:41
7!

dragoncurve 2011-08-22 19:40:42
7!

eugenepark 2011-08-22 19:40:42
7!

jasonzhang 2011-08-22 19:40:42
7!

xiaofandeng 2011-08-22 19:40:42
7!

aqua31 2011-08-22 19:40:42
7!

vanguard12888 2011-08-22 19:40:42
7!

rrusczyk 2011-08-22 19:40:45
Wow, you all sure seem excited about the number 7. Or does that ! have some special meaning?

vanguard12888 2011-08-22 19:41:06
Factorial

puwei99 2011-08-22 19:41:06
factorial

Nobodyknows 2011-08-22 19:41:06
Factorial!

eugenepark 2011-08-22 19:41:06
factorial!

aqua31 2011-08-22 19:41:06
factorial

algebralien 2011-08-22 19:41:06
factorial

thinker88 2011-08-22 19:41:06
!= factorial

rrusczyk 2011-08-22 19:41:11
Um, what's a factorial?

jasonzhang 2011-08-22 19:41:36
7x6x5x4x3x2x1

dragoncurve 2011-08-22 19:41:37
7*6*5*4*3*2*1

Sinisalo 2011-08-22 19:41:37
yes, 7!=7x6x5x4x3x2x1

rbhale12 2011-08-22 19:41:37
7!=7*6*5*4*3*2*1

mathletepower 2011-08-22 19:41:37
it means factorial(7x6x5x4x3x2x1)

ilovemath23 2011-08-22 19:41:37
7*6*5*4*3*2*1

vanguard12888 2011-08-22 19:41:37
multiply all numbers from the number n down to one

knittingfrenzy18 2011-08-22 19:41:37
7x6x5x4x3x2x1

Buckeyefan831 2011-08-22 19:41:37
7*6*5*4*3*2*1

aqua31 2011-08-22 19:41:37
7x6x5x4x3x2x1

mcqueen 2011-08-22 19:41:37
Where you multiply the number by every number less thn it down to 1.

rrusczyk 2011-08-22 19:41:41
Ah, there we go!

rrusczyk 2011-08-22 19:42:00
And why is that the answer to this problem?

dragoncurve 2011-08-22 19:42:47
because 7 people can be seated in the first chair 6 in the second and so on

cong989 2011-08-22 19:42:47
because there are 7 choices for the first chair, 6 for the second, 5 for the third, etc. and then we multiply

vanguard12888 2011-08-22 19:42:47
Because we have 7 choices for the first chair, 6 choices for the 2nd, 5 for the 3rd, so on down to 1

Mrdavid445 2011-08-22 19:42:47
7 ways for 1st seat, 6 ways for 2nd seat... on to 1 way for last seat

Sinisalo 2011-08-22 19:42:47
because we have 7 ways to pick the first chair, 6 to pick the second (one person alreaedy used) and so on!

Lord.of.AMC 2011-08-22 19:42:47
7 choices for first student, 6 choices for the second, . . ., 1 choice for the last

DragonGenius 2011-08-22 19:42:47
because 7 people can sit in the first seat, 6 in the second, 5 in the third, and so on...

Scamper 2011-08-22 19:42:47
We have 7 ways to place the first child, then 6 ways to place the second, and so on. Then we multiply the numbers together.

Nobodyknows 2011-08-22 19:42:47
For the first chair, you can choose between 7 people. For the second, you can choose between 6 people etc.

CRICKET229 2011-08-22 19:42:47
7 choices for the first seat, 6 choices for the second seat, and so on

dbug660 2011-08-22 19:42:47
Because there are 7 choices for the first seat, 6 for the second, 5 for the third and so on.

maplehill001 2011-08-22 19:42:47
7 places to put first, 6 to second...

xiaofandeng 2011-08-22 19:42:47
because in the first seat you can put one of seven people, in the second seat you can put one of six, down to one

knittingfrenzy18 2011-08-22 19:42:47
There are 7 possiblilites for the first person, and then there is six posiblilites for the next, and so on.

rrusczyk 2011-08-22 19:42:53
Good!

rrusczyk 2011-08-22 19:42:55
This is a straightforward application of multiplication: there are 7 students who could sit in the first seat. For each of these choices we make for the first seat, there are six ways to choose a student for the next seat, so there are 7 x 6 ways to seat the first two students.

rrusczyk 2011-08-22 19:43:00
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.

rrusczyk 2011-08-22 19:43:09
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.

kev2010 2011-08-22 19:43:28
5040

thinker88 2011-08-22 19:43:28
5040 ways

rrusczyk 2011-08-22 19:43:30
Indeed; this product equals 5040.

rrusczyk 2011-08-22 19:43:33
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'.

rrusczyk 2011-08-22 19:43:36
Similarly,

rrusczyk 2011-08-22 19:43:40
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

rrusczyk 2011-08-22 19:43:49
That problem was pretty simple. Let's put a wrinkle in it. Suppose we must have a girl in the first chair and a girl in the last chair. Then how many seatings are there?

rrusczyk 2011-08-22 19:43:54
What's wrong with this answer:

rrusczyk 2011-08-22 19:43:57
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:

rrusczyk 2011-08-22 19:44:00
4 x 6 x 5 x 4 x 3 x 2 x 1 seatings.

rrusczyk 2011-08-22 19:44:04
What's wrong with that?

claudiafeng 2011-08-22 19:44:48
We didn't cover the last chair.

puwei99 2011-08-22 19:44:48
you forgot about the other girl

xiaofandeng 2011-08-22 19:44:48
the last chair has to have a girl

AkshajKadaveru 2011-08-22 19:44:48
We aren't sure that the last chair will have a girl in it.

Nobodyknows 2011-08-22 19:44:48
How do we know that the last seat has a girl?

xiaofandeng 2011-08-22 19:44:48
here that student can be a boy

CRICKET229 2011-08-22 19:44:48
We ignore the requirement of a girl being in the last chair

TMNF18 2011-08-22 19:44:48
doesnt guarentee a girl in the last chair

mathguy225 2011-08-22 19:44:48
We won't necassarilly have a girl left to sit in the last chair.

Scamper 2011-08-22 19:44:48
We have to have a girl in the last chair.

rbhale12 2011-08-22 19:44:48
You're not considering the fact that a girl has to sit in the last chair

cedar10000 2011-08-22 19:44:48
there has to be a girl in the last seat

rjoshmath 2011-08-22 19:44:48
the last one could be a boy

mathwizard888 2011-08-22 19:44:48
You aren't counting the last girl restriction.

eugenepark 2011-08-22 19:44:48
the last chair might be a boy or a girl

aqua31 2011-08-22 19:44:53
bc the last one is supposed to be a girl

rrusczyk 2011-08-22 19:44:54
The problem here is the last chair - we must have a girl in that last chair, but our approach above definitely does not guarantee this. We might end up with a boy left at the end, which would violate the problem.

rrusczyk 2011-08-22 19:44:58
What do we have to do to deal with this?

ChipDale 2011-08-22 19:45:58
Put a girl in the last and first chairs first

CRICKET229 2011-08-22 19:45:59
first account for the first and last chairs

GelidIce 2011-08-22 19:45:59
Deal with the restrictions first. Seat the girls into the first and last chair first

mathwizard888 2011-08-22 19:45:59
Put the girls in the first and last chairs first.

TMNF18 2011-08-22 19:45:59
deal with both ends first

rrusczyk 2011-08-22 19:46:05
We can think to ourselves 'How would we seat the kids according to these restrictions if we had to make up a seating ourselves?' Our answer is: we'd seat the girls at the ends first, so we make sure we satisfy that restriction. What do we find?

AkshajKadaveru 2011-08-22 19:47:07

mathguy225 2011-08-22 19:47:07
we should seat girls in the first and last seats first, then fill in the remaining seats, so it is 4x3x5x4x3x2x1

math1000 2011-08-22 19:47:07
4 x 3 x 5!

ilovemath23 2011-08-22 19:47:07
4x3x5x4x3x2x1

DragonGenius 2011-08-22 19:47:07
4x5x4x3x2x1x3

rjoshmath 2011-08-22 19:47:07
4*3*5!

cong989 2011-08-22 19:47:07
4*5*4*3*2*1*3

ChipDale 2011-08-22 19:47:07
4*3*5*4*3*2*1

Buckeyefan831 2011-08-22 19:47:07
(4x3)x5x4x3x2x1

mathlete5 2011-08-22 19:47:07
4*3*5*4*3*2*1

Scamper 2011-08-22 19:47:07
We have 4 ways to seat the first girl * 3 ways to seat the second * 5! ways to seat the rest of the children

mathwizard888 2011-08-22 19:47:07
There are 4x3x5! ways.

Sinisalo 2011-08-22 19:47:07
4*3*5*4*3*2*1

eugenepark 2011-08-22 19:47:07
4x3x5!

rrusczyk 2011-08-22 19:47:13
As before, there are 4 ways to seat a girl in the first seat. Next we seat a second girl in the last seat - there are 3 girls left, so there are 3 choices. Now we have our restriction taken care of. 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.

rrusczyk 2011-08-22 19:47:42
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:

rbhale12 2011-08-22 19:47:51
4 choices for the first seat, 3 choices for the last seat, and then 5! for the others=4*3*5!=1440

DragonGenius 2011-08-22 19:47:51
1440

Rex96 2011-08-22 19:47:51
4*3*5! = 12*120=1440

ChipDale 2011-08-22 19:47:56
1440

Scamper 2011-08-22 19:47:56
1440 ways

DragonGenius 2011-08-22 19:47:56
1440

mcqueen 2011-08-22 19:47:56
1440

mathletepower 2011-08-22 19:48:03
There are then 1440 ways

cong989 2011-08-22 19:48:04
1440

ChipDale 2011-08-22 19:48:04
1440

rrusczyk 2011-08-22 19:48:06
4 x 3 x 5 x 4 x 3 x 2 x 1 = 1440

rrusczyk 2011-08-22 19:48:10
ways to seat the students such that there is a girl on either end.

rrusczyk 2011-08-22 19:48:14
This example brings up two important counting concepts.

rrusczyk 2011-08-22 19:48:18
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:

rrusczyk 2011-08-22 19:48:35
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.

rrusczyk 2011-08-22 19:48:58
However, there are other clever ways for dealing with restrictions. Let's check a couple others out:

rrusczyk 2011-08-22 19:49:03
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?

rrusczyk 2011-08-22 19:49:10
What's wrong with this solution:

rrusczyk 2011-08-22 19:49:15
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.

rrusczyk 2011-08-22 19:49:20
What's wrong?

cong989 2011-08-22 19:50:00
well, what if ali is sitting on the end?

AkshajKadaveru 2011-08-22 19:50:00
Ali could be in one of the end ones, then Brianna would have 5.

DragonGenius 2011-08-22 19:50:00
ali might be on an end chair

Nobodyknows 2011-08-22 19:50:00
Ali could be on the edge

CRICKET229 2011-08-22 19:50:00
If Ali is in the first or last seat, Brianna actually has 5 choices

mathguy225 2011-08-22 19:50:00
Ali may be sitting on the end.

eugenepark 2011-08-22 19:50:00
Ali can be on the ends

lingmao 2011-08-22 19:50:00
Ali might sit on the end

TMNF18 2011-08-22 19:50:00
what if ali is on the end

knittingfrenzy18 2011-08-22 19:50:00
The end seats! The end seats! There is only one chair next to Ali in the end chair!

xiaofandeng 2011-08-22 19:50:00
If Ali is at the end there are 5 choices

newbie101 2011-08-22 19:50:00
ali could be sittting on the ends

rjoshmath 2011-08-22 19:50:00
if Ali sits on the first chair or last chair, there is 5 choices

Buckeyefan831 2011-08-22 19:50:00
Ali could be on the end, in which case Brianna could be in one of 5 seats

mathletepower 2011-08-22 19:50:05
Ali can sit at the end!

rrusczyk 2011-08-22 19:50:06
The problem here is that there are not always 2 seats next to Ali - sometimes he may be put at the end. Hence, sometimes Brianna will have 5 choices for her seat.

rrusczyk 2011-08-22 19:50:18
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?

mcqueen 2011-08-22 19:51:25
Count the ways we CAN'T have. Then take that from the total.

ChipDale 2011-08-22 19:51:26
You can find the total number of ways to seat 7 people and then subtract the number of ways Ali and Brianna sit together

jasonzhang 2011-08-22 19:51:26
count if Bianca and ALi sit together and subtract from 7 factorial

DragonGenius 2011-08-22 19:51:26
find out how many combinations there are where ali and brianna are sitting next to each other

shengo8 2011-08-22 19:51:26
we could count the possibilities and subtract the number of possibilities that ali sits next to brianne

mathletepower 2011-08-22 19:51:26
figure out how many ways they sit together and subtract that from the total

rrusczyk 2011-08-22 19:51:34
What makes this problem hard is the restriction that Ali and Brianna are not adjacent. We know there are 7! ways to seat the students without any restrictions.

rrusczyk 2011-08-22 19:51:38
Instead of counting our desired seatings directly, we count what we don't want and subtract.

rrusczyk 2011-08-22 19:51:46
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.

rrusczyk 2011-08-22 19:51:50
In how many ways can we do the seating if Ali and Brianna are together?

eugenepark 2011-08-22 19:52:47
6!2!

ChipDale 2011-08-22 19:52:47
2*6!

rbhale12 2011-08-22 19:52:47
Consider Ali and Brianna one unit, so it's 2*6!

Nobodyknows 2011-08-22 19:52:47
6*2*5!

Michelangelo 2011-08-22 19:52:47
6x2xx5x4x3x2x1

mathguy225 2011-08-22 19:52:47
2x6!

rrusczyk 2011-08-22 19:52:51
How does that work?

eugenepark 2011-08-22 19:54:13
put ali and brianna into one group that moves together

cong989 2011-08-22 19:54:13
we know they have to be together, but within their unit, there are 2 ways to order them

TMNF18 2011-08-22 19:54:13
6! if we call alibrianna one person, and 2 for arranging which of them come first in their group

puwei99 2011-08-22 19:54:13
pretend that ali and brianna are one person. then it would be 6! Multiply by two because of order

rbhale12 2011-08-22 19:54:13
2 ways to arrange Ali and Brianna within themselves, and then there are 6 groups to arrange, so 2*6!

Nobodyknows 2011-08-22 19:54:13
six ways for 2 adjacent seats, *2 because it could be ab or ba

mathletepower 2011-08-22 19:54:13
consider ali and brianna as one person and then work it out.afterwards multiply it by 2 because they can switch places

ChipDale 2011-08-22 19:54:13
If you treat Ali and Brianna as one person you have 6! ways but you multiply by two because you can switch their positions

Michelangelo 2011-08-22 19:54:13
There are 6 positions where Ali and Brenda could sit, but they could be switched around, so we must multiply the 6 by 2. Then, there are no restrictions for the rest of the students, so 5!

mathguy225 2011-08-22 19:54:13
If you trewat Ali and Brianna as one unit, there are now six students, which results in 6! ways to seat them. However, Ali and Brianna could sit on either side of each other, so we must multiply by 2.

rrusczyk 2011-08-22 19:54:33
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.

thinker88 2011-08-22 19:54:40
2 ways to seat Ali and Brianna and 6! ways to seat the other students

shengo8 2011-08-22 19:54:40
we already have 6! for the other people so we split ali and brianna which makes 2!6!

rrusczyk 2011-08-22 19:54:48
But we must remember that 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.

rrusczyk 2011-08-22 19:54:53
So, in how many ways can we seat them so that they are apart?

ChipDale 2011-08-22 19:55:45
5040-1440=3600

cong989 2011-08-22 19:55:45
7!-6!2! = 3600ways

rbhale12 2011-08-22 19:55:45
7!-2*6!=5040-1440=3600

TMNF18 2011-08-22 19:55:45
7!-(6!*2) = 3600 ways

jasonzhang 2011-08-22 19:55:45
5040 - 1440 = 3600

maoangbang 2011-08-22 19:55:45
5040-1440

dragoncurve 2011-08-22 19:55:45
7!-1440

mathguy225 2011-08-22 19:55:45
7!-2x6!=5x6!

aqua31 2011-08-22 19:55:45
3600

rjoshmath 2011-08-22 19:55:45
7!-2(6!)=5(6!)

AkshajKadaveru 2011-08-22 19:55:45

Buckeyefan831 2011-08-22 19:55:45
3600

Nobodyknows 2011-08-22 19:55:45
3600

omega3 2011-08-22 19:55:45
3600

rrusczyk 2011-08-22 19:55:56
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.

rrusczyk 2011-08-22 19:56:05
Computing this gives 7! - 2 x 6! = 7 x 6! - 2 x 6! = 5 x 6! = 5 x 720 = 3600.

hcube 2011-08-22 19:56:08
7!-2*6!=3600

rrusczyk 2011-08-22 19:56:17
This example brings up a couple more important tactics.

rrusczyk 2011-08-22 19:56:21
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'.

rrusczyk 2011-08-22 19:56:30
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.

rrusczyk 2011-08-22 19:56:46
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!

rrusczyk 2011-08-22 19:57:24
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.

rrusczyk 2011-08-22 19:57:38
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!)

rrusczyk 2011-08-22 19:58:10
That's it for the math; I will now talk a bit about the courses.

rrusczyk 2011-08-22 19:58:26
I will let you know when it's time to ask questions about the courses.

rrusczyk 2011-08-22 19:58:32
While the discussion tonight was similar to that in our classes, there are a few BIG differences between tonight and the typical class.

rrusczyk 2011-08-22 19:58:37
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.

rrusczyk 2011-08-22 19:59:04
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. We also often have an extra assistant in our usual classes.

rrusczyk 2011-08-22 19:59:22
All of our courses offer full transcripts for each class, so if you're going to miss some classes, you'll still have access to everything that happened in class. Moreover, you'll be able to use the course message board to ask any questions you have outside of class time.

rrusczyk 2011-08-22 19:59:32
We are offering two new courses this fall: Prealgebra 1 and Game Programming.

rrusczyk 2011-08-22 19:59:47
Here are all the courses we offer this fall. Each course meets for 90 minutes each week unless otherwise noted:

rrusczyk 2011-08-22 19:59:52
[u]Introductory level: Grades 6-10[/u]
Prealgebra 1: Wed, Sept 7 - Jan 11 (1 hour)
Prealgebra 1: Mon, Sept 19 - Jan 30 (1 hour)
Algebra 1: Fri, Aug 26 - Dec 16
Algebra 1: Mon, Oct 3 - Feb 13
Introduction to Counting & Probability: Tue, Oct 4 - Jan 10
Introduction to Counting & Probability: Fri, Oct 7 - Jan 13
Introduction to Number Theory: Wed, Sept 14 - Dec 7
Introduction to Number Theory: Mon, Oct 10 - Jan 23
Algebra 2: Fri, Oct 7 - Feb 3
Introduction to Geometry: Wed, Sept 28 - Mar 28
Introduction to Geometry: Thurs, Oct 6 - Apr 5
MATHCOUNTS/AMC 8 Basics: Tue, Sept 20 - Dec 13
MATHCOUNTS/AMC 8 Basics: Thurs, Oct 13 - Jan 19
Advanced MATHCOUNTS/AMC 8: Fri, Oct 21 - Jan 27
Advanced MATHCOUNTS/AMC 8: Thurs, Nov 10 - Feb 16

rrusczyk 2011-08-22 19:59:59
[u]Intermediate level: Grades 8-12[/u]
Algebra 3: Thurs, Sept 29 - Mar 29
Intermediate Counting & Probability: Wed, Oct 5 - Feb 22
Precalculus, Fri, Sept 30 - Mar 2
AMC 10 Problem Series: Wed, Sept 7 - Nov 30
AMC 10 Problem Series: Tue, Oct 18 - Jan 24 (late: 9 PM - 10:30 PM ET)
AMC 12 Problem Series: Mon, Sept 12 - Dec 5 (late: 9 PM - 10:30 PM ET)
AMC 12 Problem Series: Fri, Oct 14 - Jan 20
AIME Problem Series A: Wed, Nov 30 - Feb 29 (late: 9 PM - 10:30 PM ET)
AIME Problem Series B: Thurs, Sept 1 - Nov 17
AIME Problem Series B: Tues, Nov 29 - Feb 28

rrusczyk 2011-08-22 20:00:11
[u]Advanced[/u]
Calculus: Tue, Oct 4 - Apr 10 (2 hours)
Group Theory: Tue, Jan 10 - May 8 (2 hours)
WOOT: September - April (2 hours, roughly every other week)

rrusczyk 2011-08-22 20:00:18
[u]Computer Science/Programming[/u]
Introduction to Programming: Mon, Sept 12 - Dec 12
Introduction to Programming: Thurs, Sept 15 - Dec 15
Game Programming: Tue, Sept 20 - Dec 13
Game Programming: Wed, Sept 21 - Dec 14

rjoshmath 2011-08-22 20:00:21
that has to be more than 25 fingers

rrusczyk 2011-08-22 20:00:28
I have two keyboards, too.

xiaofandeng 2011-08-22 20:00:33
so many classes!

rrusczyk 2011-08-22 20:00:40
No kidding. That list is ridiculous.

rrusczyk 2011-08-22 20:00:44
Let's try this:

rrusczyk 2011-08-22 20:00:47
http://www.artofproblemsolving.com/School/classlist.php

rrusczyk 2011-08-22 20:00:59
More details about each course can be found by clicking the appropriate course name at the link above.

rrusczyk 2011-08-22 20:01:13
Unless otherwise noted in the list above, classes for each course are once a week, 7:30 PM - 9 PM ET (4:30 PM - 6 PM PT).

rrusczyk 2011-08-22 20:01:29
I'm going to stick that link at the top; you can get a lot of Info there!

rrusczyk 2011-08-22 20:01:33
We offer two types of classes: subject classes and contest prep "problem series" courses. Each course has its own course homepage for enrolled students. On the course homepage, there is a variety of information about the course. Each course also has its own message board on which students can ask questions outside class time. Students even have the ability to ask questions anonymously by using an "Ask a Question" feature on the course homepage.

johnwolfgang 2011-08-22 20:01:39
What constitutes "air time"?

rrusczyk 2011-08-22 20:01:53
That does :) (By "air time", I mean getting posted in the room.)

rrusczyk 2011-08-22 20:02:02
After class each week, we make a class transcript available on the course homepage. So, if you miss a class, you still have access to everything that happened in class. The class transcript also frees you from having to take notes during class. Instead of copying everything down during class, you can focus on the math and think about the problems. The transcript will be there later when you want to review.

rrusczyk 2011-08-22 20:02:15
We also place problems on the course message board for the students to discuss each week. The following week, we post solutions to the problems.

rrusczyk 2011-08-22 20:02:24
There is an accompanying textbook for most of the subject classes (not the contest prep problem series or programming courses, nor for WOOT or Group Theory). For each of these courses, there are corresponding readings in the textbook each week. As you might expect, students who work with the textbook in addition to attending class get a lot more out of the courses! The appropriate chapters for each week are listed in the Course Information document that students can access on the course homepage upon enrolling.

rrusczyk 2011-08-22 20:02:47
The other main difference between the subject classes and the problem series courses is that each subject course has longer problem sets called Challenge Sets roughly every three weeks. These are the primary homework assignments for the subject classes. Students should write up full solutions and submit them to us for evaluation (there are thorough instructions for how to do so on each Challenge Set). These solutions will be evaluated by AoPS graders, and you will receive detailed feedback.

rrusczyk 2011-08-22 20:03:08
There are diagnostic tests available for each of the subject classes. You can find these on the Class Schedule page here: http://www.artofproblemsolving.com/School/classlist.php

rrusczyk 2011-08-22 20:03:47
To get the most out of the courses, students should spend 5-7 hours/week on the subject courses and 3-4 hours/week on the problem series courses (including class time).

rrusczyk 2011-08-22 20:03:58
We will get hundreds of questions in the next 2 hours. We will answer as many as we can. Here are the rules for how we will try process the questions as we receive them.

rrusczyk 2011-08-22 20:04:24
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.

rrusczyk 2011-08-22 20:04:44
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.

rrusczyk 2011-08-22 20:04:53
I'll take questions about the courses now. Here's the schedule again:

rrusczyk 2011-08-22 20:04:56
http://www.artofproblemsolving.com/School/classlist.php

rrusczyk 2011-08-22 20:05:02
Please note that I'll probably have a *lot* of questions tonight, so it might take me a little while to get to yours. But I will try to get to all of them!

kmom 2011-08-22 20:05:48
In an earlier math jam, there was mention that AoPS is going through an accreditation process. Is there any news on how that is progressing or on how long that will take?

rrusczyk 2011-08-22 20:05:49
I am hoping it will be in place for Fall, 2012, but it is a long, thorough process that might take longer.

aqua31 2011-08-22 20:06:32
DO u have recommended calculators for different courses?

srogers 2011-08-22 20:06:33
We don't use calculators.

mathmom29 2011-08-22 20:06:36
Do schools typically give credit for your courses?

rrusczyk 2011-08-22 20:06:37
You have to take that up with your school. Some do, but you have to negotiate that with your school.

mathmom29 2011-08-22 20:07:40
How are students graded? Is there a "participation" grade?

rcordwell 2011-08-22 20:07:58
No grades

Xcellence 2011-08-22 20:08:49
can one receive a grade for an aops course?

rrusczyk 2011-08-22 20:08:54
Actually, you can receive a grade if you need one for the subject courses. The main input for a grade is the student work on the Challenge Sets. We also look at work on the message board and on Alcumus (for courses that include Alcumus).

aqua31 2011-08-22 20:09:04
Who is rcordwell?

rcordwell 2011-08-22 20:09:21
I just started work at AoPS

rcordwell 2011-08-22 20:09:38
I'm going to be teaching one of the Algebra I courses, starting next week

Mrdavid445 2011-08-22 20:09:45
He's a ninja

Aequilipse 2011-08-22 20:09:46
I have been thru one mathcounts season and am currently taking Geometry. Would the basics or advanced MATHCOUNTS class be more suitable for me?

rrusczyk 2011-08-22 20:09:46
That's true -- he's an International Math Olympiad gold medalist! And former AoPS student!

srogers 2011-08-22 20:09:47
If you have already had some experience with MathCounts problems, we would recommend the Advanced MathCounts course

mathmom29 2011-08-22 20:10:25
Is there a limit on the number of times a student misses class?

rrusczyk 2011-08-22 20:10:26
This is the question rcordwell wanted to answer no to.

abbypad 2011-08-22 20:10:45
Can we purchase the textbooks from your site?

srogers 2011-08-22 20:10:46
Yes. When you enroll in a course, you will have the option to purchase the textbooks.

srogers 2011-08-22 20:10:59
That is, if you don't already have them.

knittingfrenzy18 2011-08-22 20:11:23
Do homeschoolers get progress reports for report cards?

rrusczyk 2011-08-22 20:11:24
Homeschoolers can request a grade at the end of the course if they need one. All students receive detailed feedback on their challenge sets.

Xcellence 2011-08-22 20:11:34
when grading, do you take into account that aops courses are harder than normal courses?

rrusczyk 2011-08-22 20:11:35
Absolutely.

MutedCurmudgeon 2011-08-22 20:11:43
does it matter what edition?

rrusczyk 2011-08-22 20:11:44
No.

cong989 2011-08-22 20:12:26
is it suggested to take more than one course at a time? (especially with the subject courses)

srogers 2011-08-22 20:12:27
Taking two subject classes (such as Intro Counting and Probability and Intro Number Theory) is a *lot* of work. Most students would choose to take one subject class and one contest prep class (such as MathCounts Basics)

mcqueen 2011-08-22 20:12:34
What is the right class for someone between Algebra 2 and PreCalc?

rrusczyk 2011-08-22 20:12:36
You can use our diagnostics to decide. You might want to try some discrete math, like our Intro or Intermediate Counting classes.

AkshajKadaveru 2011-08-22 20:13:11
at what level (contest wise) is alg 3.

srogers 2011-08-22 20:13:13
It covers AMC 10, 12, AIME, and even some USAJMO.

mooni 2011-08-22 20:13:17
Who is srodgers?

rrusczyk 2011-08-22 20:13:18
She's a curriculum developer here at AoPS for this: http://www.beastacademy.com.

mathmom29 2011-08-22 20:13:43
Is there an age limit (upper) for your classes, or can adults take them, too?

rrusczyk 2011-08-22 20:13:44
No limit. We have teachers and parents take our classes.

shengo8 2011-08-22 20:14:21
what are challenge sets?

srogers 2011-08-22 20:14:22
Challenge sets, assigned only in subject courses, are problem sets that contain more difficult material than the usual weekly homework. They are usually due about every 3 weeks or so.

Sinisalo 2011-08-22 20:14:27
I'm only in 9th grade, but I can consistently get 6-10 (11 Maximum) problems right on the AIME practice exams that I take. These are from years 2000 and up (I know the older ones are easier), should I take the WOOT class in preparation for USAJMO, or should I just take one of the AIME classes? :)

rrusczyk 2011-08-22 20:14:29
You are ready for WOOT. You should be training at a higher level than the AIME, and occasionally working on old AIME or Harvard-MIT Math Tournament problems for practice.

algebralien 2011-08-22 20:15:00
What do you teach in intro to geometry

rrusczyk 2011-08-22 20:15:02
http://www.artofproblemsolving.com/School/courseinfo.php?course_id=intro:geometry

knittingfrenzy18 2011-08-22 20:15:10
If beastacademy is a top secret project, then why do you share it with us? :P

rcordwell 2011-08-22 20:15:12
Because you're cool like that :)

Mrdavid445 2011-08-22 20:15:30
what is beast academy?

rrusczyk 2011-08-22 20:15:31
Check it out and see.

newbie101 2011-08-22 20:15:35
how do we get graded if we request for a grade?

srogers 2011-08-22 20:15:37
You can receive a grade if you need one for the subject courses. The main input for a grade is the student work on the Challenge Sets. We also look at work on the message board and on Alcumus (for courses that include Alcumus).

shengo8 2011-08-22 20:15:58
what's WOOT?

rcordwell 2011-08-22 20:16:00
Worldwide Online Olympiad Training. Basically training for the USAMO / IMO / your country's national olympiad

srogers 2011-08-22 20:16:10
Find out more about it here: http://www.artofproblemsolving.com/School/woot.php

justin2000 2011-08-22 20:16:22
Is introduction to number theory a subject course or a problem course?

srogers 2011-08-22 20:16:24
A subject course.

basurinku 2011-08-22 20:16:57
what do you teach in computer programming? Do you teach languages?

rrusczyk 2011-08-22 20:16:58
The classes are in the Python programming language. The Introduction class is an introduction to basic programming concepts and how to program. The Game Programming course is a more advanced course in which you learn about software design while programming in various environments used for games.

dbug660 2011-08-22 20:17:27
How do we send in our homework

srogers 2011-08-22 20:17:29
Weekly problems are posted on the message board. For the subject courses that include challenge sets, they may be uploaded directly to the website, emailed, faxed, or mailed in to us.

jjs.7 2011-08-22 20:17:59
what percentage of school precalc does algebra 3 cover?

rrusczyk 2011-08-22 20:17:59
Most of the algebra that is not trig or vectors/matrices.

ca01298 2011-08-22 20:18:41
Do contest prep classes have homework?

rrusczyk 2011-08-22 20:18:42
Only message board problems; there is no evaluated homework in the contest prep classes.

dbug660 2011-08-22 20:19:26
How involved should parents be in helping their child with the coursework?

rrusczyk 2011-08-22 20:19:27
You can be as involved as you feel you need to/would like to be. We ask that the students reflect this on their Challenge Sets when they turned them in.

rjoshmath 2011-08-22 20:19:52
Is there any linear algebra class

rrusczyk 2011-08-22 20:19:52
We teach linear algebra in two and three dimensions in great depth in our Precalculus class.

newbie101 2011-08-22 20:20:00
what is the difference between a subject course and a problem course?

srogers 2011-08-22 20:20:04
The classes are distinguished here: http://www.artofproblemsolving.com/School/classlist.php . Subject courses cover questions related specificallyand more in-depth to that subject. Problem-solving courses are directed more towards the specific types of problems you will see on the MathCounts/AMC10/AIME.

basurinku 2011-08-22 20:20:26
Do you have to know any basics to be a part of "Introduction to Programming"?

rrusczyk 2011-08-22 20:20:27
No; it is intended for students who have no or little expreience.

AkshajKadaveru 2011-08-22 20:20:43
im going to 6th grade and have taken all of the introductory classes except for intro geo. when i take prep tests for state mathcounts i can usually get all but some geos within the time. will intro geo help me with those?

rrusczyk 2011-08-22 20:20:44
Definitely.

Kingfisher 2011-08-22 20:21:30
If you make an error in estimating your mathematical abilities, can you move down to Prealgebra from Algebra 1?

rrusczyk 2011-08-22 20:21:32
You can drop any course before the third class starts and get a full refund. So, you can reassess where you are after a couple classes.

shengo8 2011-08-22 20:21:32
what's AIME?

rcordwell 2011-08-22 20:21:41
AIME means American Invitational Math Olympiad. Do well enough on the AMC 10 or AMC 12 and you get to take it, and do well enough on the AIME to take the USA Math Olympiad.

cong989 2011-08-22 20:21:56
which classes have alcumus?

rrusczyk 2011-08-22 20:21:57
This fall, Algebra 1, Introduction to Counting & Probability, and Prealgebra 1 will have Alcumus.

shengo8 2011-08-22 20:22:06
what kind of questions are on the challenge sets?

rrusczyk 2011-08-22 20:22:07
Hard ones :)

mathmom29 2011-08-22 20:22:49
In the classroom, would students see other students' answers like we did tonight on this MathJam?

rrusczyk 2011-08-22 20:22:50
Yes.

basurinku 2011-08-22 20:23:06
How many students are in one typical class?

rrusczyk 2011-08-22 20:23:07
30-70 depending on the course (there's a lot of variance).

justin2000 2011-08-22 20:23:20
Is there a special alcumus for those classes?

rrusczyk 2011-08-22 20:23:20
No, it is the same as everyone else has.

shengo8 2011-08-22 20:24:19
how do you have alcumus in a class?

rcordwell 2011-08-22 20:24:22
We make sure that Alcumus has plenty of good, level-appropriate problems for those classes. So if you're taking the class you can log on to Alcumus and you'll be able to solve problems that correlate with what you've been learning

itennis 2011-08-22 20:24:28
so then should one work all the end-of-chapter probls before doing the challenge sets?

rrusczyk 2011-08-22 20:24:29
You don't have to do every single problem. Just do enough until you are very comfortable with the material. (Though you should work through the problems in the main text -- that is, the ones that are discussed in the body of the text.) One thing you might do is try the Challenge Sets, then when you're stuck, do some problems in the book for more practice.

kim2013 2011-08-22 20:24:50
What is the meaning behind the name Alcumus?

rrusczyk 2011-08-22 20:24:51
We're not really sure.

aqua31 2011-08-22 20:24:55
DO you have to pay for alcumus?

rcordwell 2011-08-22 20:24:57
No

Talu 2011-08-22 20:25:35
What do you accomplish in intro to programming?

rrusczyk 2011-08-22 20:25:36
You learn the fundamentals of programming, and many details of the Python programming language. The course is for students in grades 6-12 who are just getting started with programming.

MutedCurmudgeon 2011-08-22 20:25:50
how long is each class?

srogers 2011-08-22 20:25:52
Most classes are an hour and a half long. PreAlgebra is 1 hour, and there are a few that are two hours. You'll have to check the class schedule for the course(s) you are interested in to find out exactly.

hcube 2011-08-22 20:25:56
what is alcumus? please forgive my ignorance.

rrusczyk 2011-08-22 20:25:57
It is our adaptive online learning system; you can learn more about it by clicking Alcumus atop our site.

GelidIce 2011-08-22 20:26:33
Can a class be cut due to a lack of students signing up for it?

rrusczyk 2011-08-22 20:26:35
Yes, but we have only done that once in 8 years, and that was a class scheduled in the morning. (We may try that again in a year or two.)

abbypad 2011-08-22 20:27:14
What's the youngest grade you would recommend the subject classes for?

rrusczyk 2011-08-22 20:27:15
We have some 4th graders, but they have to be very mature 4th graders, and good about working independently, to succeed in our classes.

knittingfrenzy18 2011-08-22 20:27:57
What classes are offered in the summer? (for planning purposes)

rrusczyk 2011-08-22 20:27:58
All the Intro classes, all the programming classes, all the contest prep classes, along with most of the Intermediate classes.

rjoshmath 2011-08-22 20:28:45
Is there any book that is more advanced than Calculus?

srogers 2011-08-22 20:28:47
Some people consider the Intermediate Counting and Probability book to be more advanced than the Calculus book.

Krrish 2011-08-22 20:28:51
Is the normal programming class a prerequisite for the game programming class?

rrusczyk 2011-08-22 20:28:52
No. There is a diagnostic test on the Game Programming page that will help you decide if you know enough Python already to go straight to the Game Programming class.

kev2010 2011-08-22 20:29:21
What are the times in Spring for C&P/Number theory?

rrusczyk 2011-08-22 20:29:22
We haven't decided those yet. We will choose those in September some time.

AkshajKadaveru 2011-08-22 20:29:44
after intro geo, you recommend alg 3 or intro nt or intro c&p?

rrusczyk 2011-08-22 20:29:45
Use diagnostics to see if you need Intro NT or CP. If you need either of those, start there.

dbug660 2011-08-22 20:30:33
what if the class starts going to fast and I can't keep up?:(

Talu 2011-08-22 20:30:34
If I am in the 5th grade, is the intro to programming course good for me? i am very interested in this class.

srogers 2011-08-22 20:30:35
You're always welcome to ask questions in the classroom so that the instructor or assistant can help you out some more. If you still find it is overwhelming within the first two classes, you may drop the course for a full refund.

rrusczyk 2011-08-22 20:30:35
It may be, particularly if you have had some prealgebra-level math instruction. We have had 5th and 6th graders in that course before. It will be very challenging, and make sure you are good about asking questions if you take it.

MutedCurmudgeon 2011-08-22 20:31:09
when does class end?

knittingfrenzy18 2011-08-22 20:31:09
When does this jam end?

rrusczyk 2011-08-22 20:31:10
When we run out of questions. You can leave whenever you like.

krmathcounts 2011-08-22 20:31:25
I have very little experience in programming, I've worked with LOGO for a couple of years, and I know very minimal JavaScript and html. Would there be a programming course you would recommend for me?

rrusczyk 2011-08-22 20:31:26
The Intro Programming course would probably be a good fit.

tennispro30 2011-08-22 20:32:06
how do we know if we have to purchase textbooks?

rrusczyk 2011-08-22 20:32:07
It will say so on the Schedule page, and prompt you as you check out.

qfoam 2011-08-22 20:32:55
Is the AIME Series comparable to the Intermediate series?

rrusczyk 2011-08-22 20:32:56
It is comparable in difficulty, yes.

tennispro30 2011-08-22 20:33:05
Where can we purchase textbooks?

rrusczyk 2011-08-22 20:33:06
On our website.

kim2013 2011-08-22 20:33:30
What are some competitions to boost experience besides the distinguished national level competitions?

rrusczyk 2011-08-22 20:33:30
Harvard - MIT, Purple Comet. Ask around on the message board -- there are tons of others!

knittingfrenzy18 2011-08-22 20:33:48
If I leave now, will what I missed be in the transcript?

rrusczyk 2011-08-22 20:33:49
Yes

justin2000 2011-08-22 20:34:21
In the real classes, is there any sound?

srogers 2011-08-22 20:34:23
No, the format of our classes is all text-based, just like this math jam.

mathmom29 2011-08-22 20:35:30
Does the students' ability to see others' answers pose a problem for some, e.g. the ones who are still trying to figure out the answer?

dbug660 2011-08-22 20:35:30
What if I don't type my answers in fast enough, and the problem passes and its to late to enter it?:-c

rrusczyk 2011-08-22 20:35:31
We try to give students plenty of time to answer problems. The answers you saw in the room were first sent to me. I sat on them for a while, to give others the opportunity to answer also. This is one reason this classroom can be better than a regular classroom -- here, lots of students get to answer, whereas in a regular classroom, one student gets to answer while everyone else stares out the window.

abbypad 2011-08-22 20:36:01
Where can I find the diagnostic tests you mentioned, for placement purposes?

srogers 2011-08-22 20:36:02
The diagnostic tests are listed under the description of each subject class on this page: http://www.artofproblemsolving.com/School/classlist.php. The two tests are "Are You Ready?" and "Do You Need This?"

rrusczyk 2011-08-22 20:36:05
Also, I almost certainly won't get to every question tonight, but I'll try. If I don't get to your question, please email it to me at classes@artofproblemsolving.com

itennis 2011-08-22 20:38:10
Pre-Alg has a 1 & 2 - so 2 sessions. Alg 1 seems to be 1 class session - Is the equivalent of ALL of a years worth of Algebra I covered in just 1 session?

Draco 2011-08-22 20:38:11
What is the difference between Algebra 2 and 3. Is knowledge of Algebra 1 enough to start 3?

rrusczyk 2011-08-22 20:38:12
"Algebra 1" and "Algebra 2" mean different things from school to school, and our algebra classes have a lot of material that they usually don't even teach in school. We name our courses mainly to give some indication which class a student should take. If you haven't ever taken an Algebra class, then you probably want to start with Algebra 1. If you've finished Algebra 1 here or in school, then you're probably ready for our Algebra 2 course, and so on.

basurinku 2011-08-22 20:38:17
when is the next math jam?

rcordwell 2011-08-22 20:38:26
http://www.artofproblemsolving.com/School/mathjams.php

maplehill001 2011-08-22 20:38:49
mathcounts minis is very interesting, willyou do more often in the future?

rrusczyk 2011-08-22 20:38:50
Many

DragonNova 2011-08-22 20:39:01
What class is recommended for a student who can get 4-8 on AIME

srogers 2011-08-22 20:39:03
We'd recommend our Intermediate-level courses and the AIME Problem Series classes.

rrusczyk 2011-08-22 20:39:12
(MATHCOUNTS Minis are videos I do for MATHCOUNTS; we will also do many more for our site and classes)

MATHematician5568 2011-08-22 20:39:32
What course(s) would you recommend for a student who took algebra 1 2010-2011 and will be taking geometry 2011-2012?

rrusczyk 2011-08-22 20:39:39
Introduction to Counting & Probability and Introduction to Number Theory.

diamond-star89 2011-08-22 20:39:59
what classes do you recmmend if you just started for the amc 10 this year, and you are planning to take it soon. especially if you have limtied time to do so.

rrusczyk 2011-08-22 20:40:00
AMC 10 Problem Series, Introduction to Counting & Probability.

AkshajKadaveru 2011-08-22 20:40:47
To succeed at MATHCOUNTS Nats (if I make it :-D ), what classes do you need to have taken? (i have taken both basic and advanced MC/AMC8)

rrusczyk 2011-08-22 20:40:48
The Intro courses cover pretty much all you'll need to know for Nats.

dragoncurve 2011-08-22 20:41:27
How experienced of a programmer will you be after completion of the intro and game programming classes?

rrusczyk 2011-08-22 20:41:28
This is very difficult to answer. You probably won't be ready to start working at Google, but you'll have a huge head start in become an expert programmer.

dragoncurve 2011-08-22 20:42:02
I have finished most of AoPS volume 1 and plan to finish it at the end of this month. In school I have done algebra 1, 2, geometry, and will be taking precalculus this year. I can consistently score between a 100-120 on AMC 10s, what would be the best courses for me to take?

rrusczyk 2011-08-22 20:42:03
Look at the diagnostics for Intro Counting, Algebra 3, Intermediate Counting, and Precalculus.

kev2010 2011-08-22 20:42:11
How many problems is in Alcumus?

rrusczyk 2011-08-22 20:42:12
Thousands.

rrusczyk 2011-08-22 20:42:49
Are there more questions? (If you asked one earlier and I haven't gotten to it, then ask it again now.)

shengo8 2011-08-22 20:43:34
who makes the problems in alcumus and the solutions?

srogers 2011-08-22 20:43:36
We write some ourselves, and use others from math contests, such as MathCounts.

kim2013 2011-08-22 20:43:49
will AMC 10 adjust to those who haven't competed on a national level?

rcordwell 2011-08-22 20:43:51
Yes, in the sense that the class is designed for students preparing for the AMC10. You're not expect to have competed on a national level to take the AMC10.

Sinisalo 2011-08-22 20:44:06
Why do you guys use Python? Isn't it relatively old?

rrusczyk 2011-08-22 20:44:07
It is a very good starter language. It doesn't require a compiler, and it's very easy to start programming right away with. The age of a language isn't really relevant to its value -- Lisp is ancient, and plenty of places still use that for development.

AkshajKadaveru 2011-08-22 20:44:28
what is this AoPS Volume 1? what level is it compared to the classes?

rrusczyk 2011-08-22 20:44:29
Intro level -- covers material for MATHCOUNTS and much of AMC 10/12.

Mrdavid445 2011-08-22 20:44:47
What are consquences for not buying the books for a class?

rrusczyk 2011-08-22 20:44:48
The books that go with the subject classes are required for the corresponding classes.

maoangbang 2011-08-22 20:45:30
What book should you take if you can't get to nationals Math Counts?

rrusczyk 2011-08-22 20:45:31
Work through our Introduction series of books/courses.

diamond-star89 2011-08-22 20:46:14
is the amc 10 class recommended for the beginner?

rrusczyk 2011-08-22 20:46:15
It depends on the beginner's math background. If you're getting 65 or 70 on practice AMC 10s, then you should start with the Intro courses. If you're getting 105 or so, you'll be fine in the AMC 10 Problem Series.

hidude454 2011-08-22 20:46:23
Are the class/homework problems in the textbook?

rrusczyk 2011-08-22 20:46:24
Some are, many are not.

MATHematician5568 2011-08-22 20:46:27
Do classes become more proof-oriented as they become more difficult (i.e. algebra 1 to algebra 2)?

rrusczyk 2011-08-22 20:46:28
Yes

mcqueen 2011-08-22 20:46:43
Following Akshaj's question what couse reponds to Volume 2?

rrusczyk 2011-08-22 20:46:44
We don't have a course that goes directly with Volume 2.

Draco 2011-08-22 20:47:03
How does Volume 1 compare to the subject classes? Does it cover Intro to Geo/Algebra/Probability/NT?

rrusczyk 2011-08-22 20:47:04
Similar subject coverage, but not as comprehensive as the Intro books, and not as in-depth.

dragoncurve 2011-08-22 20:47:12
If I score between a 100 and 120 on AMC 10s, how much do you think the problem series class will raise my score by?

rrusczyk 2011-08-22 20:47:12
Impossible to say!

itennis 2011-08-22 20:47:35
Is there a final exam or are the diagnostic questions enough to ensure a knowledge base?

srogers 2011-08-22 20:47:37
There are no tests or exams in the courses. There are weekly message board problems. Some courses also include work on Alcumus, and subject classes involve challenge sets.

diamond-star89 2011-08-22 20:47:39
what do you do in the amc 10 class?

rrusczyk 2011-08-22 20:47:39
We solve past AMC 10 problems and talk about important strategies you'll need for future AMC-10 problems.

diamond-star89 2011-08-22 20:48:51
will studying for the amc help with studying for the SAT's?

rrusczyk 2011-08-22 20:48:52
Yes. Students who work through our Intro series thoroughly in preparation for the AMC 10 tend to find the SAT very easy!

dragoncurve 2011-08-22 20:49:03
For the amc 10 problem series class, are the problems only ones from past exams, or are many of them similar ones from other sources?

rrusczyk 2011-08-22 20:49:04
They are nearly all from past tests.

MATHematician5568 2011-08-22 20:49:31
At what level of class do you introduce proof?

rrusczyk 2011-08-22 20:49:32
Pretty much at the beginning. We will even have some proof-like discussions in Prealgebra.

AMC12b150 2011-08-22 20:49:40
Are the message board problems comparable in difficulty to the Challenge Set problems?

rrusczyk 2011-08-22 20:49:42
Yes.

Sinisalo 2011-08-22 20:50:28
do Intermediate Courses review over introductory material, and then begin the real Intermediate difficulty?

rrusczyk 2011-08-22 20:50:29
Yes, there is a little review at the beginning of Intermediate classes for the corresponding Intro material.

dragoncurve 2011-08-22 20:50:55
So, if I have already worked through many of the past amc 10 exams, will the problem series be of any value to me?

rrusczyk 2011-08-22 20:50:56
Hard to say -- you may well be better off with subject classes in the areas that give you the most difficulty.

itennis 2011-08-22 20:50:58
Does Alcumus prep for math competitions sufficiently? How do you take practice exams for the AMCs that you're talking about?

srogers 2011-08-22 20:51:01
Alcumus does have problems from various math competitions, but for more in-depth practice and preparation, you'll want to look into the problem solving series for the particular contest you are looking to compete in. The practice exams are available in the contest section of the website.

kev2010 2011-08-22 20:51:06
What are the other times for math jam?

rrusczyk 2011-08-22 20:51:07
http://www.artofproblemsolving.com/School/mathjams.php

diamond-star89 2011-08-22 20:51:28
which intro books are most essential for preparing for the amc 10?

rrusczyk 2011-08-22 20:51:29
All of them. They all include AMC 10 problems and subjects that are important for the AMC 10.

Draco 2011-08-22 20:54:14
Which class is for Intermediate Algebra?

rrusczyk 2011-08-22 20:54:17
Algebra 3

MutedCurmudgeon 2011-08-22 20:54:27
can we leave now?

rrusczyk 2011-08-22 20:54:28
You can leave whenever you like.

mcsnuffle 2011-08-22 20:54:58
what is alcumus

rrusczyk 2011-08-22 20:54:59
It's our online learning system. You can learn more about it by clicking Alcumus on the top of our site.

MATHematician5568 2011-08-22 20:55:23
Do you offer any classes that mainly teach how to write proofs (like a proof writing course)?

rrusczyk 2011-08-22 20:55:24
Not yet, but we might in the next year or so. It has been on the todo list for a couple years.

hutyputy66 2011-08-22 20:55:44
Are you planning to introduce any other programming classes?

rrusczyk 2011-08-22 20:55:45
Yes, but we haven't decided which ones. There will likely be at least one for Java programming.

Weegee13 2011-08-22 20:56:10
What do you do if we find bugs in alcumus?

rcordwell 2011-08-22 20:56:12
Report them! There's a bug report feature.

Draco 2011-08-22 20:56:25
Are your classes yummy?

rrusczyk 2011-08-22 20:56:26
Delicious.

itennis 2011-08-22 20:56:48
how does one knowwhether a math jam is of their level, e.g., for beginners?

rrusczyk 2011-08-22 20:56:49
They are rated on a 0-10 scale on the schedule:

rrusczyk 2011-08-22 20:56:50
http://www.artofproblemsolving.com/School/mathjams.php

Eterna 2011-08-22 20:56:57
So for Algebra 1 & 2 it uses the same textbook?

rrusczyk 2011-08-22 20:56:58
Yes.

Weegee13 2011-08-22 20:57:33
I'm planning to take class on AMC 10, what do we learn in there?

rrusczyk 2011-08-22 20:57:35
You do a lot of problems from old AMC 10 tests, and learn strategies that are helpful for the AMC 10.

rrusczyk 2011-08-22 20:57:58
Are there any more questions?

MATHematician5568 2011-08-22 20:58:56
Do classes offer reinforcement of topics learned earlier in the course?

rrusczyk 2011-08-22 20:58:57
To the extent that many subjects in math are cumulative, yes. We don't do focused review over and over again in our courses, though.

jli10 2011-08-22 20:59:04
will the aime classes have the same material as last year's classes?

rrusczyk 2011-08-22 20:59:05
Yes.

negativebplusorminus 2011-08-22 20:59:39
If I have only taken Algebra 3, should I take AIME or should I take more intermediate series?

rrusczyk 2011-08-22 20:59:40
Tough to say, but I would wager you'll learn more in Interm Counting or Precalculus -- they're very thorough courses.

tc1729 2011-08-22 21:00:00
What class would be similar level as AoPS volume 2?

rrusczyk 2011-08-22 21:00:00
The Intermediate classes and the AMC 12/AIME classes.

BeaconWatch24 2011-08-22 21:01:19
If you have already taken a class previously, is it logical to take it again sometime later to reinforce the material?

rrusczyk 2011-08-22 21:01:20
Sure, some students do that. rcordwell took our Olympiad Geometry course twice (6 or 7 years age). That seems to have worked -- he won the USA Math Olympiad and won a gold medal at the International Math Olympiad.

basurinku 2011-08-22 21:01:36
AMC 8 is for what grade typically?

rrusczyk 2011-08-22 21:01:37
Anyone in grade 8 or below.

mathmoth 2011-08-22 21:01:48
Do you plan to add an automated computer program checker for the programming course, for instance, ejudge?

rrusczyk 2011-08-22 21:01:49
Not in the near future, but maybe some day :)

hidude454 2011-08-22 21:02:12
can i take intro to counting and probability and intro to geometry at the same time? will it be hard to handle?

rrusczyk 2011-08-22 21:02:13
I would only do this if you have a lot of free time. Expect that to take 10-15 hours a week to get the most out of both courses.

basurinku 2011-08-22 21:03:51
What are some tips in doing well in these math compititions?

rrusczyk 2011-08-22 21:03:54
Lots of practice. Nothing beats practice. And reading AoPS books and taking AoPS classes of course!

tc1729 2011-08-22 21:04:50
Do any of the classes help for preperation in Mathematical Modeling e.g. the Comap MCM and HiMCM contests?

rrusczyk 2011-08-22 21:04:51
Not really, though the programming course might. I have been hoping those programs would become more prominent so that thre would be enough interested students for us to build a course on that material.

usernamehi 2011-08-22 21:05:05
How can you improve your AMC 10?

rrusczyk 2011-08-22 21:05:06
I love getting to re-use answers: "Lots of practice. Nothing beats practice. And reading AoPS books and taking AoPS classes of course!"

BeaconWatch24 2011-08-22 21:05:36
What would you think are the minimum requirements for taking the Olympiad Training course? (i.e. an average of xx points in Competition A, etc.?)

rrusczyk 2011-08-22 21:05:36
If you're consistently getting above 5 on the AIME, you should be ready to go.

MATHematician5568 2011-08-22 21:07:23
Do courses teach "shortcuts" or ways to be quicker in math contests?

rrusczyk 2011-08-22 21:07:23
The courses teach strategies for solving hard problems. We don't give a laundry list of gimmicks that work on very particular problems, but rather focus on general strategies that you can use for lots of types of strategies.

rrusczyk 2011-08-22 21:07:32
*types of problems, that is.

MATHematician5568 2011-08-22 21:08:37
Who invented artofproblemsolving.com?

rrusczyk 2011-08-22 21:08:38
The person whose username is at the top of the username list in the classroom.

tc1729 2011-08-22 21:09:00
Will mastery of all the topics in Volume 2 and beyond almost guarantee USAMO qualification?

rrusczyk 2011-08-22 21:09:00
Complete mastery of those topics will sure help. I don't think anything is a guarantee!

wehac 2011-08-22 21:09:19
what books should i get to help get my AMC 10 score up? What about AIME?

rrusczyk 2011-08-22 21:09:20
AMC 10 -> Intro level and Volume 1. AIME -> Intermediate level and Volume 2.

jmclaus 2011-08-22 21:09:56
Would it be reccomended to take an AMC class if we're taking woot? I can already score a 120 but I want to do a little bit better.

rrusczyk 2011-08-22 21:09:57
Actually, I'd train on the AIME to get my AMC 10/12 score up from 120. The easier AIME problems are a lot like the hard AMC 10/12 problems.

EuclidGenius 2011-08-22 21:10:59
What is the difference between Volume 1 and Volume 2 (other than the difficulty)

rrusczyk 2011-08-22 21:11:00
The difficulty is pretty much the only difference.

humzaiqbal 2011-08-22 21:11:19
When would Olympiad geo be brought back?

rrusczyk 2011-08-22 21:11:19
We haven't decided whether we will offer it this Spring or next Spring.

jasonzhang 2011-08-22 21:12:15
How would you prepare for the countdown round other than ftw since i memorized some ftw questions?

rrusczyk 2011-08-22 21:12:16
If you have mastered all the FTW questions, I think it's time for you to move on to harder math questions. Notice that the 2010 MATHCOUNTS National Champ became a 2011 USAMO winner. I'm guessing he spent much of 2009-2010 doing much harder math than Countdown Round problems.

wehac 2011-08-22 21:12:56
What grade should you start training for the USAMO?

rrusczyk 2011-08-22 21:12:57
When you're ready to handle the math. A precious few are ready as early as 5th or 6th grade, while most are never ready for it.

rrusczyk 2011-08-22 21:13:18
Most commonly, students who take the USAMO seriously start in 8th-10th grade, though there are many exceptions.

EuclidGenius 2011-08-22 21:13:46
what kind of math is on the USAMO?

rrusczyk 2011-08-22 21:13:46
Hard, interesting math, covering many non-calculus topics.

r31415 2011-08-22 21:14:11
Will you be publishing Intermediate Geometry to help for AIME-USAMO soon?

rrusczyk 2011-08-22 21:14:12
No; we have shelved that project for a while. We may get to it someday, but we have a lot of other projects ahead of it.

hrithikguy 2011-08-22 21:14:50
if someone is taking WOOT and calculus, would they be able to handle the workload of also taking intermediate counting and probability and precalculus?

rrusczyk 2011-08-22 21:14:51
If they did nothing else at all, then maybe. No eating. No drinking. No sleeping. (Seriously, that would be a pretty heinous workload.)

AruKasera 2011-08-22 21:15:06
Will going to nationals boost my chance to be accepted to an IVY league? Probably not...

rrusczyk 2011-08-22 21:15:07
I doubt the Ivies care about middle school...

wehac 2011-08-22 21:15:15
When is geometry coming to alcumus?

rrusczyk 2011-08-22 21:15:18
Maybe next summer.

EuclidGenius 2011-08-22 21:15:26
What is a good class to take to prepare for high-school calculus?

rrusczyk 2011-08-22 21:15:26
Algebra 3/Precalculus.

EuclidGenius 2011-08-22 21:16:42
Is the AoPS calculus harder than high school calculus? In what ways?

rrusczyk 2011-08-22 21:16:43
We have a much greater focus on rigor, on understanding why the tools work they do, and less focus on routine calculation.

EuclidGenius 2011-08-22 21:17:19
What is the next project/book/class you plan to bring to AoPS?

rrusczyk 2011-08-22 21:17:20
Well, there's this: http://www.beastacademy.com.

rrusczyk 2011-08-22 21:17:33
We'll also be pounding out a ton of videos starting in a few weeks :)

rrusczyk 2011-08-22 21:17:42
If I can figure out how my camera works....

rrusczyk 2011-08-22 21:18:03
Looks like I've run out of questions to answer!

humzaiqbal 2011-08-22 21:18:46
What areas of math would you make videos for?

rrusczyk 2011-08-22 21:18:47
Various areas. I'm starting with the Prealgebra class, but hope to find time to jump around a bit.

EuclidGenius 2011-08-22 21:18:49
That looks so cool for younger kids!!! Im sure theyll love it :) I wish I had that when I was in elementary school.

rrusczyk 2011-08-22 21:18:57
Us too, that's why we're making it.

rrusczyk 2011-08-22 21:19:35
If you have any questions later, you can email me at classes@artofproblemsolving.com. If you need specific course recommendations, please include the student's math background and I will make recommendations.

rrusczyk 2011-08-22 21:19:45
Thank you for attending the Math Jam!

AoPS Fall Classes

Facilitator: Richard Rusczyk