| Transcript
for the Math
Jam "AoPS Classes Math Jam"
on Oct 15. |
| Math Jam hosted by rrusczyk
(Richard Rusczyk ). |
rrusczyk19:30:33
Hello, and welcome to an Art of Problem Solving Math Jam. Today we'll be discussing the MATHCOUNTS/AMC 8 Basics, Advanced MATHCOUNTS/AMC 8, Introduction to Number Theory, AMC 10, and AMC 12 Problem Series. (These are five different courses.)
rrusczyk19:30:45
My name is Richard Rusczyk. I founded Art of Problem Solving and have written several Art of Problem Solving textbooks.
rrusczyk19:30:53
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.
rrusczyk19:31:10
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. This also means that only well-written comments will be dropped into the classroom, so please take time writing responses that are complete and easy to read. Also, only moderators can enter into private chats with other people in the classroom.
rrusczyk19:31:33
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.
rrusczyk19:31:41
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.
rrusczyk19:32:00
In this Math Jam, we will start off by doing a few sample problems. Then I will discuss the courses and take questions about the courses. 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.
rrusczyk19:32:42
The problems we will discuss tonight are particularly relevant to the MATHCOUNTS and Introduction to Number Theory classes. Let's get started with them!
rrusczyk19:32:53
rrusczyk19:33:15
How should we start?
algebra133719:33:40
convert it into 2s and 5s because they multiply to become 10
dmosn19:33:40
2x5=10 making an extra digit
rrusczyk19:33:51
Why do we like powers of 10?
mathmansid19:34:05
they are easy to deal with
iamnew19:34:05
there easy to deal with
MathTwo19:34:12
they have zeroes at the end
algebra133719:34:12
because they are easy to use
aca19:34:12
they are easy to deal with
rrusczyk19:34:14
It's easy to count the digits of powers of 10.
rrusczyk19:34:23
So, how do we convert to powers of 10 here?
iamnew19:34:48
the 4^20 into 2s
jumblies19:34:49
change the fours into twos
mathmansid19:34:49
4^20=2^40
rrusczyk19:35:01
We convert the 4's to 2's.
rrusczyk19:35:03
Then what?
PowerOfPi19:35:23
combine powers of 2 and 5
dmosn19:35:23
2^40*5^36=10^36*2^4
iamnew19:35:23
2^40 times 5^36 equals 10^36 times 2^4
PowerOfPi19:35:23
combine 5s and 2s
mathmansid19:35:23
Connect them with the fives
lindy19:35:23
4^20 x 5^36 = 2^40 * 5^36 = 10^36 * 2^4
rrusczyk19:35:42
Great; the 2's combine with 5's to give 10's.
rrusczyk19:35:59
So, how many digits are there?
iamnew19:36:08
38
hi how are you doing toda19:36:08
38
MathTwo19:36:08
38
aggarwal19:36:08
38</span>
sreyesh19:36:08
38
lindy19:36:10
36+2 = 38
mathmansid19:36:17
38
rrusczyk19:36:19
rrusczyk19:36:43
Let's try another.
rrusczyk19:36:44
rrusczyk19:36:53
The exclamation point is a 'factorial'. 4! = 4 x 3 x 2 x 1, and factorials for all other positive integers are defined similarly - we multiply all the numbers from the given positive integer down to 1.
rrusczyk19:36:57
Do we have to multiply all that out to evaluate the given expression?
$LaTeX$.19:37:12
no
Iggy Iguana19:37:12
no
Aeq19:37:12
no.
MathTwo19:37:12
no
iamnew19:37:12
no
PowerOfPi19:37:12
no
pingala19:37:12
nope
rrusczyk19:37:18
What do we do instead?
mathmansid19:37:35
Factor the denominator
iamnew19:37:35
factor out the 5!
mathmansid19:37:35
no. just start by factoring the denominator
algebra133719:37:35
no, factor the 6! into 6*5!
lindy19:37:35
factor a 5! in the denominator
jumblies19:37:35
extract 5! from the numerator and denominator
rrusczyk19:37:53
We factor! What does the denominator become if we factor out 5!
algebra133719:38:27
8*5!
aggarwal19:38:27
5!(6+1+1)
mathmansid19:38:27
8*5!
sreyesh19:38:27
8(5!)
algebra133719:38:27
8* 5!
Iggy Iguana19:38:27
8 5!
rrusczyk19:38:30
rrusczyk19:38:37
So, what do we get for our answer?
lindy19:38:55
90
pingala19:38:55
90
aggarwal19:38:55
90
frtian19:38:55
90
algebra133719:38:55
6!/8 = 90
Iggy Iguana19:38:55
90
jumblies19:38:55
6!/8=90
MathTwo19:38:55
6!/8 = 90
rrusczyk19:38:59
rrusczyk19:39:15
Clever factoring is extremely useful in math problems, and often is helpful in MATHCOUNTS.
mathmansid19:39:28
which courses are these problems from?
rrusczyk19:39:34
The MATHCOUNTS classes.
rrusczyk19:39:36
The next problem is an example of a problem that would be on the harder end of the Basics class and the easier end of the Advanced MATHCOUNTS/AMC 8 class.
rrusczyk19:39:41
rrusczyk19:40:02
Yikes! It will take a long time to compute 99!
iamnew19:40:14
get rid of the factorials above 5
rrusczyk19:40:17
why?
algebra133719:40:43
well, 5! onwards has a last digit of 0, so we just use 1! to 4! and calculate that
math_galois19:40:43
> 5! the last digit is 0
dmosn19:40:43
all factorials above 5 have a last digit of 0
Iggy Iguana19:40:43
5! and above have 0's as the last digits'
algebra133719:40:43
they have a units digit of 0
MathTwo19:40:43
well...all of the factorials from 5! to 99! have a 0 at the end
rrusczyk19:40:50
We don't get intimidated by the 99!. We only want the last digit. Most of these terms have last digit of 0.
rrusczyk19:40:56
Only the first 4 terms have a nonzero units digit.
rrusczyk19:41:17
From 5! on, all the factorials end in 0.
rrusczyk19:41:25
So, we only have to worry about the first 4 terms:
rrusczyk19:41:39
1 - 2 + 6 - 24
rrusczyk19:41:43
So, what is the answer?
MathTwo19:41:57
1-2+6-24=-19, but watch out
Aeq19:41:57
-19
sreyesh19:41:57
-19
mathwiz1234519:41:57
-19
rrusczyk19:42:01
Watch out for what?
GreatGray19:42:04
-19
arbala19:42:04
-19
rrusczyk19:42:19
Indeed, these terms add to -19. What are we looking for?
algebra133719:42:21
we want the last digit
rrusczyk19:42:26
So, is the answer 9?
mathwiz1234519:42:41
no
dmosn19:42:41
no, it's 1
rorys19:42:41
no, 1
rrusczyk19:42:43
1?
rrusczyk19:42:44
Why?
PowerOfPi19:43:08
But since we add 99!, it must be positive and the last digit is 1
lindy19:43:08
no, we need to add multiples of 10 to -19, and we end up with 1
frtian19:43:08
120-19
rorys19:43:08
because you must ad the later digits
GreatGray19:43:14
because it's negative
rrusczyk19:43:18
The answer isn't 9 because our sum is clearly positive. (We add a huge number, 99!, at the end.) All those terms with a zero units digit clearly have a positive sum, so our expression equals -19 + (something big that ends in zero). Thus we have a final digit of 1, not 9.
rrusczyk19:43:49
Now, before we go on, I should introduce our lovely assistant.
rrusczyk19:43:56
He will help you sometimes if you have questions.
rrusczyk19:44:03
His name is Matt Superdock, matt276eagles. He's currently in his first year at Princeton, was twice a USAMO Honorable Mention, and is one of the best Guitar Hero and Rock Band players in the world.
matt276eagles19:44:22
Hey everyone :)
rrusczyk19:44:27
So, if you have any math questions, speak up, and he'll help you out!
rrusczyk19:44:37
(I'll let you know when to start asking questions about the classes.)
rrusczyk19:44:49
Now, let's do a couple more problems.
rrusczyk19:45:15
The last two problems are problems that would only appear in the Advanced class, and are like some of the problems we'll do in Introduction to Number Theory.
rrusczyk19:45:25
rrusczyk19:45:53
Before we tackle this problem, what's a similar problem that some of you may know how to do already?
pingala19:46:10
find the # of poisitive integers first????
algebra133719:46:10
finding the number of factors in an integer
Iggy Iguana19:46:10
find number of divisors of 792
rrusczyk19:46:12
Let's get rid of that "even" restriction first.
rrusczyk19:46:31
This is one of my favorite strategies: turn the problem into an easier one I know how to do first.
rrusczyk19:46:43
How many positive integral divisors does 792 have?
rrusczyk19:46:50
Where do we start with that problem?
aggarwal19:46:59
prime factorize 792
MathTwo19:46:59
prime factorize 792
algebra133719:47:08
we find the prime factorization
jumblies19:47:10
factor it into primes?
aca19:47:10
prime factorize
rrusczyk19:47:12
And what is the prime factorization?
aggarwal19:47:24
2^3*3^2*11
math_galois19:47:24
792 = 2^3x3^2x11
$LaTeX$.19:47:24
2^3*3^2*11?
pingala19:47:24
2^3*3^2*11
rrusczyk19:47:26
rrusczyk19:47:44
How do we use this to count the divisors?
pingala19:48:04
so positive divisors are 4*3*2=24
aggarwal19:48:04
(3+1)(2+1)(1+1)
iamnew19:48:04
4*3*2
rrusczyk19:48:08
Why does that work?
PowerOfPi19:48:12
add one to exponents and multiply
rrusczyk19:48:19
But. . . . Why does *that* work?
MathTwo19:49:23
2^3 has 2^0, 1, 2, 3; 3^2 has 0, 1, 2; 11^1 has 0, 1.
Iggy Iguana19:49:24
you can use 2 so that it is 2^0, 2^1, 2^2 or 2^3 and it's the same for 3 and 11
frtian19:49:27
the exponent can be 0
rrusczyk19:49:34
rrusczyk19:50:10
All we're doing here is counting the number of ways we can choose the powers of 2, 3, and 11 in a divisor of 792. If you don't understand what we're doing here, speak up and matt276eagles will help you out.
rrusczyk19:50:26
Now, how do we adjust this to deal with the original problem of counting *even* divisors?
Iggy Iguana19:50:47
but they have to be even so you can't use 2^0
Iggy Iguana19:50:47
no using 2^0
sreyesh19:50:47
no 2^0
PowerOfPi19:50:53
let a not equal 0
rrusczyk19:51:05
We can't let the power of 2 be 0. How does that adjust our count?
iamnew19:51:27
3*3*2?
Iggy Iguana19:51:27
3 x 3 x 2 = 18
PowerOfPi19:51:27
3(2+1)(1+1)
math_galois19:51:27
3*3*2
rrusczyk19:51:48
rrusczyk19:51:58
rrusczyk19:52:22
Here's another approach you could have taken to solve the problem; see if you can figure out on your own why it works:
frtian19:52:23
devide 792 by 2
rrusczyk19:52:59
We'll do one more problem, and then we'll talk about the classes.
rrusczyk19:53:07
rrusczyk19:53:26
Who wants to convert to base 10?
math_galois19:53:50
no
Iggy Iguana19:53:50
not me!!
PowerOfPi19:53:50
no
dmosn19:53:50
not me!
MathTwo19:53:50
not me
rrusczyk19:53:53
Me neither.
GreatGray19:53:56
that would work
rrusczyk19:54:01
Yes, it would work!
Iggy Iguana19:54:12
it would take lots of time
MathTwo19:54:13
but it would take a long time
rrusczyk19:54:14
But, let's see if we can do something a little slicker :)
rrusczyk19:54:29
Why might we think there's a nicer way to do this particular problem?
PowerOfPi19:55:05
3^2=9
redreoicy19:55:05
3^2=9
lindy19:55:05
3^2 = 9
$LaTeX$.19:55:05
b/c 9=3^2 ???
iamnew19:55:05
9 =3^2
pingala19:55:05
3^2=9
dmosn19:55:05
9=3^2
mathwiz1234519:55:05
9 is the square of 3
jumblies19:55:05
because 9 is 3^2
rrusczyk19:55:22
rrusczyk19:55:46
But how?
rrusczyk19:56:02
How can we write the number we are given so that we can use the fact that 3^2 = 9?
rrusczyk19:56:29
What does it mean that the number is in "base 3"?
aca19:56:54
only the digits 0,1,2 are used
mathmansid19:56:57
That we use the digits 0, 1, 2
rrusczyk19:57:02
But what do the digits mean?
jumblies19:57:18
it means that each digit is a successive power of 3
PowerOfPi19:57:18
each digit to the left has a higher power of 3
GreatGray19:57:18
1, 3, 9, 27, and so on
iamnew19:57:18
that every didgit coming from the right is one higher power of 3
rrusczyk19:57:29
Exactly, so we can write the number like so:
rrusczyk19:57:34
PowerOfPi19:57:52
Now, convert even powers to powers of 9
rrusczyk19:58:03
PowerOfPi19:58:48
factor 3
redreoicy19:58:48
become 3* an even power?
rrusczyk19:58:51
rrusczyk19:58:58
How does that help us finish?
GreatGray19:59:37
we convert it back into digits
rrusczyk19:59:41
And what do we get?
lindy20:00:27
2200102 = 2*3^6 + 2*3^5 + 1*3^2 + 2*3^0 = 2*9^3 + 6*9^2 + 1*9^1 + 2*9^0 = 2612
frtian20:00:27
2612 base 9
mathwiz1234520:00:27
2612
iamnew20:00:27
2612?
aca20:00:27
2612
rrusczyk20:00:33
rrusczyk20:00:54
Any questions about that problem? We cover number bases very thoroughly in the Number Theory course.
mathmansid20:01:53
Does the Number Theory course cover the number theory concepts on the AMC 10?
rrusczyk20:01:57
Yes.
math_galois20:02:10
so if it's not 9, eg:5 we have to convert to base 10?
rrusczyk20:02:26
Yes, if the bases didn't have a nice relationship, then we have to go the nasty route.
pingala20:02:28
how did you get 2612????
rrusczyk20:02:41
I read them off the coefficients of the powers of 9.
rrusczyk20:02:56
2*9^3 + 6*9^2 + 1*9^1 + 2*9^0
rrusczyk20:03:06
This is how number bases work (even our base 10).
pingala20:03:18
Ohhh u remove the 0's
rrusczyk20:03:21
Exactly.
aca20:03:26
when converting from base 3 to 18, do the sets of three digits make a digit in base 18?
rrusczyk20:03:34
Is it 18 that works that way?
aca20:03:58
no, 27, sorry
GreatGray20:04:02
no it's 27
iamnew20:04:02
no 27 i think
arbala20:04:02
no it is 27
rrusczyk20:04:09
Exactly! And, yes that's how it works.
rrusczyk20:04:52
I'll now go through some information about the MATHCOUNTS classes, and then take questions about them.
rrusczyk20:04:55
MATHCOUNTS
rrusczyk20:05:03
This fall, we are offering two different MATHCOUNTS/AMC 8 classes: MATHCOUNTS/AMC 8 Basics and Advanced MATHCOUNTS/AMC 8.
rrusczyk20:05:09
The MATHCOUNTS/AMC 8 Basics course will meet for 12 weeks on Fridays, starting October 23, at 7:30 PM Eastern / 4:30 PM Pacific. Each class is 90 minutes, and each is 7:30 - 9 PM ET (4:30 - 6 PM PT). This class is for students just getting started with the type of problem solving required for success in MATHCOUNTS and the AMC 8.
rrusczyk20:05:21
Our Advanced MATHCOUNTS/AMC 8 is for more experienced students, such as those who are training for State MATHCOUNTS, with hopes of qualifying for National MATHCOUNTS. The Advanced MATHCOUNTS/AMC 8 course will meet for 12 weeks on Wednesdays, starting November 4, at 7:30 PM Eastern / 4:30 PM Pacific. Each class is 90 minutes, and each is 7:30 - 9 PM ET (4:30 - 6 PM PT).
rrusczyk20:05:42
Each class will be taught by Joshua Zucker. Joshua has been a Math Olympiad Summer Program invitee, a member of the first US Physics Olympiad team, and a top-10 scorer on the Putnam. He holds a BS in physics and an MS in mathematics from Stanford, as well as an MS in astrophysics from UC Berkeley. He has taught at levels ranging from summer camps for gifted elementary school students through remedial arithmetic at community college. He was a middle and high school teacher in Palo Alto, CA and was formerly a problem writer for MATHCOUNTS
rrusczyk20:05:57
While there is overlap in topics between the two classes, there will be almost no overlap in problems. Topics covered include methods of counting, probability, algebraic techniques, geometry, word problems, number theory, and more.
rrusczyk20:07:01
This class is a Problem Series class, meaning that the major focus of the class will be working through various contest problems. Although there will be weekly problem sets for each class posted on the message board, students do not submit their homeworks to be graded, and there is no personalized instructor feedback on the solutions. (However, the instructors will be monitoring the message board to answer questions and comment occasionally on the students' discussions there.)
rrusczyk20:07:10
Each course will also include a whole class that is a single giant Countdown Round contest!
rrusczyk20:07:19
Are there any questions about either of the two MATHCOUNTS courses?
mathmansid20:07:32
I am correct in saying that there is a great difference in the difficulty of MATHCOUNTS and AMC 8? I have done well on practice AMC 8 tests, but have had a lot of trouble with MATHCOUNTS questions.
rrusczyk20:07:47
It depends a lot on the level of MATHCOUNTS -- there's a much wider range of difficulty in MATHCOUNTS.
allnewRIOT20:07:50
Will there be any 6th grade mathcounts in them?
rrusczyk20:07:58
Yes, in the Basics class.
aca20:08:54
i heard MATHCOUNTS has lightning round courses at the end of each competition that allow little or no time for thinking, is this true?
rrusczyk20:08:59
Yes, MATHCOUNTS has a round called the "Countdown round" on which speed is *extremely* important. It's not an essential part of the competition for most levels, and you can proceed through the levels of MATHCOUNTS without being particularly strong at the "Countdown round".
allnewRIOT20:09:31
Does it cost money?
rrusczyk20:09:37
Yes; the fees for the classes are here:
py10920:10:03
what we just did,are we going to do something like that in class?
rrusczyk20:10:09
Yes, classes will be much like that.
aggarwal20:10:20
how can we be in mathcounts if our school does not participate in mathcounts
rrusczyk20:10:35
That's a question you'd have to ask the people at MATHCOUNTS (www.mathcounts.org)
MathTwo20:10:47
Will the practice problems in the MATHCOUNTS classes be taken off the real tests?
rrusczyk20:10:48
Most of them. We make some of them up.
mathmansid20:11:39
Do the Mathcounts classes cover what the introductory AOPS courses offer, or only some parts of them?
rrusczyk20:11:40
Our Intro courses are much more thorough than the Problem Series courses, and go to much greater depth in the material. The Problem Series classes are extra practice, while the subject classes offer more thorough instruction.
rrusczyk20:11:50
(Please note: you only need to ask your question once)
eggplant20:12:07
About how many questions are covered in each class?
rrusczyk20:12:08
It varies a lot. We go at a pace similar to what you saw tonight.
MathTwo20:12:32
The problems that you make up...how hard will they be? Like harder than the real tests, easier, about the same, etc.
rrusczyk20:12:39
All over. Some easier, some harder.
Aeq20:13:11
as in standard required math, e.g, Algebra 2 trig, geometry, etc.
rrusczyk20:13:12
For the MATHCOUNTS classes, at least some experience with Prealgebra for the Basics, and experience with Algebra for Advanced.
aggarwal20:13:38
is mathcounts more important than AMC
rrusczyk20:13:39
Depends on your goals and interests. At the middle school level, most students find MATHCOUNTS more important, I think because you can get to Nationals.
rrusczyk20:14:11
Depends more on your math level than your grade. If you find MATHCOUNTS really hard, start with Basics. If you find a lot of the problems pretty easy, then go with Advanced.
mathISuber20:14:13
i am an 8th grader which course do you suggest i take, advanced or beginner
eggplant20:14:33
If you miss two or three classes what happens?
rrusczyk20:14:34
There is a transcript made of every class that you can use to review the material.
sreyesh20:15:00
do these classes correspond to the Art of Problem Solving book
rrusczyk20:15:13
The problem series classes do not correspond to books. The subject classes do.
countdarx20:16:09
I am a 7th grader in Algebra 1 Honors and I have MATHCOUNTS experience. Which class do you suggest?
Aeq20:16:09
I am a 6th grader (taking Algebra 1), which course would you recommend?
rrusczyk20:16:11
The answer to that depends mainly on how easy/hard you find MATHCOUNTS, as indicated in my answer above. You can try the Basics class, and drop it if it is too easy. If you drop before the third class, you get a full refund. (You cannot drop after the third class starts.)
pingala20:16:13
If you are a high schooler (9th,grade and above) you cannot take MATHCOUNTS, right???
rrusczyk20:16:16
correct.
sparkles25720:16:18
does mathcounts cover a wide range of topics?
rrusczyk20:16:19
yes
mathmansid20:16:25
How do the advanced MATHCOUNTS problems compare to the AMC 8 and 10?
rrusczyk20:16:39
The very hardest MATHCOUNTS problems can be as hard as moderately hard AMC 10 problems.
$LaTeX$.20:16:42
Are we doin AMc 10/12 problems today?
rrusczyk20:16:52
No; we won't be doing any more problems tonight.
allnewRIOT20:17:06
Will there be probloms similar to the ones tonight on the middle school competitions?
rrusczyk20:17:08
Yes
lindy20:17:24
how much overlap material is present between the AOPS books and the Problem Series courses?
rrusczyk20:17:25
Similar topics are covered, but different problems.
sreyesh20:18:06
how do you practice the concepts covered in the class afterwards
rrusczyk20:18:16
We post extra problems on the class message board for students to discuss.
iamnew20:18:42
wheres that?
rrusczyk20:18:51
There will be instructions for that when you enroll in the course.
algebra133720:19:14
would i need to take the class if i get in the 40 range on state level tests?
rrusczyk20:19:16
Depends on your goals -- if you're fine-tuning for Nationals, you might get something out of it. But I'd recommend you start looking to harder material, like the AMC 10/12.
mathmansid20:19:30
Do the problem solving classes cover every bit of the corresponding textbooks?
rrusczyk20:19:32
The subject classes do pretty much.
GreatGray20:19:42
are the last 15 minutes reserved for more questions, or will you talk about the classes a little more?
rrusczyk20:19:58
I will talk a little more about the other 3 courses when there are no more questions.
math_galois20:20:21
is there any deadline for enrolling the class?
rrusczyk20:20:23
We close enrollment 2 weeks after the class starts, though some of these classes will likely fill, so you shouldn't wait too long.
Aeq20:20:27
when is the next math jam session?
GreatGray20:20:27
do you often do classes like this?
rrusczyk20:20:41
There's the schedule.
aggarwal20:20:45
can mathcounts consist of students from diffrent schools or do all the students have to be from the same school
rrusczyk20:20:55
Again, that's a question for MATHCOUNTS. I don't know the answer to that one.
aca20:20:58
is the subject material in the Art of Problem Solving books the same as in the AMC courses
rrusczyk20:21:06
Similar subjects, different problems.
rrusczyk20:21:13
Introduction to Number Theory
rrusczyk20:21:21
Many students who already know how to solve MATHCOUNTS level problems about divisibility, base numbers, and divisor counting might think they have little need for this class, but many of the students who have made the most of this class were participants at national MATHCOUNTS and the AIME and found many of the problems discussed in class very challenging.
rrusczyk20:21:28
The Introduction to Number Theory class covers divisibility problems, clever uses of prime factorization, base numbers, linear Diophantine equations, the Euclidean Algorithm, and covers the mechanics of modular arithmetic in thorough detail. There are also many other topics covered in this course that are rarely mentioned in math books at all, but these topics become increasingly important as you move to higher mathematics.
rrusczyk20:21:47
For example, the topics covered in this course are crucial to an understanding of such areas as cryptography and computer science.
rrusczyk20:21:53
Here are a few more kinds of problems that we will be tackling in class:
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(These are on the hard end of the problems we'll do!!!)
rrusczyk20:22:29
The Introduction to Number Theory class will be taught by Ari Nieh. Ari studied mathematics at Harvey Mudd College and UC Berkeley, completing his PhD in quantum topology in 2007. As an undergraduate, he was an Outstanding Winner of the 2001 COMAP Mathematical Contest in Modeling. He won both the Outstanding Graduate Student Instructor Award and Teaching Excellence Award for his teaching at UC Berkeley. He has worked at Canada/USA Mathcamp since 1998 as a counselor, instructor, and choir conductor, and joined the AoPS staff in 2009. In his spare time, he enjoys cooking, photography, comics, and puzzles.
mathmansid20:23:00
For students preparing for AMC 10, would you recommend your Problem Solving Books, or the specific Subject books, like intro to number theory?
rrusczyk20:23:02
In general, I recommend the subject books for deeply understanding the topics, and then using the problem solving books for extra practice and fine-tuning.
rrusczyk20:23:07
One more word about this number theory class. If you do not know modular arithmetic well enough to use it on most any problem up to AMC-12 level, this is a class that you would benefit from taking.
rrusczyk20:23:12
The course will meet for 12 weeks on Tuesdays, starting November 3. Each class starts at 7:30 PM Eastern / 4:30 PM Pacific, and is 90 minutes long.
rrusczyk20:23:20
The homework for the class consists of weekly problems that will be posted to the class message board -- for these problems, you do not turn your solutions in, however you may post them to the message board if you like. The class also has 4 longer problem sets for which you should write up your full solutions and submit them. These solutions will be evaluated by AoPS graders, and you will receive detailed feedback.
rrusczyk20:23:28
Are there any questions about the Number Theory course?
rrusczyk20:24:05
AMC 10 and AMC 12 Problem Series
rrusczyk20:24:11
The AMC 10 Problem Series starts on October 20, and meets every Tuesday from 7:30-9:00 PM Eastern. The course is designed to cover a large portion of the curriculum tested on the AMC 10 exam.
rrusczyk20:24:16
The class will be taught by Valentin Vornicu. Valentin was a 2-time participant at the International Math Olympiad, and won prizes at numerous national math competitions in Romania. Valentin has a Master's degree in Mathematics from the University of Bucharest and founded the MathLinks website in 2002 (which merged with Art of Problem Solving in 2004).
rrusczyk20:24:21
The AMC 12 class starts on October 19, and meets every Monday from 7:30-9:00 PM Eastern. The course is designed to cover a large portion of the curriculum tested on the AMC 12 exam.
rrusczyk20:24:29
The class will be taught by Sean Markan. Sean participated in numerous math and science programs in high school, including the Math Olympiad Summer Program in 2001 and the US Physics Team in 2000 and 2002. He also won the Mandelbrot Competition in 2002. He graduated from MIT with a degree in Physics in 2006.
rrusczyk20:24:38
These classes are Problem Series courses, meaning that the major focus of the class will be working through various AMC problems. Although there will be weekly problem sets for each class, students do not submit their homeworks to be graded, and there is no personalized instructor feedback.
rrusczyk20:24:43
Are there any questions about the AMC courses
mathISuber20:25:34
what score must you get in the amc/8 to appear iun amc/10
rrusczyk20:25:36
Anyone in 10th grade or earlier can take the AMC 10 -- you don't need to qualify for it.
mathmansid20:25:57
What sort of preparation do students need for the AMC 10 course?
rrusczyk20:25:59
Experience with problem solving -- tackling hard problems (unlike the ones you typically see in school)
algebra133720:26:01
will they use problems from past AMC tests?
rrusczyk20:26:13
Yes. We use a lot of problems from past AMC tests.
aca20:26:15
what is covered in these courses and what are some examples of problems we will encounter in the AMC 10 course
rrusczyk20:26:36
Take a look at AMC 10 problems -- most of the problems in the class will be in the #15 through #25 range.
Aeq20:26:51
so the number at the end denotes the grade?
rrusczyk20:27:02
It denotes the maximum grade of participants.
iamnew20:27:47
what score do you have to get on the AMC 8 to be invited to the AMC 10
rrusczyk20:28:14
I'm not sure, you can check the AMC website for that info, but you don't have to be invited to take the AMC 10. You can sign up independent of your AMC 8 score.
Aeq20:28:16
therefore an 8th grader could do AMC/10?
rrusczyk20:28:27
Correct, and many do.
aca20:29:32
what is the next level up from the AMC 10?
rrusczyk20:29:51
If you pass the AMC 10, you are invited to take the AIME, which you can read about at the AMC site: www.unl.edu/amc
rrusczyk20:30:06
Any more questions about the courses?
David214320:30:32
Is this class reccomended for people who can qualify for USAMO?
rrusczyk20:30:52
No - these students should take harder classes, like our Intermediate Counting, our Precalculus, or our WOOT classes.
aca20:30:54
could someone take both the AMC 10 and 12 in the same year?
rrusczyk20:31:09
Yes; the AMC is given on two different dates. You can take the AMC 10 on one and the AMC 12 on the other.
rrusczyk20:32:09
That's it for the Math Jam tonight. If you have any more questions about the classes, you can write me at classes@artofproblemsolving.com. Thanks for coming tonight!
