| Transcript
for the Math
Jam "AoPS Classes Math Jam"
on Nov 1. |
| Math Jam hosted by markan
(Sean Markan ). |
markan18:30:53
Hello, and welcome to another Art of Problem Solving Fall 2007 Classes Math Jam!
markan18:31:04
Tonight we'll be discussing the MATHCOUNTS Problem Series.
markan18:31:15
My name is Sean Markan, and I'm the instructor for MATHCOUNTS this fall.
markan18:31:20
Introduction of the Virtual Classroom
markan18:31:23
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.
markan18:31:35
The classroom is moderated: students can type into the classroom, but only the moderators can choose a comment to drop into the classroom. 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.
markan18:31:42
Note that it is not possible for the instructor to personally respond to every comment that you submit -- please do not take it personally if your comment is not posted or responded to! I will try to respond to all questions to the extent that I can.
markan18:31:52
In addition, the virtual classroom is LaTeX enabled. LaTeX allows users to make nice equations and other math expressions. If you would like to learn how to write in LaTeX, click on the tab on the left side panel of our site and there is a tutorial and reference guide there.
markan18:31:59
Using LaTeX in the virtual classroom is slightly different than using it on the message board or in a LaTeX editor. If anything you type up in a post uses LaTeX, then you must use a semicolon (;) to begin your post. For example, if you type
markan18:32:05
markan18:32:10
This message will look like this when posted in the classroom:
markan18:32:15
markan18:32:20
Just remember, if your post uses LaTeX, use the semicolon (;) to begin your post!
markan18:32:25
One last thing: we recommend not to use a wireless connection while in the classroom. These have a tendency to cause disconnections. Please use a wired connection if possible.
markan18:32:41
MATHCOUNTS
markan18:32:48
The MATHCOUNTS Problem Series is a 12 week course designed to cover one by one the areas of problem solving covered by the MATHCOUNTS competition. Topics covered including methods of counting, probability, algebraic techniques, word problems, number theory, and more.
markan18:33:03
I am the instructor of the MATHCOUNTS Problem Series this fall.
markan18:33:16
The course will be taught twice this season: once on Tuesdays and once on Thursdays.
markan18:33:26
Students will have to pick one or the other, and then attend only on the day they chose.
markan18:33:45
The first class for both sections is next week.
markan18:33:55
Classes run from 7:30-9 pm eastern time.
markan18:34:19
To let you get a sense of how the class will be run, I'm going to do some example problems now.
markan18:34:36
After that, I'll take questions, and after that, we'll do a practice countdown round (I'll explain what that is when we get to it).
markan18:34:48
Here's our first example problem:
markan18:34:51
markan18:35:11
Where can we start with this problem?
andrewliu18:35:33
one of the 2 equal 2
nikki18:35:33
the numbers have to be 2 and 3 since they are the only 2 consecutive primes
krakola4518:35:33
2 and 3 are the only consecutive prime numbers
markan18:35:40
Since either p or p + 1 is even, one of them must be even, so one of them must be 2, the only even prime. Since 1 isn?t prime, the other one must be 3.
Now, how do we find the smallest composite number that is neither a multiple of 2 nor 3?
istos18:35:48
We are looking for a composite number not divisible by 2 or 3
markan18:35:52
Yep.
xpmath18:35:59
25,since the smallest is the square of the smallest prime besides 2 and 3
markan18:36:04
Indeed.
markan18:36:08
markan18:36:21
Here's the next problem.
markan18:36:26
markan18:36:31
How do we start?
xpmath18:36:55
One must b 2
nikki18:36:55
think of possible primes that sum up to 30
markan18:37:03
how do we know one must be 2?
instantnoodles18:37:18
30 is a even number
azhang18:37:18
30 is an even number
xyz@yahoo.com18:37:18
30 is even
markan18:37:21
No matter what, one of the primes must be 2. If we have 3 numbers with an even sum, at least one of them is even. There's only one positive even prime, and that's 2.
markan18:37:25
So now what must we do?
tennisstar18:37:42
2 primes added up must be 28
kosarajua18:37:44
we must find two primes adding up to 28
mz9418:37:54
think of primes that add to 28
mz9418:37:59
17&11?
uvadel2k18:38:03
11 and 17
xpmath18:38:07
since 23+5=28, and 17+11=28
markan18:38:22
Our only options are 11 & 17, and 5 & 23.
markan18:38:26
Which has a larger product?
xyz@yahoo.com18:38:37
11 and 17
azhang18:38:37
11,17,2
RollandWu18:38:37
11 and 17
markan18:38:43
markan18:38:46
What is the answer to the problem?
someperson0118:38:56
17*11*2=374
llolloll18:38:56
374
tennisstar18:38:56
374
markan18:39:02
markan18:39:22
markan18:39:39
This is a tougher problem than most similar problems at MATHCOUNTS. In fact, I took the last question on a sprint round and added 'that are even'. But I wanted you all to take a shot at a problem that requires a little more thought than plugging into a formula.
RollandWu18:39:52
Prime factorize
scissorblades18:39:52
Prime factor 792
nikki18:39:52
find the prime factorization first and then the number of divisors
policecap18:39:52
prime factorization
markan18:39:54
Ok.
markan18:39:56
What is it?
alkjash18:40:11
markan18:40:15
markan18:40:24
What do we know about a divisor of 792?
markan18:41:45
Many of you have given me the answer already, but can you explain how you're getting it?
markan18:42:01
In general, what does the prime factorization of a factor of 792 look like?
alkjash18:42:19
Its only possible divisors are 2, 3, and 11?
markan18:42:38
Good, only those numbers will appear in the prime factorization of a factor of 792.
markan18:42:48
And you can have at most 3 2's, 2 3's, and 1 11.
xpmath18:42:51
markan18:42:57
rman18:43:12
minus the odd divisors 3x2
markan18:43:23
Right, a can't be 0, because then the divisor would be odd.
scissorblades18:43:28
"That are even" implies that the power of 2 in it must be at least one. So (3+1-1)*(2+1)*(1+1)=3*3*2=18
xpmath18:43:34
Now, to be even, a number must have atleast one factor of 2. So, ;$a\ge{1}$
markan18:43:54
So what's the final answer?
xpmath18:44:06
18
policecap18:44:06
18
alkjash18:44:06
18
guyinPA18:44:06
18
markan18:44:16
markan18:44:38
Alright, now let's take some questions.
markan18:44:51
Feel free to ask about the class, the online school in general, etc.
guyinPA18:45:36
is this how the course will be taught
markan18:45:49
Yes, more or less. I'll post a problem, and then we'll discuss it.
pingala18:46:00
do we have to pay for next class?
rrusczyk18:46:01
The MATHCOUNTS Problem Series is not free. The cost is $150 for the whole course.
markan18:46:13
Some of the problems will be more involved than the ones we did today though.
bobbob010018:46:56
what happens if you miss one class... maybe you are busy
markan18:47:09
That's fine; there are transcripts made of each class, and you'll have access to them on our website.
markan18:47:13
You can just read the transcript to see what happened in class.
mz9418:47:24
is this the same course as the summer one?
markan18:47:28
Yes, for the most part.
xpmath18:47:38
What level is the difficulty of the class?
rrusczyk18:47:40
The MATHCOUNTS Problem Series is designed for students with some problem solving experience. It's best for students preparing for state or national level MATHCOUNTS. A student with very little background in algebra, for example, would have a lot of difficulty.
mathgeek7618:47:40
what if you miss a class, can you look at the transcript later?
markan18:47:43
Yes.
krakola4518:48:00
Just wondering.. What are the prizes if you win the national MATHCOUNTS?
rrusczyk18:48:01
Look at the MATHCOUNTS website; it changes from year to year.
azhang18:48:09
does aops have any free public classes besides math jams?
markan18:48:19
No, just the math jams.
saichilakapati18:48:27
do you need any books for the mathcounts class
MathSports18:48:28
were those problems the average difficulty of the course?
rrusczyk18:48:29
The first two are easier than average, the last is a bit harder than average.
markan18:48:52
No, but if you want some recommendations for books, we can provide some.
Eruanna18:49:02
are all of them MATHCOUNTS related problems?
rrusczyk18:49:03
All of the problems in the course are at or near MATHCOUNTS level.
ll0ll0ll18:49:18
are there refunds?
markan18:49:27
You can drop a class any time before the 3rd meeting for a full refund.
kosarajua18:49:31
is the math class over?
rrusczyk18:49:34
No - after the Q&A session, we will play a game that's a lot like a massive CountDown Round
MathSports18:49:34
the classes will be 1 hour, right?
markan18:49:44
1 and a half
sudeepa18:50:04
We are new here. My daughter is in 5th grade and a Math whiz. What course should we start off with?MATHCOUNTS will be a little advanced for her, I guess
pingala18:50:06
this class is for free right?
this is just the intro. for MATHCOUNTS?
rrusczyk18:50:07
I would suggest the Introduction to Algebra class, followed by the Intro Counting & Number Theory classes.
markan18:50:17
Yes, this math jam is free (that's how you got here :)).
ll0ll0ll18:50:24
will there be homework assigned?
markan18:50:43
Yes, there is homework assigned, but it is not graded.
markan18:50:51
Each week we post problems on our online message board for students to solve.
markan18:51:04
They can also discuss them there, and ask questions if they need help.
guyinPA18:51:19
will there be a countdown each evening
markan18:51:29
Probably not.
ChileMama_218:51:39
This is moving very quickly for us; if a student thinks more slowly, would the classes still be useful to him or her?
rrusczyk18:51:41
This depends on the student - if the student is willing to ask questions and review the transcript when he falls behind, then he should be OK. You may also find he adjusts to the pace after a couple weeks. (Keep in mind that, for good or ill, speed is very important in MATHCOUNTS.) We have assistants in each class to help students who are falling behind.
PurpleOwnz18:51:41
Will we just do problems in class?
mz9418:52:14
ok, well, is this cd rd the same as the summer one?
rrusczyk18:52:19
The one we do tonight is not the same as in the summer, but the one in the course is.
markan18:52:33
Mostly we'll do problems, but when we discuss them we'll also talk about general problem solving strategies, mathematical theorems and definitions, etc.
azhang18:52:37
what happened to ashley ahlin?!?!??!?!?!?!
rrusczyk18:52:40
Ashley is teaching our Intro Counting class this fall.
xyz@yahoo.com18:52:42
Is this the same course as last year? in the fall
markan18:52:45
Yes.
jck51518:52:49
I just joined. did you guys do some problems already?
rrusczyk18:52:50
Yes
saichilakapati18:52:52
do we need any books for the mathcounts class
markan18:52:58
There are no required books.
ll0ll0ll18:53:15
about how many problems will be introduced per class?
rrusczyk18:53:18
Anywhere from 10-30, depending on the class. Usually around 20.
llolloll18:53:32
do you know of any good number theory books?
boogiepop9018:53:45
Which one is harder, AMC12 or Mathcount?
markan18:53:45
We recommend the AoPS Introduction to Number Theory book.
rrusczyk18:53:46
AMC 12
ll0ll0ll18:54:06
will geometry be included in mathcounts?
markan18:54:09
Yes.
krakola4518:54:14
are there any calculus courses in aops?
markan18:54:26
Not yet, but we're considering it.
ChileMama_218:54:41
Is the pace in the Intro to Algebra course comparable to the pace here tonight?
markan18:55:08
I would say algebra is quite a bit slower-paced.
mathgeek7618:55:12
if your new to math counts would this be a worthwhile class?
rrusczyk18:55:14
It depends on your math background. If you have no algebra, this class will be very hard. If you have some algebra, are generally tops in your math classes, then the class could be a good fit. Keep in mind, you can try the class twice then drop with a full refund if you find it's not a good fit.
markan18:55:24
(Or at least it assumes less prior knowledge on the part of the students.)
ll0ll0ll18:55:37
will homework include solutions?
markan18:55:40
Yes.
alkjash18:55:48
How many classes long is the course?
markan18:55:53
12
scissorblades18:55:55
I am a mathcounts coach at my school. Would a printed transcript of this class be a good teaching tool?
rrusczyk18:55:57
It would be a good guide for a teacher to use with his or her class. Just handing the printed transcript to the students might confuse them.
rman18:56:19
do you give us assignments before calss or after class?
rrusczyk18:56:21
After
ll0ll0ll18:56:22
will there be limited spaces for the math lessons?
markan18:56:26
No.
kosarajua18:56:35
When is each class?
markan18:56:50
It meets twice a week, Tuesdays and Thursdays, but each student must pick a day to attend and then stick to oit.
markan18:56:52
*to it.
markan18:56:59
It's 7:30-9 pm eastern time.
sudeepa18:57:02
Can we have a transcript of todays Math Jam?
rrusczyk18:57:03
Yes, it will be in the transcripts section of the Math Jams pages.
MathSports18:57:18
How many kids in a class
rrusczyk18:57:19
We expect around 40 - 45 in each class.
ll0ll0ll18:57:38
will people who didnt pay be able to review the transcripts?
markan18:57:42
No.
kosarajua18:58:05
What grade level is the curriculum recommended to?
rrusczyk18:58:08
We recommend MATHCOUNTS for high performing students in grades 6-8. Some rare students are ready for it earlier.
ll0ll0ll18:58:26
about how much of mathcounts is number theory?
rrusczyk18:58:27
This is a bit of a guess, but I'd say 15ish%
PurpleOwnz18:58:42
Do we need
kosarajua18:58:42
For some reason, I cannot type
uvadel2k18:58:42
9
kosarajua18:58:42
Why can't I type?
mz9418:58:42
12
markan18:58:53
Oops.
markan18:59:02
Those of you asking why you can't type, it's because the classroom is moderated.
PurpleOwnz18:59:08
If you miss Tuesday can you join Thursday?
markan18:59:12
The moderators see your messages first and decide which ones to pass to the class.
rrusczyk18:59:18
No; we are keeping students with their days.
ll0ll0ll18:59:42
What if I cannot afford the math lessons?
rrusczyk18:59:44
We will have more Math Jams throughout the year.
rman18:59:57
will we do random problems or old mathcounts problems
rrusczyk18:59:59
Both.
andrewliu19:00:08
are all mathjames free?
markan19:00:12
Yes.
ChileMama_219:00:27
will you do a math jam that's a sample of intro to algebra?
markan19:00:40
We've already done one; the transcript should be on our Math Jams page.
xpmath19:01:05
I'm just asking, do you know of any intermediate level number theory books?
rrusczyk19:01:08
Engel's Problem Solving Strategies and Zeitz's Art and Craft of Problem Solving have decent sections on number theory. There's some intermediate number theory in AoPS Volume 2, too.
ChileMama_219:01:23
thanks; I presume that's available even if we didn't sign up for it, since the jams are free?
markan19:01:26
Right.
pingala19:01:38
when is the math jams?
markan19:01:47
There's a schedule on our website under Community > Math Jams.
markan19:02:14
Ok, we're going to start the countdown round now.
markan19:02:22
I'll take more questions afterwards.
markan19:02:48
before we get started I would like to explain the game we are going to play today. I will post problems and as soon as I receive three correct responses I will post those responses. Each respondent will score 1 point for a correct answer. Only a student's first submitted answer will count.
markan19:03:06
Additionally, the three correct respondents will be allowed to explain the solution. An additional 1 point will be awarded to best solution. If all solutions are equal, the extra point will be awarded to the first of the three students who answered the question correctly. After the correct answers are posted the three respondents will have at most one minute to prepare their solutions. I will let you know when there are ten seconds left.
markan19:03:22
One more thing. The problems are all written in TeX and some students report slower loading of the TeX than others. Unfortunately, this is something that I cannot help. Try to enjoy the game and the problems and learn something even if it's not as easy to be one of the first three with the correct answer.
markan19:03:26
Now, let's get started!
markan19:03:45
xpmath19:04:21
-4
guyinPA19:04:21
-4
alkjash19:04:21
-4
markan19:04:27
Ok, explanations?
markan19:05:30
10 seconds
xpmath19:05:44
The product is 1, when we solve the resulting quadratic, x=-4
markan19:05:48
Ok, here's the next question:
markan19:05:57
someperson0119:06:23
-4
RollandWu19:06:23
-4
guyinPA19:06:23
-4
markan19:06:28
Explanations?
markan19:07:32
By the way, in class I'll be spending more time explaining each question, rather than just posting a couple student responses.
markan19:07:34
10 sec
someperson0119:08:03
(5/6)/(2/3)=5/4, so it is so (8/4)/(-2/4) is 8/-2=-4.
markan19:08:11
krakola4519:08:41
13
virtuoso19:08:41
13
xpmath19:08:41
13
markan19:08:46
Explanations?
markan19:09:35
10 sec
krakola4519:10:05
The worst possible scenario is if you pick 4 cards of each color. If you pick one more, You have 5 cards of any color.
markan19:10:27
virtuoso19:11:04
11/21
xpmath19:11:04
11/21
someperson0119:11:04
11/21
markan19:11:11
Explanations?
markan19:11:38
10 sec
xpmath19:11:57
The probabilities add to one, so we subtract and find it's 11/21.
markan19:12:06
markan19:12:13
Actually, skip that one.
markan19:12:19
I'll give you a different problem.
markan19:12:25
tennisstar19:13:26
9
rman19:13:26
9
panjia12319:13:26
9
markan19:13:32
How come?
markan19:14:48
10 sec
panjia12319:15:05
the zeroes are (-2+-sqrt80)/2, we want the integers between the zeroes, there are 9 of them
rman19:15:27
markan19:15:48
Ok, halftime. Here are the scores I have so far.
markan19:15:53
alkjash = 1
markan19:16:00
guyinPA = 2
markan19:16:04
krakola = 2
markan19:16:07
panjia = 2
markan19:16:09
rman = 1
markan19:16:12
Roland = 1
markan19:16:18
somperson = 3
markan19:16:19
tennis = 1
markan19:16:21
virtuoso = 2
markan19:16:23
xpmath = 5
markan19:16:45
We'll do 5 more.
markan19:16:48
xpmath19:18:17
18rt3
alkjash19:18:17
18rt3
rman19:18:17
18rt(3)
markan19:18:22
why?
markan19:18:30
(By the way, it seems I made a mistake with the half-time scores....they're being recomputed.)
markan19:19:19
10 sec
xpmath19:19:46
The side length is 6, the vertices form an equilateral triangle, side length 6rt2. The formula for that with side x is x^2rt3/4, subbing in, gives 18rt3
markan19:19:56
krakola4519:20:56
7/20
policecap19:20:56
7/20
guyinPA19:20:56
7/20
markan19:21:07
Explanations?
markan19:22:20
10 sec
guyinPA19:23:02
((x+y)^2+2xy)/x^2y^2=1/x^2+1/y^2 (100+40 )/400
markan19:23:09
I'll post mine too:
markan19:23:14
markan19:23:35
Ok, updated scores:
rrusczyk19:23:38
xpmath: 12
krakola: 7
someperson, virtuoso, guyinPa: 5
rman: 4
markan19:24:05
guyinPA19:24:38
1/9
policecap19:24:38
1/9
virtuoso19:24:38
1/9
markan19:24:42
Why?
markan19:25:42
10 sec
virtuoso19:26:00
Ratios: Richard to Dave to Naoki = 6x: 2x:1x -->Naoki: 1x/9x = 1/9
markan19:26:17
someperson0119:26:46
15 min
guyinPA19:26:46
15
RollandWu19:26:46
15min
markan19:26:52
Explanations?
markan19:27:47
10 sec
RollandWu19:28:22
hiw trip is 65x3=195 miles long, so including rest he takes 195/60=3.25 hours, which is 15 minutes more
markan19:28:25
Ok, last question.
markan19:28:32
xpmath19:29:35
1/4
lokito19:29:35
1/4
panjia12319:29:35
1/4
markan19:29:43
Why?
markan19:30:45
10 sec
panjia12319:31:16
doing f(-2) with some computation, we get -2. but then we don't need to calculate f(f(-2)), sincef(-2)=-2, so f(f(-2))=f(-2)=-2. So the answer is -2^(-2)=1/4
markan19:31:24
Alright, here's the final standings:
markan19:31:29
xpmath = 15
markan19:31:31
guyinPA = 10
markan19:31:36
someperson = 8
markan19:31:45
virtuoso, krakola = 7
markan19:31:52
policecap, rman, Roland, panjia = 4
markan19:32:10
Good job everyone!
policecap19:32:13
can we have more questions? That didn't feel like much .
markan19:32:22
You should take the class :).
markan19:32:29
Alright, feel free to ask questions if you have any.
usbleuflame19:32:39
When is the actual class?
markan19:32:48
Starts next week.
markan19:32:54
One section runs Tuesdays, one section runs Thursdays.
markan19:33:01
Students should pick one.
markan19:33:06
We meet 7:30-9 pm eastern time.
Eruanna19:33:22
are we going to go back over those problems tonight?
markan19:33:35
Unfortunately, no, but feel free to ask about them on the message board.
usbleuflame19:33:41
are you the teacher for those classes?
markan19:33:45
Yes.
v2math19:34:27
what happens if one class is over 45 students ?
markan19:35:12
If the classes get really big we'll split them into two sections
markan19:35:19
But I'm not sure what our cutoff is.
paqui_259019:35:35
what are the topics of the classes?
Eruanna19:35:35
are there going to be anymore problems tonight?
usbleuflame19:35:35
are these problems from the Art of Problem Solving Books?
rrusczyk19:35:50
The problems are mostly from old MATHCOUNTS tests.
markan19:36:16
You can see the syllabus here:
markan19:36:26
No more problems tonight.
v2math19:37:12
so the student can take either Tuesday or Thursday classes
Harini19:37:12
can we get the transcript of this math jam?
markan19:37:19
v2math: Yes.
markan19:37:32
You can get the transcript from our website. Go to community and then math jams.
llolloll19:37:43
are there high school level courses?
rrusczyk19:37:44
Yes; you can see a list of all our classes here:
Invasean19:39:01
I just enrolled the mathcount class for next week, may I know the class is the same type this class (count down) or other type (like spring round question?)
rrusczyk19:39:10
The first 11 classes are not 'countdown rounds' - they are full discussions of each problem and the important problem solving strategies needed to solve it. The last class is a 90-minute countdown round.
markan19:40:10
Thanks everyone for coming.
markan19:40:14
I hope to see you in the class.
