| Transcript
for the Math
Jam "AoPS Classes Math Jam"
on Feb 18. |
| Math Jam hosted by rrusczyk
(Richard Rusczyk ). |
rrusczyk19:32:48
Hello, and welcome to an Art of Problem Solving Math Jam. Today we'll be discussing three Introduction classes that will start during the first week of March: Introduction to Algebra, Introduction to Counting & Probability, Introduction to Geometry.
rrusczyk19:32:59
For each class, we will go through a couple example problems, and then discuss how the class will work.
rrusczyk19:33:25
I'll let you know when it is time to ask questions about the courses. Please hold your questions until then.
rrusczyk19:33:26
My name is Richard Rusczyk. I founded Art of Problem Solving and have written several Art of Problem Solving textbooks.
rrusczyk19:33:34
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.
rrusczyk19:33:47
The classroom is moderated: students can type into the classroom, but only the moderators can choose a comment to drop into the classroom. So, when you send a message, it will not appear immediately, and may not appear at all. This helps keep the class organized and on track. 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.
rrusczyk19:34:11
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. I will let you know when to start asking questions about the classes.
rrusczyk19:34:44
In this Math Jam, I will briefly describe a course, then go through a few example problems. Then, I will hold a question-and-answer session about that class.
rrusczyk19:35:02
We'll start with the Introduction to Algebra course.
rrusczyk19:35:21
I'll describe the class, go through one sample problem, and then take questions about the course.
rrusczyk19:35:25
Introduction to Algebra
rrusczyk19:35:30
Introduction to Algebra is intended to cover all the fundamental concepts of Algebra, including the following:
rrusczyk19:35:36
expressions
equations
quadratics and other polynomials
complex numbers
graphing
functions
sequences and series
exponents and logarithms
rrusczyk19:35:47
In terms of what schools usually call Algebra 1 and Algebra 2, our course covers
rrusczyk19:35:55
* essentially all the algebraic topics in Algebra 1
* most of the algebraic topics in Algebra 2
* certain advanced topics (like telescoping sums and piecewise functions)
rrusczyk19:36:06
The reason I referred to 'algebraic topics' is that schools often teach the basics of geometry and counting in their algebra classes. Instead of teaching those topics in our algebra classes, we teach them in our Geometry and Counting & Probability classes, as part of a deeper exploration of those subjects.
rrusczyk19:36:21
Introduction to Algebra, like all our classes, emphasizes problem solving and conceptual understanding rather than rote memorization. So in addition to teaching students how to manipulate equations, we teach them why the techniques are logically sound, and we talk about general problem solving strategies. Our class meetings are largely interactive, meaning that most of the time is spent solving problems. As much as possible, the students do the solving; the teacher only guides them along and provides useful hints.
rrusczyk19:36:56
(In other words, the classes are not mainly the instructor lecturing and you reading, like this introduction has been. You'll be thinking about math problems and answering questions.)
rrusczyk19:37:01
There are a couple major goals of Introduction to Algebra:
rrusczyk19:37:05
Students should develop the ability to translate a situation (which might be a real-life situation, a puzzle, etc.) into the abstract language of equations, and then manipulate the equations to develop insight into the original problem. This skill is the key that opens the door to numerous other fields of study, like higher math, chemistry, physics, and engineering.
rrusczyk19:37:31
The real world is the taking-off point which motivates many mathematical concepts. Once one begins to study those concepts, many new questions arise: Do all equations have solutions? Is every number a fraction? Can we invent a number whose square is negative? We delve into some of these questions so that students gain an appreciation for the structure of mathematics, the ability to think abstractly, and the confidence to tackle very difficult questions.
rrusczyk19:37:52
I'm now going to run through an example algebra problem to give you a taste of the mechanics of the class.
rrusczyk19:37:56
Ready for some math?
AIME_is_hard19:38:05
yes
TheMan199819:38:05
yes
cmpgm88@yahoo.com19:38:05
YEAH!!!
Aeroalon19:38:05
Yep.
qwertythecucumber19:38:05
yup!!!
physwiz19:38:05
yes
skylord581619:38:05
Yes
all4math19:38:05
Bring it on
rrusczyk19:38:13
All right, here's the problem:
rrusczyk19:38:16
What's the solution to the following equation?
rrusczyk19:38:20
rrusczyk19:38:33
Where do we start?
rrusczyk19:39:06
I see a lot of you suggesting that we square both sides. Yikes! That looks scary. Is there something simpler we can do?
rrusczyk19:39:13
People have suggested this:
rrusczyk19:39:17
rrusczyk19:39:19
After all, the square root of the square of a number seems to be the original number. For example,
rrusczyk19:39:23
rrusczyk19:39:29
Let's try this and see where it goes. What's our new equation if we do this?
skylord581619:39:42
x-2x=1
Aeroalon19:39:42
x-2x=1
rrusczyk19:39:44
rrusczyk19:39:52
What does this give?
saszs19:40:05
x = -1
qwertythecucumber19:40:05
x=-1
sanjeevonweb19:40:05
x-2x = 1, -x = 1, x=-1
skylord581619:40:05
x=-1
venkataraman19:40:05
x=-1
rrusczyk19:40:16
We can combine like terms on the left to get -x = 1, so x = -1.
rrusczyk19:40:25
Alright, now, it's always a good idea to check your work by plugging your solution into the original equation. Let's do that. Does it work?
rrusczyk19:41:05
I see a lot of yesses. I suggest you substitute again!
venkataraman19:41:12
NO
skylord581619:41:12
no
nt81158114719:41:12
But this doesn't work when we plug it back in! We get 1+2=1???
SarahM19:41:12
No way!
rrusczyk19:41:23
If we plug x = -1 into
rrusczyk19:41:27
rrusczyk19:41:45
rrusczyk19:41:55
Uh-oh! Our solution didn't work!
rrusczyk19:42:15
Uhoh! Is x = -1 a solution?
CubeX19:42:34
hmm, this is confusing
cmpgm88@yahoo.com19:42:35
NOOOO!
coco32119:42:35
no
jessica.waz.here19:42:35
no
CubeX19:42:35
no
rrusczyk19:42:36
No, x = -1 is not a solution because it does not satisfy the equation.
ailujailub19:42:48
Now what?
rrusczyk19:43:02
Good question. Do we just give up and say no solution, or is there a solution?
rohan21019:43:09
yeah our solution is -1/3
aliceindia19:43:09
not but x = -1/3 can be one too
rrusczyk19:43:20
Bold claim! Is x = -1/3 really a solution to this equation?
AIME_is_hard19:43:37
Of course
rohan21019:43:37
yeah!!!!! =)
qwertythecucumber19:43:44
yes; plugging in shows just that
rrusczyk19:43:55
Yes, it works. Putting x = -1/3 in the left side does give:
TheMan199819:43:57
it works , 1/3+2/3=3/3
rrusczyk19:44:06
It gives 1/3 + 2/3 on the left, which is 1.
cmpgm88@yahoo.com19:44:09
How did we reach that?
Ispxye_6019:44:10
how did you get x=- 1/3 ??
ailujailub19:44:23
Yes that works but how do we arrive there?
rrusczyk19:44:27
Excellent question!! Let's see how we find this solution.
rrusczyk19:44:42
First, we'll investigate our original solution and try to figure out where we went wrong.
rrusczyk19:45:00
We missed the solution x = -1/3, and found a solution that didn't work. So somewhere we must have made a faulty assumption. Where?
Ispxye_6019:45:27
that rt x^2 was x
TheMan199819:45:27
sqrtx^2=x
Aeroalon19:45:27
Square root of X^2 doesn't have to equal x.
rrusczyk19:45:31
It was wrong to assume that
rrusczyk19:45:34
rrusczyk19:45:37
We can only make this assumption if we know that x is positive. If x is negative, what does
rrusczyk19:45:40
rrusczyk19:45:43
come out to?
venkataraman19:45:54
if x was negative then it would equal -x
manbugbeebee19:45:54
The square root of x^2 can also equal -x.
venkataraman19:45:54
-x
AIME_is_hard19:45:54
it equals -x when x is negative
rrusczyk19:46:00
rrusczyk19:46:16
Let's try solving the equation again, this time assuming x is negative. What does the equation become if x is negative and we simplify the square root?
AIME_is_hard19:46:45
-x-2x=1
nt81158114719:46:45
-x-2x=1
qwertythecucumber19:46:45
-x-2x=1
rrusczyk19:46:53
Ispxye_6019:46:57
-3x =1
Ttocs4519:46:57
-3x=1
Aeroalon19:46:57
rrusczyk19:47:01
This reduces to
rrusczyk19:47:05
Ispxye_6019:47:10
x=-1/3
remy114019:47:10
-3x=1, so x=-1/3.
AIME_is_hard19:47:10
-x-2x=1 so -3x=1 and x=-1/3
skylord581619:47:10
-1/3=x
rrusczyk19:47:24
rrusczyk19:47:29
Now we've found the solution.
rrusczyk19:47:36
This problem illustrates the importance of not making any hidden assumptions when you attempt to solve an equation. You must keep *all* possible solutions under consideration rather than assuming the solution is positive.
rrusczyk19:47:51
You can find more questions like those we cover in the course by checking out the Post Test for the course here:
rrusczyk19:50:06
The course will meet for 27 weeks on Wednesdays, starting March 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). The last day of the class is September 2.
rrusczyk19:48:09
This course will use a textbook in conjunction with the course: our own Introduction to Algebra book. The material covered in the textbook is roughly equivalent to the material covered in the course. You can see the table of contents and some excerpts from the book here:
rrusczyk19:48:54
The book is required for the course. Students will be able to read additional material that complements the lectures, and will have access to a large number of practice problems at varying levels of difficulty. We recommend that students read the corresponding chapter(s) in the book before each lecture, and attempt some of that chapter's Review and Challenge Problems after each lecture.
rrusczyk19:49:19
The course will be taught by Dan Zaharopol. Dan has taught math at numerous programs across the country. He has been an instructor at Canada/USA Mathcamp (and was voted best instructor there), at the Boston Math Circle, and with the Splash and HSSP programs at the MIT Educational Studies Program. Dan participated in numerous local and national math competitions in high school and was a finalist in the 1999 USA Computing Olympiad. He holds an SB from MIT in mathematics, and two MS's from the University of Illinois in mathematics and teaching mathematics.
rrusczyk19:49:41
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, but you may post them to the message board if you like. The class also has 11 Challenge Sets for which you should write up your full solutions and submit them. You will receive thorough feedback for your work on these Challenge Sets that will comment both on your mathematical accuracy and how well you write solutions.
rrusczyk19:50:41
I'll now take some questions. I'm receiving a lot of questions, so it might be a while before I get to yours!
kookamunga19:50:45
How hard was this question compared to the overall Intro to Algebra textbook?
rrusczyk19:51:10
Probably slightly easier than average. Typically, we build up to problems like this, and then go on to harder ones.
rrusczyk19:51:28
Also, please only ask your question once, rather than over and over.
venkataraman19:51:30
Wait the course runs for 27 weeks????!!!!
rrusczyk19:51:33
Yes.
saszs19:51:39
Is this a free class
HAARS2619:51:39
dOES THIS COURSE COST MONEY
rrusczyk19:52:00
It is not free; you can visit our Online Classes page to learn about registration fees. The Math Jam is free.
asiangenius31419:52:03
do you have to attend every time??
rrusczyk19:52:27
No. There is a full transcript made of every class, so you can review the whole class whenever you like after class.
subus19:52:35
is there audio with this class
rrusczyk19:52:44
No. Here is an explanation why:
skylord581619:53:05
I already took Algebra, but I got this one wrong, so would it help me to retake Algebra?
Jericho kid19:53:05
should i take this course if I already took Math A regent in New York?
rrusczyk19:53:16
There are diagnostic tests on this page:
rrusczyk19:53:39
There is one to see if you are ready, and another to determine if you need the course (that is, if you already know how to do most of the material in the course).
rrusczyk19:54:32
This course is considerably harder than a typical Algebra 1 course, and it is not uncommon for students to take this class after taking a regular Algebra 1 class (it is also not unusual for students to take this as their Algebra 1 class, and get a much more thorough class than you typically see in school).
all4math19:54:40
how will this help us on MATHCOUNTS or AMC
CubeX19:54:41
Does this help in MATHCOUNTS?:-o
rrusczyk19:55:16
Yes, these classes will all help a great deal with math contests. We teach many of the strategies and tactics needed for success on math contests, and use many contest problems in our book and class.
cmpgm88@yahoo.com19:55:19
May we please move on to the next class on the agenda?
sravyasiri19:55:19
are we going to do more math problems...just wondering
rrusczyk19:55:39
We'll do so after I take the questions -- it will probably be about 10-15 minutes if you want to take a break.
azninvasion59419:55:41
is the class like this (in a chat room)
rrusczyk19:55:47
Yes, this is the format of the class.
parakeet19:55:49
can you give a harder than average example???
rrusczyk19:56:04
The diagnostic test "Do You Need This?" on the link above has several.
LMB12319:56:18
How old are most of the students in the class? I'm in middle school -- is this appropriate for me?
rrusczyk19:56:29
Most of the students in the Intro Algebra class are in middle school.
nt81158114719:56:48
What makes an AoPS class "worth it", that is, what more value do I get from it than buying an AoPS or similar book and posting any questions I have on the forum or asking a smart friend?
rrusczyk19:57:28
Good luck finding a similar book :)
rrusczyk19:57:35
As for what additional you get from the class,
rrusczyk19:58:26
you get an experienced instructor who knows a scary amount of math, you get a peer group that no school in the country has, you have the opportunity to ask questions in real time as you think of them, you get detailed feedback on your homework.
rrusczyk19:58:47
You may have access to many of these things on your own, and that's great -- you may be just fine with the textbook.
rrusczyk19:59:14
Some people learn better with just a book. Others need the structure of the classroom (which is another advantage of the course -- it gives you a clear schedule).
Colette19:59:20
What happens when you enter in a private conversation with the instructor?
rrusczyk19:59:53
You talk 1-on-1 about whatever issue needs to be discussed. Each course has an assistant who will sometimes work 1-on-1 with people who need a little extra help.
LMB12319:59:56
Do you have a refund policy? What if I have a really hard time learning this way? This is my first internet class.
rrusczyk20:00:11
Yes - if you drop a course before the third class, you will receive a full refund.
mike470020:00:15
how many people are tipically in the class
rrusczyk20:00:32
30-50. If more than that enroll, we often split the course into two sections.
mark029520:00:34
if you want take this class, you must type very fast, otherwise you may miss something...can we ask question throughthe email other than calss time?
rrusczyk20:00:47
There is a course message board on which you can ask questions at any time.
aliceindia20:00:58
can others see what you whispher to us Sir ?
rrusczyk20:01:00
No
soulspeedy20:01:08
Are these classes also helpful for AMC 10?
rrusczyk20:01:12
Absolutely.
melinda20:01:24
Do some schools allow a student to take this class instead of a math class at school or do most kids wind up taking an algebra class at school and also this class? I'm trying to figure out how to present this to the school...a private school that does not differentiate instruction in math and spends 2 years on prealgebra.
rrusczyk20:01:37
Yikes. I can see why you are looking for something else.
rrusczyk20:02:16
Some schools will allow our classes to "count", though most students take these in addition to school. We are happy to explain our courses to your school officials if they are interested in learning more.
venkataraman20:02:18
What about Amc 12, is this class helpful?
rrusczyk20:02:21
Yes.
Geniuscide20:02:26
so how does a typical lesson proceed?
rrusczyk20:02:54
Much like the sample problem -- we go through a series of related problems that are solved by the students, with the instructor drawing out the key points.
Colette20:02:59
My school doesn't let anybody skip grades, and math is very easy/boring. Can this help???
rrusczyk20:03:24
You just described why a great many of our students take our classes. They're bored to tears in their regular math class and looking for something more interesting and challenging.
LMB12320:03:26
Why is this class better than highering a private tutor?
rrusczyk20:03:59
Unless you have access to very good tutors, our instructors are probably better than your tutors. Unless you have access to very bad tutors, our classes are probably considerably less expensive than a tutor.
melinda20:04:10
In the future how will this class format interface with the Alcumus? Will you offer both? Or will Alcumus replace this format? When will this class be available on Alcumus?
rrusczyk20:04:34
I'll discuss this in relation to the Introduction to Counting class, which will be integrated with Alcumus this spring. (I'll describe Alcumus then)
saszs20:05:01
Is the homework compulsory, is it very challenging
rrusczyk20:05:33
It is not required, but strongly recommended. It is very challenging. We almost never have anyone get every question correct on a homework set.
vasudha20:05:35
is your class designed for very fast learners
rrusczyk20:05:37
Yes.
qntty20:05:42
How much material does the class cover in relation to an Alebra I/II class?
rrusczyk20:05:51
All of Algebra I, much of Algebra II
LadyCthulhu20:06:09
Are there any prerequisites?
rrusczyk20:06:31
No formal prerequisites -- you can look at the diagnostic tests to determine if you are ready.
rrusczyk20:06:35
They are here:
physwiz20:06:40
If you have already done an intermediate algebra course what is the next step through AoPS.
rrusczyk20:06:50
Any of the other Intermediate classes would fit.
venkataraman20:06:53
Any Precalculus Taught?
rrusczyk20:07:03
Not in Intro Algebra, but we will have a Precalc class in the fall.
silverfang1320:07:06
What happens when someone doesn't understand alot of the material
rrusczyk20:07:24
We have a class assistant to help if you ask questions, and you can use the class message board.
rrusczyk20:07:39
I'm going to move on to the next course, and then take more questions after that.
rrusczyk20:07:52
(If you still have questions about the Algebra course, you can ask them then!)
kookamunga20:08:04
How would you rank the four Introduction series textbooks, from easiest to hardest?
rrusczyk20:08:17
Algebra, then Counting & Number Theory about the same, then Geometry.
rrusczyk20:08:20
Introduction to Counting & Probability
rrusczyk20:08:24
In the Introduction to Counting and Probability class, we cover basic and intermediate counting concepts, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
rrusczyk20:08:33
The main emphasis of this class is learning how to take an organized approach to counting, and understanding that nearly all of counting is learning when to use the basic arithmetic operations division, multiplication, addition, and subtraction (and of course why to use them when you use them).
rrusczyk20:08:55
Students completing this course, who work most of the problems, should come out of the course knowing how to tackle any MATHCOUNTS counting problems, most AMC 10 and AMC 12 counting problems, and even some AIME counting problems. The concepts in this course are also crucial to understanding computer science.
rrusczyk20:09:01
We'll now take a look at a couple of sample problems from the course, which highlight some of the tactics we'll investigate in this class.
rrusczyk20:09:12
rrusczyk20:09:41
Make sure you explain your answer!
cmpgm88@yahoo.com20:10:14
coco32120:10:14
7x6x5x4x3x2x1
Aeroalon20:10:14
We have a total of 7 students and 7 seats, so there are 7! ways. 7 for the first seat, 6 for the second, etc. to 1 for the last.
rrusczyk20:10:19
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.
rrusczyk20:10:24
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.
skylord581620:10:26
7 choices for first chair, 6 for next, 5 for next, and so on and so forth. So it should be 7! or 5040
rrusczyk20:10:36
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.
venkataraman20:10:41
7 ways for the first seat 6 ways for the second seat 5 ways for the third seat
7!=5045
rrusczyk20:10:45
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'.
rrusczyk20:10:48
Similarly,
rrusczyk20:10:51
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
rrusczyk20:10:58
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?
rrusczyk20:11:06
What's wrong with this answer:
rrusczyk20:11:12
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:
rrusczyk20:11:18
4 x 6 x 5 x 4 x 3 x 2 x 1 seatings.
rrusczyk20:11:21
What's wrong with that?
AIME1520:11:40
we still need a girl in the last chair
Aeroalon20:11:40
A girl must be in the last chair.
Ispxye_6020:11:40
b/c it didn't consider the girl being in the last chair
venkataraman20:11:40
a girl has to be in the last chair!
rrusczyk20:11:47
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.
rrusczyk20:12:13
What do we have to do to deal with this?
cmpgm88@yahoo.com20:13:02
account for the two girls, then continue
FantasyLover20:13:02
Pick 2 girls and let them seat first
Ttocs4520:13:02
consider the last chair first
rrusczyk20:13:17
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 for the number of seatings?
Aeroalon20:13:36
There must be a girl in the first chair, so we have 4 choices for that. Then a girl in the last chair, 3 choices. The remaining 5 students can be seated in anyway. So it's 4x3x5! = 4x3x5x4x3x2x1.
subus20:13:36
4x3x5! or 5!x12 or 120x12 or 1440?
AIME1520:13:36
4*3*5*4*3*2*1
ailujailub20:13:36
4*3*5*4*3*2*1
cmpgm88@yahoo.com20:13:36
rrusczyk20:13:57
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.
ailujailub20:14:22
4 x 3 x 5 x 4 x 3 x 2x 1
ailujailub20:14:23
in other word 5! x 12
LMB12320:14:23
5!x4x3
rrusczyk20:14:24
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:
rrusczyk20:14:28
4 x 3 x 5 x 4 x 3 x 2 x 1 = 1440
rrusczyk20:14:32
ways to seat the students such that there is a girl on either end.
rrusczyk20:14:37
This example brings up two important counting concepts.
rrusczyk20:14:49
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:
rrusczyk20:14:59
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.
rrusczyk20:15:27
However, there are other clever ways for dealing with restrictions. Let's check a couple others out:
rrusczyk20:15:31
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?
rrusczyk20:15:42
What's wrong with this solution:
rrusczyk20:15:48
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.
rrusczyk20:15:55
What's wrong with that solution?
Colette20:16:20
Ali can be in the first chair
Ttocs4520:16:20
if Ali is on the edge, there is only one not allowed seat
FantasyLover20:16:20
Ali can seat in either first or last chair
AIME_is_hard20:16:20
if ali is at either end, then brianna has 5 choices
rrusczyk20:16:28
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.
rrusczyk20:16:36
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?
qwertythecucumber20:16:48
i would use complementary counting
FantasyLover20:16:48
complementary counting
rrusczyk20:16:51
What's that?
nustrebhtuc120:17:02
just use complementary counting and count number of ways with them next to eachother than subtract from total
ailujailub20:17:02
You do complementary counting and find all of the ways they can sit together then subract those ways from
kookamunga20:17:02
Find the number of ways to seat Ali and Brianna next to each other... then subract that from the number of ways with no restrictions
Aeroalon20:17:02
Counting what you don't want.
rrusczyk20:17:05
Exactly.
TheMan199820:17:14
counting whats not there, the nsubtracting that from the whole
rrusczyk20:17:17
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.
rrusczyk20:17:22
Instead of counting our desired seatings directly, we count what we don't want and subtract.
rrusczyk20:17:29
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.
rrusczyk20:17:38
In how many ways can we seat Ali and Brianna if they are together?
rrusczyk20:18:20
I see a lot of different answers. Give me some justification for your answers.
Aeroalon20:19:04
FantasyLover20:19:04
Ali and Brianna can seat together in 6 ways, and they can change seats so *2, and the rest can seat in 5! ways so it's 6*2*5!
rrusczyk20:19:20
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.
rrusczyk20:19:29
But 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.
rrusczyk20:19:40
So, in how many ways can we seat them so that they are apart?
nustrebhtuc120:20:10
7!-6!*2
jessica.waz.here20:20:10
7!-(6!*2)
AIME_is_hard20:20:10
3600
CubeX20:20:10
3600 ways!:)
Aeroalon20:20:10
We subtract 6!*2 from 7!.
rrusczyk20:20:23
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.
rrusczyk20:20:34
How can we compute this number quickly?
TheMan199820:20:48
Aeroalon20:20:48
Factor it.
qwertythecucumber20:20:48
factor out 6!
aznkid71120:20:48
Taking out the common factor 6!
rrusczyk20:20:52
We write 7! - 2 x 6! = 7 x 6! - 2 x 6! = 5 x 6! = 5 x 720 = 3600.
rrusczyk20:21:05
(That's even faster than your calculator if you know what you're donig!)
rrusczyk20:21:13
This example brings up a couple more important tactics.
rrusczyk20:21:17
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'.
rrusczyk20:21:27
Second, when your restriction is that some of your items must remain together when putting them in a row, a useful tactic is to consider the items all together as a single item, as we did AliBrianna above. Then you separately consider how many ways you can order the items within the group.
rrusczyk20:21:39
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!
rrusczyk20:22:16
The first of these three problems was considerably easier than most of the problems we will do in the course. The second and third are closer to the middle in difficulty, though they are still a good bit easier than the average problem.
rrusczyk20:22:33
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 slower than we did here (in which we introduced 4 general tactics in two problems!)
rrusczyk20:22:41
You can find more questions like those we cover in the course by checking out the Post Test for the course here:
rrusczyk20:22:51
The course will meet for 12 weeks on Mondays, 7:30 PM - 9 PM Eastern, starting March 2. The course ends May 18. Each class is 90 minutes.
rrusczyk20:23:18
Classes are a good bit more organized than what we just went through -- there are fewer students, and there's an assistant instructor to handle questions.
rrusczyk20:23:25
I'm alone here :)
rrusczyk20:23:33
The course will be taught by Ashley Ahlin. Ashley was the first female to win a medal at National MATHCOUNTS, placing 3rd in 1987. She also won 1st place in the Westinghouse Science Talent Search. Later, Ashley served on the MATHCOUNTS problem writing committee and spoke at the national awards banquet. She has taught at the high school and college levels, and in summer programs for all age levels. Ashley finished her Ph.D. in math at the University of Chicago in 2001.
rrusczyk20:23:47
This course will use a textbook in conjunction with the course: our own Introduction to Counting & Probability book. The material covered in the textbook is roughly equivalent to the material covered in the course. You can see the table of contents and some excerpts from the book here:
rrusczyk20:24:11
The book is required for the course. Students will be able to read additional material that complements the lectures, and will have access to a large number of practice problems at varying levels of difficulty. We are recommending that students read the corresponding chapter(s) in the book before each lecture, and attempt some of that chapter's Review and Challenge Problems after each lecture. We also expect to spend some class time answering students' questions about problems from the textbook.
Aeroalon20:24:17
Will the entire Introduction to Counting & Probability book be covered from cover to cover?
rrusczyk20:24:22
Pretty much, yes.
rrusczyk20:24:30
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 Challenge Sets -- for which you should write up your full solutions and submit them. These solutions will be read, and you will receive detailed feedback.
rrusczyk20:25:14
This course is also supplemented by our revolutionary online learning system, Alcumus. Alcumus consists of a database of problems and video lessons, and is backed by an algorithm that delivers problems to students based on their performance on previous problems. Throughout the course, students will be given guidelines about what they should be doing with Alcumus, which will provide much of the basic practice required to master the material. Because students will have Alcumus to reinforce the basics, most of the message board problems and Challenge Sets will focus on harder material.
ligeo19520:25:40
How long will we have for each challenge set?
rrusczyk20:25:43
3 weeks.
rrusczyk20:25:48
Are there any questions about this class or the textbook?
nustrebhtuc120:25:58
do u have a class for Intermediate Counting and Probability, it seems a littlke hard to learn without an instructor
rrusczyk20:26:17
Yes, we have an Intermediate Counting class starting in March, too. There is a Math Jam about that classs on Monday, March 2.
AIME1520:26:20
How come the chalenge sets are 3 weeks, it's 8 weeks for the classes I've taken.
rrusczyk20:26:37
We've changed the intro classes starting this spring -- shorter Challenge Sets, less time to do thim.
physwiz20:26:39
Can we watch this later. Is it recorded?
rrusczyk20:26:50
The transcript will be available on the Math Jams pages.
CubeX20:26:55
isn't it hard to teach these lessons all by yourself?:whistle:
rrusczyk20:26:57
Yes :)
Jericho kid20:27:00
what is the avg. age of students in this class?
rrusczyk20:27:20
Most of the students in Intro Counting are grades 7-9, with some 6th graders and some 10th graders.
all4math20:27:22
What is Pascal's triangle
rrusczyk20:27:31
Take the class or read the book and find out ;)
cmpgm88@yahoo.com20:27:39
Is there a more advanced class?
rrusczyk20:27:45
Yes, the Intermediate Counting class.
Aeroalon20:27:47
Will there be a Introduction to Number Theory class beginning in March?
rrusczyk20:27:59
No; the next Intro Number Theory class starts in June.
LMB12320:28:02
Should I take the Intro to Algebra course before counting and probability?
rrusczyk20:28:24
If you don't have a solid algebra background, yes. If you have had a regular school Algebra 1, that's enough algebra for the Counting class.
all4math20:28:30
About how much does each class cost
rrusczyk20:28:41
This varies by class. You can read about them here:
ailujailub20:28:44
I'm in 6th grade and came in as 1st 6th grader in the chapter for mathcounts, would this be suitible for me
rrusczyk20:29:06
Possibly. Almost certainly the Intro Algebra class would be right. The counting would depend on how much Algebra you already know.
qwertythecucumber20:29:20
you got your intros and intermediate texts. what's next?
rrusczyk20:29:29
Sleep. Those took a long time to write:)
saszs20:29:31
When you say solid what do mean by saying a solid algebra backround?:-o
rrusczyk20:29:34
Algebra 1
Aeroalon20:29:36
Where exactly would this class fit into a standard Algebra I, Geometry, and Algebra II schedule?
rrusczyk20:30:03
It doesn't, because the typical curriculum has a very bad hole in it -- it doesn't cover much discrete math because it is too focused on calculus.
rrusczyk20:30:43
This is a very large failing of the math curriculum -- it's becoming a computerized world, and the math of computers is discrete math more than algebra.
rrusczyk20:30:58
Here's an article we wrote on this topic:
Aeroalon20:31:01
So most of the material in this book isn't covered in a standard school curriculum?
rrusczyk20:31:18
Correct, much of it is not (or it is only lightly covered -- just the basic facts, no real problems.)
aznkid71120:31:29
Is there a book about Calculus in AoPS?
rrusczyk20:31:36
There will be by the end of the year.
LMB12320:31:39
What is an example of an algebra 1 level problem? I'm iin sixth grade, I'm not sure if I've had it.
rrusczyk20:31:51
Look at the "Are You Ready?" test on this page:
AIME_is_hard20:32:07
are there going to be intermediate geometry or intermediate number theory books?
rrusczyk20:32:09
Some day :)
cmpgm88@yahoo.com20:32:16
What is the "For the Win" program? Could it help with this class?
rrusczyk20:32:29
That's mainly a game for MATHCOUNTS Countdown round preparation.
ritwik_anand20:32:32
what is discrete math?
rrusczyk20:32:38
Read that article and see.
Aeroalon20:32:41
What about an "Advanced Algebra" book? xD
rrusczyk20:32:46
In a couple years :)
janeandraka20:32:50
So my Algebra 1 class is focused on calculus
rrusczyk20:32:58
Yes -> it is on the path to calclulus.
mark029520:33:03
how many days we can recieve the textbook?
rrusczyk20:33:24
Two shipping options: fast (3-5 days) or slow (2-3 weeks). Slow is cheaper. See the bookstore for details.
kookamunga20:34:00
What Introduction Series class would you recommend the most for someone studying for mathcounts?
rrusczyk20:34:32
All of them are suitable for MATHCOUNTS. If you're just getting started in problem solving math, I'd recommend the algebra (particularly if you haven't taken an Algebra 1 class).
rrusczyk20:35:20
After that, the Counting class is the most important -- many top teams spend the lion's share of their time on this topic (Jeff Boyd, coach of 3 of the last 4 national champ teams told me he spends half his time on counting. Guess what book he uses :) )
azn_invazn20:35:43
Does the Intro to Algebra class include many things that are not in normal Algebra classes?
rrusczyk20:35:54
Yes - much of the course fits that description.
CubeX20:35:57
Does he use AoPS?
rrusczyk20:36:00
:)
AIME_is_hard20:36:08
theres a class specifically for mathcounts
aznkid71120:36:08
Are there any classes for Advanced Mathcounts? I got a flyer from Mathcounts that was a gift certificate to AoPS for 20$ and there was a class called "Mastering Mathcounts" that said it was on November 11th.
rrusczyk20:36:24
We are offering the MATHCOUNTS - specific classes in the summer.
motu120:36:30
I haven't finished the Algebra 1 course, so which Introduction Series Class would you recommend
rrusczyk20:36:40
If you've started Algebra 1, you're probably ready for the counting.
rrusczyk20:36:51
You can use the diagnostic tests on the site to help you decide.
CubeX20:37:03
Can you give me a link to the summer mathcount class?
rrusczyk20:37:15
Diagnostics, and links for the MATHCOUNTS classes, can be found here:
ritwik_anand20:37:17
is the course based on the Aops books?
rrusczyk20:37:19
Yes
silverfang1320:37:25
i'm in sixth grade and haven't taken any AoPS courses yet. is it too hard to take more than one course at once?
AIME1520:37:44
no, as long as you spend a little time
rrusczyk20:37:52
Depends on how much time you have. For the Intro classes, you should expect to spend 5-8 hours/week. If you have plenty of time, you can take 2.
janeandraka20:37:56
I got 3rd in chapter of anne arundel county and top 6th grader would this help me
rrusczyk20:38:00
Congrats, and yes.
HAARS2620:38:02
ARE THE DIAGNOSTIC TESTS FOR ALL AGES
rrusczyk20:38:05
Yes.
aznkid71120:38:07
I would recommend to a lot of people getting ready for MATHCOUNTS to use Introductory to Counting and Probability because it helps A LOT
aliceindia20:38:15
The classes are really helpful as the teacher is there to help you with what you don't know and also you need to spend time with it..
rrusczyk20:38:18
Unpaid endorsements :)
venkataraman20:38:37
When is ALCUMUS going to be extended to other topics such as geiometry?
rrusczyk20:38:49
Algebra this summer and fall. Number theory after that.
rrusczyk20:39:08
Let's do some more math, and then I'll take more questions.
rrusczyk20:39:26
But first, a word from our sponsor:
Aeroalon20:39:30
I would recommend the Introduction to Counting and Probability book as well, I have only gone through a few chapters but have already seen many places where I could have used the information for MATHCOUNTS. :)
rrusczyk20:39:32
Introduction to Geometry
rrusczyk20:39:50
In the Introduction to Geometry class we cover all the fundamentals of geometry. We will start with a few days covering the basic tools such as triangle congruence, similarity, power of a point, relationships between angles and circles, etc., then dive into using those tools and more to solve increasingly difficult problems.
rrusczyk20:40:17
Most of the problems in the course will be at the MATHCOUNTS and AMC-10 level of difficulty, but we will be throwing in a few harder problems occasionally to show how to use very basic ideas to solve very challenging problems.
rrusczyk20:40:20
Here's a sample problem:
rrusczyk20:40:24
In the diagram shown, DEOC is a square. The radius of circle O is 6 in. What is the number of inches in AC? Express your answer in simplest radical form.
rrusczyk20:40:34
rrusczyk20:40:50
In order to find AC, what will we need?
FantasyLover20:41:09
CO
ritwik_anand20:41:09
find the side length of the square
Aeroalon20:41:09
OC.
subus20:41:09
OC
concorde20:41:09
the length of the side of the square
qwertythecucumber20:41:09
CO
kite4520:41:09
length CO
rrusczyk20:41:12
We need AO, which we already have, and OC. How can we find OC?
all4math20:41:33
The sides of the square which has a diagonal of 6
rrusczyk20:41:40
OC is a side length of a square.
rrusczyk20:41:48
We know the 6 inch radius of the circle is also the diagonal of the square. Now what is the side length of the square?
nustrebhtuc120:42:00
or use 45-45-90 short cut
aznkid71120:42:00
6/sqrt2
qwertythecucumber20:42:00
divide that by sqrt2
Ispxye_8520:42:00
6/rt2
concorde20:42:00
6/sqrt2
aznkid71120:42:00
6/sqrt2
rrusczyk20:42:04
Because the diagonal has length 6 and OC is a side, we have:
rrusczyk20:42:09
rrusczyk20:42:15
How do we find AC?
qwertythecucumber20:42:26
pythagorean theorem
FantasyLover20:42:26
pythagorean theorem
aznkid71120:42:26
pythagorean theorem
TheMan199820:42:26
now use pythagorean theorem
rrusczyk20:42:33
And what do we get?
Ispxye_8520:42:36
how did you simplify that?
rrusczyk20:42:53
Good question: I multiplied the numerator and denominator by sqrt(2):
rrusczyk20:43:22
rrusczyk20:43:29
And what's AC?
Kathy020920:43:42
3 times the root of 6
ritwik_anand20:43:42
3 square root 6
kookamunga20:43:42
3sqrt6?
janeandraka20:43:46
3 radical 6
rrusczyk20:43:52
We have a right triangle (AOC), so we use the Pythagorean Theorem:
rrusczyk20:44:00
rrusczyk20:44:20
That problem was on the easy end of the problems that are covered in the Intro Geometry class.
rrusczyk20:44:57
Next problem:
rrusczyk20:44:59
Sector OAB is a quarter of a circle of radius 3 cm. A circle is drawn inside this sector, tangent at three points as shown. What is the number of centimeters in the radius of the inscribed circle? Express your answer in simplest radical form.
rrusczyk20:45:29
rrusczyk20:46:04
We need the radius of the small circle, so what should we do with our diagram?
ritwik_anand20:46:16
connet points of tangencies
rrusczyk20:46:21
Connect them to what?
FantasyLover20:46:36
Draw the center of the circle
TheMan199820:46:36
draw 3 lines, to each point of tangency
Ispxye_8520:46:36
center
janeandraka20:46:36
center of circle
ligeo19520:46:36
the center pt of the smaller circle
rrusczyk20:46:48
We want the radius of the small circle, so we add radii to our diagram.
rrusczyk20:47:04
In general, when we have tangency, it's often helpful to draw radii to points of tangency.
rrusczyk20:47:19
Why do we like to draw radii to points of tangency?
Ttocs4520:47:37
It makes right angles
ritwik_anand20:47:37
right angles
math_galois20:47:37
make right triangles
TheMan199820:47:40
to create rectangles, right triangles, etc.
rrusczyk20:47:42
We like to draw radii to points of tangency because we get right angles
rrusczyk20:47:45
We like right angles.
all4math20:47:48
What are tangencies?
rrusczyk20:48:00
Where the circle touches another curve at one point without crossing it.
rrusczyk20:48:22
Here are the radii drawn to points of tangency:
rrusczyk20:48:23
rrusczyk20:48:43
Notice that we give a variable to the radius, r.
rrusczyk20:49:02
This is a key strategy in many geometry problems: assign a variable to what you seek and try to build an equation for it.
rrusczyk20:49:05
Now what?
TheMan199820:49:08
we have a square
qwertythecucumber20:49:08
we see a square!
rrusczyk20:49:14
We notice that HOGP is a square. How will the square help us?
FantasyLover20:49:30
AIME_is_hard20:49:30
Draw PO
AIME_is_hard20:49:30
rrusczyk20:49:49
Drawing a diagonal in the square will give us a radius of the large circle (FO) in terms of r.
rrusczyk20:49:54
Because the side length of the square is r, the diagonal is r*sqrt2.
rrusczyk20:50:01
rrusczyk20:50:16
Now what?
CubeX20:50:38
well, r*sqrt 2 + r=3
TheMan199820:50:38
r+rsqrt2=3
AIME_is_hard20:50:38
FantasyLover20:50:38
rrusczyk20:50:43
We set up an equation and solve it. We know that OF is a radius, so OF = 3. However, we can write OF = OP + FP = r*sqrt(2) + r.
rrusczyk20:50:52
Now we have an equation and we can solve for r. What do we find?
aznkid71120:51:17
r(sqrt2+1)
TheMan199820:51:17
(1+sqrt2)r=3
rrusczyk20:51:21
Keep going!
Kathy020920:51:31
3 times root of 2 minus 3
FantasyLover20:51:31
ligeo19520:51:31
r=3rt2-3
rrusczyk20:52:03
rrusczyk20:52:26
But that's not the same as what everyone else posted?
rrusczyk20:52:33
What do we do now?
ailujailub20:52:41
I don't get the way to solve the equation
rrusczyk20:52:56
We factored out r on the right side, and then we divided by 1+sqrt(2).
Aeroalon20:53:06
Rationalize the denominator.
venkataraman20:53:07
they rationalized the denominator
Kathy020920:53:07
We need to conjugate it to simplify the denominator
ligeo19520:53:07
get rid of the radical in the denominator
rrusczyk20:53:10
We multiply both the top and bottom by 1-sqrt2.
rrusczyk20:53:20
rrusczyk20:53:27
(This sort of simplification is covered in the Intro Algebra class.)
rrusczyk20:53:31
Notice that we don't just sit and stare at the problem and wait for it to solve itself. We have to add lines and variables so we can build equations.
rrusczyk20:53:40
The first of those two problems is on the easy end of problems we will discuss. The second is a bit easier than average. All the geometric tools we use to solve problems, such as all the special relationships we used to solve these two problems today, will be taught in the class. We don't expect students to have any background knowledge in geometry.
rrusczyk20:53:48
You can find more questions like those we cover in the course by checking out the Post Test for the course here:
rrusczyk20:54:15
This course is a full geometry course. The equivalent (and a bit beyond) of a typical honors geometry course.
rrusczyk20:54:49
Many students take this in addition to a regular geometry class.
randomcanadiangirl20:54:52
does that mean that if you take this class, can you pass the semester exams for geometry 1?
rrusczyk20:55:06
If you do the work in this class, you should find your school geometry easy.
saszs20:55:09
A full geometry class is the 9th grade course right?
rrusczyk20:55:12
Yes.
rrusczyk20:55:13
The course will meet for 24 weeks on Tuesdays, starting March 3, at 7:30 PM Eastern / 4:30 PM Pacific. Each class is 90 minutes, and the last class is on August 11.
rrusczyk20:55:20
The course will be taught by Joshua Zucker. Joshua joined AoPS as a part-time instructor in 2007. He discovered his love for number theory at Dr. Arnold Ross's summer program at Ohio State University a bit over 20 years ago. 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, for ten years was a problem writer for MATHCOUNTS, and is the proud father of three children
rrusczyk20:55:37
This course will use a textbook in conjunction with the course: our own Introduction to Geometry book. The material covered in the textbook is roughly equivalent to the material covered in the course. You can see the table of contents and some excerpts from the book here:
rrusczyk20:55:55
The book is required for the course. Students will be able to read additional material that complements the lectures, and will have access to a large number of practice problems at varying levels of difficulty. We recommend that students read the corresponding chapter(s) in the book before each lecture, and attempt some of that chapter's Review and Challenge Problems after each lecture.
venkataraman20:56:06
Did he teach Advanced Mathcounts and AMC8
rrusczyk20:56:10
Yes, he did.
rrusczyk20:56:16
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 8 longer problem sets for which you should write up your full solutions and submit them. These solutions will be read, and you will receive detailed feedback.
sravyasiri20:56:21
will this geometry course help you improve in school?
rrusczyk20:56:24
Yes.
rrusczyk20:56:38
The rest of this Math Jam will be questions & answers about the classes.
rrusczyk20:56:45
There will be no more mathematics.
kookamunga20:56:48
Will you be doing the other Math Jams, Mr, Ruscyzk?
rrusczyk20:56:53
Many of them, yes.
randomcanadiangirl20:57:08
how do you write exponents and radicals on this message board??
rrusczyk20:57:26
With LaTeX. You can click on the math that other people have written to learn how they did it.
concorde20:57:29
does the geometry course cover euclidian geometry
rrusczyk20:57:45
Yes, the course is Euclidean geometry.
saszs20:57:57
What's Euclidean geometry
rrusczyk20:58:12
What we just did :) (What you think of as geometry is Euclidean Geometry)
kookamunga20:58:17
I've only taken one class, which was taught by Mr. Zucker, so I don't know how the other instructors compare but he was awesome, if that helps anybody
concorde20:58:28
In the high school which I will be attending next year, the students are divided into 2 different geometry courses. One is an honors geometry, and one is what the school calls honors and accelerated. Will this course help
rrusczyk20:58:42
Certainly, this course would help you with that one.
sravyasiri20:58:45
can we sign out if we dont have any more questions?
rrusczyk20:58:47
Yes.
randomcanadiangirl20:58:50
If you're taking algebra 1, and you only did ok on the self test, should you take this?
rrusczyk20:59:08
I would recommend the Intro Counting class first.
crazyasianvampire20:59:10
Where can you find the self test?
mtwister20:59:30
Do you have plans to offer classes at a different time of day? Weekends?
rrusczyk20:59:57
Probably not -- we have polled several times on this, and the time slot we use is by far the most popular.
aznkid71121:00:09
When we sign up, do we just enter the code if you have a certificate?
rrusczyk21:00:26
It will be clear as part of the checkout procedure where to enter gift certificate codes.
randomcanadiangirl21:00:28
what is "counting"?
rrusczyk21:01:10
It covers how to count things (which is much more complicated and interesting than it sounds!) It provides the foundation of discrete math, which is an area of mathematics that is very important for understanding computer science.
saszs21:01:14
Do you think algebra 2 is two advanced for a sixth grade extra class
rrusczyk21:01:33
Depends on the sixth grader, but I wouldn't recommend it. I would recommend our Counting and Number Theory classes instead.
rrusczyk21:01:48
More interesting, and you'll get the algebra 2 eventually anyway.
aznkid71121:01:51
Of all the books, what is the best book for Mathcounts?
rrusczyk21:01:58
Our Intro series :)
rrusczyk21:02:11
And when prepping for Nationals, Volume 1 of Art of Problem Solving.
TheMan199821:02:14
is algebra 2 intermediate algebra?
rrusczyk21:02:33
We cover much of it in our Intro Algebra class, and the rest in Intermediate.
crazyasianvampire21:02:56
If the series it too advanced, what would you recommend using?
rrusczyk21:03:10
If you're not yet ready for our Intro books, I recommend trying MOEMS problems.
melinda21:03:30
What curriculum do you suggest for elementary school math instruction (homeschooling) and prealgebra? We have used Singapore math thru 6A and are planning to use Singapore Math's prealgebra book "New Elem Mathematics" for grades 6 and 7 but not sure when to stop with that curriculum and switch over to your class (to avoid overlap).
rrusczyk21:04:12
Many homeschoolers use the elementary Singapore math and then switch over to AoPS, particularly if their children are particularly strong at and interested in mathematics.
gihun957821:04:20
Is the Vlume 1 and 2 of Art of Problem Solving good for those students who are starting to prepare for AMC?
rrusczyk21:04:23
Yes
Aeroalon21:04:25
MOEMS?
saszs21:04:25
What does moems stand for
rrusczyk21:04:34
Math Olympiad in the Elementary and Middle Schools
Jericho kid21:04:47
what are the book titles for your intro series?
janeandraka21:05:06
are volume 1 and 2 good for state round mathcounts
rrusczyk21:05:17
volume 1, yes. Volume 2 is much more advanced.
saszs21:05:29
If any of you like to read about mathematicians you should read the book Count Down and watch hard problems
rrusczyk21:05:45
Those are nice for seeing and reading about winners of these sorts of contests.
rrusczyk21:05:56
(And the author of CountDown is a great guy, too :) )
aznkid71121:06:00
Is there any chance of getting work at AoPS when I grow up? :-D
rrusczyk21:06:29
Sure -- many of our past students are our assistants now (they're at MIT or Harvard or Stanford or Princeton or CalTech. . . )
crazyasianvampire21:06:33
Wow did you write CountDown?
TheMan199821:06:33
who is the author of count down?
saszs21:06:48
Steve Olson
rrusczyk21:06:50
Steve Olson (but yes, I'm a pretty good guy, too :) )
cmpgm88@yahoo.com21:06:54
Is there a "For the Win" prgram for advanced math students?
rrusczyk21:07:01
Not yet. Maybe someday.
CubeX21:07:03
Which is harder: The Basics or Algebra 1?:-o
rrusczyk21:07:06
Basics.
ligeo19521:07:11
how much harder are the intermediate classes than the intro classes?
rrusczyk21:07:16
A lot harder, yes.
motu121:07:19
What do you learn in Algebra2 that you don't learn in Algebra1
rrusczyk21:07:44
That varies a great deal from school to school, mainly because there isn't much general agreement on what those classes are.
vasudha21:07:47
my 4th grader is brezing through in class .any suggestion what he could qualify for at aips
rrusczyk21:07:56
Have him take a look at the PreTest for Intro Algebra.
rrusczyk21:08:18
It's possible he's ready -- we do have 4th graders in that class, but it's rare.
rrusczyk21:08:41
If he's not ready (either mathematically, or in terms of maturity), I'd recommend using some of the MOEMS problems with him until he is.
janeandraka21:08:52
is there a course covering the basics volume 1
rrusczyk21:09:08
There's not one tied to it, the way we have classes tied to our other books.
vasudha21:09:10
my only fear is that your classes go too fast for him
rrusczyk21:09:42
That may be, which is why you might want to wait until he's a little older. One strategy some parents use is to work with the young ones themselves with our text until they get a little older.
rrusczyk21:09:59
That way, they've seen the basics once before they take the class, and can handle the pace better.
cat12321:10:01
are you going to offer intro to algebra class in the fall?
rrusczyk21:10:03
Yes.
Aeroalon21:10:07
Which would be most beneficial for MATHCOUNTS: Volume 1: the Basics, Introduction to Counting & Probability, Introduction to Geometry, or Introduction to Number Theory?
rrusczyk21:10:25
Depends on the level. I'd put them in this order for State/Nats prep:
rrusczyk21:10:41
Intro Counting, Vol 1, Intro NT, Intro Geometry
rrusczyk21:10:56
For Chapter prep, I'd leave Vol 1 and Geometry off the list.
Aeroalon21:11:03
Starting from most to least?
rrusczyk21:11:05
Yes
gihun957821:11:10
Although I didn't start to learn intermediate problems, if I study Volume 1 and 2 of Art of Problem Solving and practice with previous AMC problems, would it increase my math skills and AMC score?
rrusczyk21:11:15
Absolutely.
cmpgm88@yahoo.com21:11:17
As a 9th grader who loved MathCounts, is there a High School alternitive for Mathcounts? (I'm going to attempt to get my school system involved if there is...)
rrusczyk21:11:51
Some contests to look at: AMC (www.unl.edu/amc), ARML (www.arml.com), Harvard-MIT, USAMTS, iTest, Purple Comet (and there are many others).
saszs21:11:53
How hard is the putnam exam
rrusczyk21:12:01
Very hard (that's a college contest)
Jericho kid21:12:03
what is the best way to make up a class if one has to be missed?
rrusczyk21:12:30
There is a full transcript made of every class that you can review after class.
rrusczyk21:12:41
There is a class message board you can use to ask questions.
gihun957821:12:44
How long does it usually take to ship the textbooks if I order them? (without charging any extra for faster delivery.)
rrusczyk21:12:59
You'll get them in either 3-5 days and pay more or 2-3 weeks and pay less.
LMB12321:13:01
As a 6th grade student, can I begin AoPS with the Counting and Probability course in March and then take the Introduction to Algebra course this summer when you are teaching it? I've done fairly well on both pretests. Thanks!
rrusczyk21:13:04
Sure.
all4math21:13:08
What happens if you don't do your homework
rrusczyk21:13:13
You don't learn as much.
saszs21:13:16
How about ARML
rrusczyk21:13:24
AMC - level difficulty.
aznkid71121:13:27
I don't know what Nationals is like. Can we do a hard problem? Or is it copyright?
rrusczyk21:13:33
Ask on the MATHCOUNTS message board.
ligeo19521:13:35
If i'm currently taking algebra 2 would it be better to take the intro or the intermediate algebra?
rrusczyk21:13:48
Intro would probable be too basic for you.
saszs21:13:58
How do you solve the problem: How many of the integers from 1-1000 incluive can be expressed as the difference of the squares of two nonnegative integers?
rrusczyk21:14:08
We cover problems like that in the Intro Algebra class.
TheMan199821:14:45
how much harder is the intermediate algebra class than a regular intermediate algebra class?
rrusczyk21:14:57
It's much harder than what you'll see in school, if that's what you're asking.
aznkid71121:15:02
So is this class right now for free? or is this just a taste of whats going to be in the classes
rrusczyk21:15:10
Not sure what you're asking. This math jam is free.
gihun957821:15:12
For the Volume 1 and 2 of Art of Problem Solving, is it a collection of problems that can benefit us or the mixture of concept lessons and problems for learning?
rrusczyk21:15:19
It has lessons in addition to problems.
cmpgm88@yahoo.com21:15:36
Can we use problems from this site to teach others, or is it considered copyright violation?
rrusczyk21:15:52
You can use occasional problems -- you can give away transcripts, etc.
aznkid71121:16:29
I just noticed that you don't have any more books of the "All Time Greatest Mathcounts Problems." Why?
rrusczyk21:16:34
We ran out, I guess
parakeet21:16:39
The Intro Algebra and the Intro Geometry classes both seem to run concurrently, on Wednesdays and Tuesdays respectively. Is it practical to register for both classes, in terms of weekly homework loads and challenge sets? ANy advice?
rrusczyk21:17:13
Depends on how much time you have -- you should expect to spend 5-8 hours/week on the course to get the most out of it.
rrusczyk21:17:29
If you have a lot of time, you can handle 2 classes at once, but you might want to wait until the summer to double up.
LMB12321:17:37
What if I begin a course and take 3 or less classes (Counting and Probability) and it is too difficult...would I be able to transfer to the Algebra course?
rrusczyk21:17:38
Yes.
Kathy020921:17:54
I'm currently studying Alegebra 2 along with the book, Intro to Algebra. I found it a little difficult to understand a few questions. So, I decided to take this class and I'm wondering what other book I should study next.
rrusczyk21:18:24
After the Intro Algebra book, I would strongly recommend the Intro Counting and Intro Number Theory books. You're quite young to be getting started with that, so you have plenty of time to explore!
cmpgm88@yahoo.com21:18:35
How can we reach you if we still have more questions?
rrusczyk21:18:48
Write classes@artofproblemsolving.com if you have questions after the Math Jam.
cat12321:18:55
Are the Problem Solving Books to be used after one completes the Intro books?
rrusczyk21:19:02
If you are very interested in contests, yes.
rrusczyk21:20:04
That's it for the Math Jam tonight. It's past my bedtime! If you have any more questions about the classes, please feel free to write me at classes@artofproblemsolving.com!
