| Transcript
for the Math
Jam "AoPS Classes Math Jam"
on Sep 26. |
| Math Jam hosted by DPatrick
(Dave Patrick ). |
DPatrick19:29:57
Hello, and welcome to the first Art of Problem Solving Fall 2007 Classes Math Jam!
DPatrick19:30:06
My name is Dave Patrick, and I am an instructor at the AoPS Online School.
DPatrick19:30:16
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.
DPatrick19:30:28
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.
DPatrick19:30:53
Also, only moderators can enter into private chats with other people in the classroom.
DPatrick19:31:07
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.
DPatrick19:31:27
Today we will be discussing two of our upcoming fall classes:
- Introduction to Counting & Probability (starts October 8 and runs for 12 weeks)
- Introduction to Geometry (starts October 5 and runs for 24 weeks)
DPatrick19:31:42
There will be other Math Jams in the coming weeks to discuss to discuss the remainder of our fall schedule.
DPatrick19:31:59
All of our online classes take place in this Virtual Classroom.
DPatrick19:32:12
Introduction to Counting & Probability
DPatrick19:32:21
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.
DPatrick19:32:41
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).
DPatrick19:32:59
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.
DPatrick19:33:21
We'll now take a look at a sample problem from the course, which highlights some of the tactics we'll investigate in this class.
DPatrick19:33:28
DPatrick19:33:39
Usually, after posting a problem, the instructor will also post a link to the problem, as I just did above. This way, the student can click on the link and keep the problem open in a separate window, so that he or she can follow along with the solution. (If clicking on the link doesn't do anything, try holding down the Ctrl key as you click. If it still doesn't work, you may need to change the settings on your pop-up blocker.)
virtuoso19:34:09
7!
virtuoso19:34:09
5040
diwa_vijay19:34:09
5040
tennisstar19:34:09
7!=5040
speedcuber19:34:09
7!
DPatrick19:34:17
Right.
DPatrick19:34:25
This is a straightforward application of multiplication: there are 7 students who could sit in the first seat.
DPatrick19:34:34
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.
DPatrick19:34:43
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.
DPatrick19:34:51
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.
DPatrick19:35:05
As some of you already knew, 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'.
DPatrick19:35:20
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?
DPatrick19:35:42
(remember, there are 4 girls and 3 boys in the group.)
DPatrick19:36:07
What's wrong with this answer:
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:
4 x 6 x 5 x 4 x 3 x 2 x 1 seatings.
What's wrong with that?
diwa_vijay19:36:52
there can be a boy in the last seat in that method
tennisstar19:36:58
there isn't a girl in the last chair
DPatrick19:37:12
Right -- 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.
DPatrick19:37:41
What do we have to do to deal with this?
LHM19:38:13
1st put the 2 girls into the first and last chairs
diwa_vijay19:38:27
solve for the first and last and then put 5! in the middle
virtuoso19:38:27
4 choices for 1st seat, 3 choices for last seat, then 5! choices for the remaining people in the middle seats
DPatrick19:38:32
Good. 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.
virtuoso19:38:48
4*3*5!
tennisstar19:38:48
4x3x5x4x3x2x1
nasafan19:38:48
4*3*5!=1440?
tennisstar19:38:48
you have 4 choices for the first girl in the first chair, 3 choices for the girl in the last chair, so now you have 5 people left
DPatrick19:39:00
Exactly. 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.
DPatrick19:39:11
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:
4 x 3 x 5 x 4 x 3 x 2 x 1 = 1440
ways to seat the students such that there is a girl on either end.
DPatrick19:39:27
This example brings up two important counting concepts.
DPatrick19:39:34
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.
DPatrick19:39:46
This brings us to our second important counting concept:
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.
DPatrick19:40:06
Let's change up the problem again:
DPatrick19:40:11
DPatrick19:40:27
What's wrong with this solution:
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.
What's wrong?
DPatrick19:41:41
What happens if Ali is seated at the end of the row?
tennisstar19:41:49
you don't know if ali will be sitting at the end of the row
ChaosTheory19:41:58
Then there is only one place Brianna can't sit.
yuria19:42:07
then Brianna has 5 choices
speedcuber19:42:12
then there's one more place for brianna
DPatrick19:42:14
Right. 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.
DPatrick19:42:24
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.
xpmath19:42:31
complimentary counting
virtuoso19:42:31
Approach: Total Possible # of Ways - # of ways Ali and Brianna are together
DPatrick19:42:51
Yes. Instead of counting our desired seatings directly, we count what we don't want and subtract from the total.
DPatrick19:43:09
We know there are 7! ways to seat the 7 students 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.
DPatrick19:43:27
In how many ways can we seat the students if Ali and Brianna are together?
virtuoso19:43:43
7! (Total) - 6!*2 (Treat Ali and Brianna as one person, but they can rotate - Ali-Brianna, or Brianna-Ali)
xpmath19:43:43
consider Ali and Brianna as one person?
xpmath19:43:43
2x6!
DPatrick19:43:58
Good. 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.
DPatrick19:44:13
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.
DPatrick19:44:36
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.
LHM19:44:46
3600
virtuoso19:44:46
Answer: 3600
DPatrick19:44:47
We write 7! - 2 x 6! = 7 x 6! - 2 x 6! = 5 x 6! = 5 x 720 = 3600.
DPatrick19:45:00
This example brings up a couple more important tactics.
DPatrick19:45:07
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'.
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.
DPatrick19:45:30
These three basic examples show why it is pointless to memorize your way through counting - I can ask zillions of variations of the above questions. Instead of memorizing your way through each variation, you should learn when to add, when to subtract, when to multiply, and when to divide. Since you already know how to perform these operations, once you know when to do them, you know how to count!
DPatrick19:45:57
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 little easier than the average problem.
DPatrick19:46:10
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!)
DPatrick19:46:26
You can find more questions like those we cover in the course by checking out the Post Test for the course here:
DPatrick19:46:50
The course will meet for 12 weeks on Mondays, starting October 8, at 7:30 PM Eastern / 4:30 PM Pacific. (There are no classes on November 19 or Dec 17-31.) Each class is 90 minutes.
DPatrick19:47:06
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.
DPatrick19:47:32
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:
DPatrick19:48:03
(Note: all of these links will be in the transcript of this Math Jam, which will appear on the web site shortly after the Jam is finished, so you don't need to copy or click on them now.)
DPatrick19:48:22
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.
DPatrick19:48:55
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 two longer problem sets -- a midterm and a final -- for which you should write up your full solutions and submit them. These solutions will be read, and you will receive detailed feedback.
xpmath19:49:17
how would we submit them?
DPatrick19:49:31
By mail, email, or fax. You'll received detailed instructions at the appropriate time.
DPatrick19:50:24
I'll answer more questions about the classes at the end of the Math Jam, but right now, let me talk about another of our fall classes, Introduction to Geometry.
DPatrick19:50:44
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.
DPatrick19:50:56
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.
DPatrick19:51:04
Here's a sample problem:
DPatrick19:51:26
DPatrick19:51:49
virtuoso19:52:23
OD=6, as it is also a radius of Circle O
DPatrick19:52:36
Good - how does that help us?
xpmath19:52:47
CO=6/rt2
ChaosTheory19:52:47
So the side of the square is 6/(root2)
virtuoso19:52:58
Using the 45-45-90 special triangle ratio, we know that CO=6/(sqrt.2)
xpmath19:52:58
CO=3rt2
DPatrick19:53:12
Excellent: triangle OCD is an isosceles right triangle, so we have:
DPatrick19:53:16
nasafan19:53:34
Pythagorean Theorem
virtuoso19:53:34
Then, use Pythagorean theorem
xpmath19:53:34
pythagorean theorem gives AC=3rt6
DPatrick19:53:50
To finish the problem, we use the Pythagorean Theorem on triangle AOC to find AC:
DPatrick19:53:58
DPatrick19:54:15
(Don't worry if you don't know these terms already -- we're going to cover them in the course!)
DPatrick19:54:32
Here's a slightly harder problem:
DPatrick19:54:41
DPatrick19:54:58
nikki19:55:11
what is tangent?
DPatrick19:55:21
"Tangent" means that the circle touches but doesn't cross.
DPatrick19:55:46
We need the radius of the small circle, how can we find it?
DPatrick19:56:33
We need to find something that's not yet drawn in our picture. So let's draw the radius. Where should we draw it?
tennisstar19:57:07
from the middle of the circle to one of the 3 tangent points
virtuoso19:57:07
Center to the tangent points
Darklegacy5219:57:15
from the tangent point to the center of the small cirlce's point?
DPatrick19:57:25
Sure. Let's draw a radius to each point of tangency and label each with length r. We like to draw radii to points of tangency because we get right angles.
DPatrick19:57:31
DPatrick19:57:41
Now what?
virtuoso19:58:01
PGOH is a square
xpmath19:58:08
We form a square
yuria19:58:08
use the square to solve the problem?
DPatrick19:58:19
That's a good observation: we have a square. How does that help us?
tennisstar19:58:42
GO or HO is = to r, because pgoh is a square
nikki19:58:42
we know that HO is the small radius
diwa_vijay19:58:51
the sides=the radius
DPatrick19:58:57
True...but how does that help us?
DPatrick19:59:12
Can we write any other lengths in terms of r?
xpmath20:00:10
Rrt2+r=3
xpmath20:00:19
diagonal of square +r= radius of large quarter circle
seungoak20:00:26
the diagnonal in the square is r rt2 according to the 45-45-90 triangle theorem, so 3=r+r rt2
DPatrick20:00:35
Good! If I draw in PO we can see this more clearly:
DPatrick20:00:41
DPatrick20:00:55
Because the side length of the square is r, the diagonal is r*sqrt2.
DPatrick20:01:05
But OF is now a radius of the big circle, so OF = 3.
DPatrick20:01:13
Now we have an equation and we can solve for r!
DPatrick20:01:22
DPatrick20:01:46
To finish, what can we do to make this answer a bit nicer?
xpmath20:02:04
multiply by 1-rt2
xpmath20:02:04
top and bottom I mean
ChaosTheory20:02:04
Rationalize.
virtuoso20:02:04
put the radical on the top
DPatrick20:02:25
Right, we don't like to leave radicals in the denominator, so we multiply both the top and bottom by 1-sqrt2.
DPatrick20:02:30
DPatrick20:02:47
Notice that we didn'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.
DPatrick20:02:57
The first of those two problems is on the easy end of problems we will discuss. The second is a bit easier than average.
DPatrick20:03:07
Again, don't worry if you don't know the terminology: it will all be covered in the course.
DPatrick20:03:20
You can find more questions like those we cover in the course by checking out the Post Test for the course here:
DPatrick20:03:34
The course will meet for 24 weeks on Fridays, starting October 8, at 7:30 PM Eastern / 4:30 PM Pacific. (There are no classes on November 23 or Dec 21-Jan 4.) Each class is 90 minutes.
DPatrick20:03:52
Oops, I think that date is wrong...
DPatrick20:04:01
October 5 is the first class.
DPatrick20:04:25
The course will be taught by Richard Rusczyk. Richard is the founder of Art of Problem Solving, one of the co-authors of the original Art of Problem Solving textbooks, and author of Art of Problem Solving's Introduction to Algebra and Introduction to Geometry textbooks. He is also one of the co-creators of the Mandelbrot Competition, and the Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a participant in the Math Olympiad Summer Program 1987, 1988 and 1989, the only perfect scorer on the 1989 AIME, and a USA Mathematical Olympiad winner (1989).
DPatrick20:04:48
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:
DPatrick20:05:06
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.
DPatrick20:05:26
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 read, and you will receive detailed feedback.
DPatrick20:05:54
Are there any questions about either of the classes that I discussed today, or about our classes or books in general?
speedcuber20:06:04
about what grade level would you say this course is for?
DPatrick20:06:21
Generally grades 6-10, but students younger or older often take them too.
Graviton00720:06:33
what math level?
DPatrick20:06:52
Use the classes' pre-tests and post-tests to judge the level. They are available on the Classes pages of our website.
LHM20:07:02
What if you can finsh about 70 percent for the Geometry Post Test, should you take the class?
DPatrick20:07:27
In this case, you're probably better off just getting the textbooks and reading the sections that you haven't yet mastered.
LHM20:07:39
I will be missing the whole class every week, I can only read the transcrupt, is that good? I won't be able to ask ?s.
DPatrick20:07:51
You can always still ask questions on the class message board.
DPatrick20:08:05
And the books may also have the answers to your questions.
ChaosTheory20:08:21
If we are unable to take Introduction to Counting and Probability, what are some other resources and books you suggest? How about Geometry?
DPatrick20:08:50
Obviously we would recommend our books first. We don't have any other programs that we specifically recommend, but you can check our Resources pages on the website and/or ask on the Forum.
Nerd_of_the_Ages20:09:01
When is the next time you will offer the next Intro to Geometry?
DPatrick20:09:26
Possibly in the spring of 2008: we're putting together our Spring/Summer schedule as we speak. We hope to have in out in a couple of weeks.
LHM20:09:35
How Much hw do you get in both classes?
Aquila20:09:35
Is there any grading system?
DPatrick20:09:57
We'll have weekly problems posted to the message board. You can post your solutions there if you like.
DPatrick20:10:14
We'll also have longer problem sets, one every 6 weeks. These you write up and turn in to receive commetns.
DPatrick20:10:17
..comments.
DPatrick20:10:35
There are no "grades". We don't give you a letter or numerical score. We give you commentary and feedback.
Rational20:10:39
DO you send report to parents?
DPatrick20:10:40
No.
samsun518820:10:46
any plans to add audio to the classroom? how about using WebEx to broadcast the live class meeting?
DPatrick20:11:18
We have what we think are excellent reasons for not doing this. Please see the "How Classes Work" page on our website to read them, or use the following link:
LHM20:11:41
is most of the HW from the book? If not, where are they from
DPatrick20:11:59
Some will be from the book; other problems will be from past contests like MATHCOUNTS and the AMC>
nikki20:12:03
how long is the intro to geometry course?
DPatrick20:12:04
24 weeks.
wintel88820:12:29
When are you goint to offer 'Intermediate of Algebra'?
DPatrick20:12:41
Probably in the spring, once the new textbook is complete.
Rational20:12:45
How long it takes to get the book after sign up?
DPatrick20:13:14
We'll send it out right away. We recommend that you choose the Priority Shipping: it should take 2-5 days. If you choose the economy shipping, it'll take 2-3 weeks.
speedcuber20:13:24
what grade would you suggest this class is for?
DPatrick20:13:59
Counting & Probability is generally for grades 6-10; Geometry for grades 7-10. C&P requires a little algebra, but not much; Geometry requires that you've had some algebra experience.
tennisstar20:14:17
if i only know 3 questions on the probability test, is the course too difficult for me?
DPatrick20:14:48
If you're taking about the post-test (the "Do I Need This?" test), then no, the course would be ideal for you.
ChaosTheory20:14:57
How can we get formal credit for AoPS classes?
DPatrick20:15:21
You'll have to ask your school what their procedure is, and let us know.
Aquila20:15:27
How do you grade our homework?
DPatrick20:15:46
We'll read it and provide comments on each problem that you submit. You'll be able to download your personal commentary from our website.
Nerd_of_the_Ages20:16:00
When is the next time you offer Intermediate Number Theory. I want to wait a bit to let my algebra skills improve.
DPatrick20:16:11
It starts October 16th; I don't know when it will be offered again.
yuria20:16:17
Is there math jam for Intro to Algebra?
DPatrick20:16:31
Yes, on October 4th (same time).
diwa_vijay20:16:46
what if my parents want a report
DPatrick20:16:57
You can show them your problem set feedback, but beyond that, we don't do any "reporting".
ChaosTheory20:17:10
If we are homeschooled, how can we show credit for AoPS classes?
DPatrick20:17:31
Same answer: you'll have to figure out how you want the "credit", and then let us know. We don't issue grades or formal reporting.
Darklegacy5220:17:38
would these intro courses help me if i want to do well on the amc10? i already have had experience with the amc and i want to get into aime
DPatrick20:17:59
Yes: both courses will have a lot of AMC-level problems.
ChaosTheory20:18:08
How much of the Introductory Algebra material is covered in AoPS Volume I?
DPatrick20:18:37
Some (you can compare the books' tables of contents on our website), but the Intro Algebra material is covered in a lot more detail in the Algebra book and course.
seungoak20:18:43
how will feedback be set up?
DPatrick20:19:01
You'll be able to download it directly from the website. It's easy -- instructions will be given at the appropriate time.
Rational20:19:26
Do you think 5th grader ( with a little pre-algebra) is ready for introduction to Algebra
DPatrick20:20:08
If you can solve most of the problems on the pre-test (the "Am I Ready?" test on the Classes web page from this class), then you should be ready. It depends how "little" the "little pre-algebra" is.
Graviton00720:20:15
Are there any tools for teachers that you provide?
DPatrick20:20:37
None specifically for teachers, but teachers sometimes enroll in our classes to sharpen their problem-solving skills.
Aquila20:20:41
What about SAT? Does this class improve my skills for SAT?
DPatrick20:21:08
To the extent that the classes will help with your overall problem-solving skills, they will help with the SAT. Most students who complete our classes find the SAT easy by comparison.
diwa_vijay20:21:20
If we have a strong skill in mathcounts, enough for maybe a 25 out of 30 and a 7 out of 8, would these classes help me
DPatrick20:21:52
Hard to say -- those are strong MC numbers. Try the classes' post-tests and see how well you do.
Nerd_of_the_Ages20:21:55
Will the workload be pretty bad if we register for both classes at the same time?
DPatrick20:22:38
Not necessarily. We often have students take 2 or 3 classes at once. But it's not necessarily something that we would recommend.
seungoak20:23:04
how long does it take to grade homework?
DPatrick20:23:30
We try to get them done in 1-2 weeks. Since you show all your work, it takes some time to read them all. We want to be able to give you specific comments!
ChaosTheory20:23:48
If we take two or three of the introductory/intermediate subject classes, then do you think it will necessary to also take the AMC classes?
DPatrick20:24:28
Probably not. Aside from the "AMC test-taking strategy" aspect of the classes, which is relatively mino, the Intro classes together should give a solid background for the AMC.
Aquila20:24:33
How much should we spend daily to prepare for the classes? The chapters in the book have quite a few problems at the end. Should we solve all of them before each class?
DPatrick20:25:13
No -- we recommend reading the text before class, but waiting to solve the exercises and problems until after class. (Some of them will be part of the weekly homework sets.)
DPatrick20:25:37
It's hard to say how much time you'll spend, but we generally say about 2-6 hours per week.
Rational20:25:49
How many students in a class maximum?
DPatrick20:26:36
There's no definite maximum. 40-50 students is typical; we may occasionally go larger. If the class gets too larger, we'll split it into 2 groups.
yuria20:26:43
Can a person speed up in the course if s/he finds the content is easy to learn and understand?
DPatrick20:26:59
You can certainly read ahead in the books, but the lectures will stay on the same schedule.
Graviton00720:27:36
How do your books compare to those of CPM?
DPatrick20:27:40
Sorry, I'm not familiar with those.
Aquila20:28:23
Are you going to have "Intermediate Geometry" class (and book) in the future. I have taken the geometry class in school and can solve most of the post-probelms, but I would like to be able to solve more complicated ones, like those you post on your talent-search website
DPatrick20:28:49
Not in the near future, maybe in 2009. There's not a great deal of student demand for that class at the moment.
Rational20:29:05
How can I make up if I missed a class?
DPatrick20:29:29
A transcript of each class is posted on our website, for you to review whenever is convenient. The weekly homework sets will also remain on the website for the duration of the class.
DPatrick20:30:15
If you have any further questions, you can always post them in our "Classes Information" forum on our website, or you can email classes@artofproblemsolving.com.
DPatrick20:30:30
Thanks for attending tonight!
Nerd_of_the_Ages20:30:45
At the end of the classes, what's the best way to save the transcripts on to your computer?
DPatrick20:31:13
We have upgraded our transcription procedure so that you can create printer-friendly version of the transcript to save or print.
DPatrick20:31:27
There's a big "Print" button on each transcript.
ChaosTheory20:31:48
Thank you for your time!
ChaosTheory20:31:53
Nerd_of_the_Ages : I turn all of the transcripts into pdfs [you can find free pdf converters online], then I combine them all into one big pdf.
