| Transcript
for the Math
Jam "AoPS Calculus Math Jam"
on Sep 9. |
| Math Jam hosted by DPatrick
(Dave Patrick ). |
DPatrick19:28:19
Hello and welcome to the AoPS Calculus Class Math Jam!
DPatrick19:28:25
Today we'll be discussing the new AoPS Calculus class. I'm Dave Patrick, and I'll be the instructor of the class.
DPatrick19:28:37
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.
DPatrick19:28:52
The classroom is moderated: students can type into the classroom, but only the moderator (that's me) can choose a comment to drop into the classroom.
DPatrick19:29:01
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.
DPatrick19:29:14
I will try to respond to all questions to the extent that I can.
DPatrick19:29:23
However, first, I will describe the calculus class, and then afterwards I will answer any questions that you might have.
DPatrick19:29:34
The AoPS Calculus class is a course in single-variable calculus. This course covers all of the standard single-variable calculus topics: limits, continuity, derivatives and their applications, definite and indefinite integrals, infinite sequences and series, plane curves, polar coordinates, and basic differential equations.
DPatrick19:29:55
At the conclusion of the course, students should have sufficient preparation to take the AP Calculus BC exam; however, "AP exam preparation" is not the main focus of the course. (Note: the AP exam is not offered by Art of Problem Solving—you will have to privately arrange to take the exam at your local school if you are interested.)
DPatrick19:30:15
This class will differ from the "typical" high-school calculus class in two ways.
DPatrick19:30:24
First, our primary focus will be to understand the concepts of calculus, and not just to learn a bunch of algorithms in order to compute things. In particular, we will not spend a large amount of time doing "real-world applications" of calculus; rather, we will be focusing on the mathematical content of calculus. Nor will we spend a lot of time playing with graphing calculators, as the class will focus more on concepts than on calculation.
DPatrick19:30:50
Second, we will be tackling much more difficult problems than those in a typical calculus course or on the AP exam. We will routinely discuss Putnam-level calculus problems (the Putnam is a college undergraduate-level math contest). Rather than do the same basic exercises over and over, we will stretch our understanding with difficult, challenging problems.
DPatrick19:31:19
On the other hand, the course is not "rigorous" in the sense that a college-level Real Analysis course would be. Although we will try to gain a thorough conceptual understanding of many calculus concepts, we will not commit to rigorously proving every result.
DPatrick19:31:44
A course like the one that I've described requires a highly self-motivated student in order to succeed. Students will have to take it upon themselves to do a lot of work on their own between class sessions in order to master the material.
DPatrick19:32:02
The course will meet once per week for 24 weeks, on Tuesdays from 7:30-9:00 PM Eastern / 4:30-6:00 PM Pacific, starting on October 14. (We won't meet on Nov 25, Dec 13, or Dec 20; the last day of class is April 14.)
DPatrick19:32:22
There will 3 different types of "homework" for this class.
DPatrick19:32:32
1. Most classes will have some associated lecture notes that will go into more detail about topic(s) in the class. Often these notes will contain proofs of results that are discussed during class (without proof). Students interested in a more rigorous study of calculus should read the lecture notes, but otherwise they can be considered supplementary and optional.
DPatrick19:33:01
2. Each class will have a weekly problem set that will be posted on the class's message board. Some of the problems on this set will be "routine" problems to reinforce basic concepts. As mentioned above, we will not be doing very much of this in class, so it is important to solve these basic review problems in order to master the material. Other problems on the weekly sets will be more difficult and will challenge students' understand of the material. Students should work on these problem on their own, but do not turn them in for evaluation.
DPatrick19:33:36
3. There will be 6 longer Challenge Problem sets (one set every 4 weeks). These will be almost entirely composed of more difficult problems (as opposed to "routine" exercises). Students should write up complete solutions to these problems and submit them for instructor feedback.
DPatrick19:33:59
Calculus has significantly more outside-of-class work than other AoPS classes. Students should be prepared for this.
DPatrick19:34:17
Also, and we cannot stress this enough, students who do not have a solid algebra background will not be successful in this course. It is vital that students have mastered the basic high-school math curriculum -- algebra, geometry, trigonometry --before attempting a calculus course.
DPatrick19:34:38
To this end, there is a diagnostic test on our website:
DPatrick19:35:04
Students should be able to solve most (if not all) of the problems on the diagnostic, with little difficulty, before considering enrolling in the calculus class. We will be doing only a very brief review of precalculus concepts, and students who do not have a solid precalculus background will quickly be behind.
DPatrick19:35:29
Taking calculus as the "next" course after an algebra or trigonometry course is not the right decision for many students. See our articles "The Calculus Trap"and "Why Discrete Math Is Important" in the Resources section of our website for more discussion of this.
DPatrick19:35:50
We are not using a textbook for this class. As mentioned earlier, most of the classes will be supplemented with lecture notes that will be posted on the website.
DPatrick19:36:07
Some students may wish to purchase a standard college-level calculus textbook to use as a reference. If you are doing so, it is only necessary to get a "single-variable" version of the book (many large calculus textbooks come in multiple varieties); however, you may want to get the "full" version if you anticipate taking multivariable calculus in the future.
DPatrick19:36:28
We recommend that students have a graphing calculator to use as a tool in their study of calculus, and to have it with them at each class session. However, this is not required, and we will not be emphasizing calculator techniques.
DPatrick19:36:38
Note that the AP Calculus exam (which Art of Problem Solving does not offer nor endorse) requires a graphing calculator; a list of AP-approved calculators is on the College Board website.
DPatrick19:36:58
The fee for the course is $425. The course may be dropped for a full refund anytime before the 3rd class session. After the 3rd class session, the entire course fee is non-refundable.
DPatrick19:37:11
As mentioned earlier, I will be the instructor for the course. There will also be a teaching assistant (whom it will be has not been finalized yet).
DPatrick19:37:23
That's it for my overview...are there any questions?
bwu19:37:41
what grade is this normally for?
DPatrick19:37:50
Calculus is "normally" taken by college freshmen.
DPatrick19:38:14
In recent years, more and more students have been taking it in high school. This is not necessrily a good thing (see our article "The Calculus Trap" for more discussion of this).
sbk2017119:38:25
if we can do the AoPS volumes one and two books, will we be ready?
DPatrick19:38:42
Mastery of algebra is the most important prerequisite. Trigonometry and geometry is also important.
DPatrick19:38:58
If you have "mastered" Volume 2, you should be fine.
chenhsi19:39:02
Are the class meetings mandatory?
DPatrick19:39:20
No, and if you have to miss a class, then you will be able to read the class's transcript at any time on the website.
DPatrick19:39:36
However, the advantage of attending the live class session is that you can ask questions in real time.
Ruirui19:39:48
do u recomend a freshman(high school) taking this course?
halfandhalf19:39:48
What is the mininum grade that you could be in order to do this class?
DPatrick19:39:56
It depends; there is no universal answer to this.
DPatrick19:40:39
Generally we would recommend students have mastered all our other classes (including Intermediate Algebra, Counting & Probability, and Trigonometry/Complex Numbers) before proceeding to calculus.
aglee9219:40:47
if i'm taking calc right now, would you still recommend this class? how much would be overlap?
DPatrick19:41:24
I think it would be a bit confusing. There would be a lot of overlap. I would take one or the other, it doesn't make too much sense to do both at the same time.
sbk2017119:41:31
will this help on the AP calc AB exam as well?
DPatrick19:41:45
"help" is the wrong word...this class is not intended to "help" on the AP exam.
DPatrick19:42:01
The AP exam questions (AB or BC) are much easier than the type of problems we'll be doing in this class.
tommy9319:42:14
Could you do a short class demo?
DPatrick19:42:42
No...the difficulty with this is that calculus is a very conceptual subject. I can't just "do a calculus problem" without covering a lot of concepts.
wordnerd19:43:01
Do you know how much of the material covered in this course is used in a calculus-based AP Physics course?
DPatrick19:43:20
You'll certainly learn enough calculus to go on to a physics course.
DPatrick19:43:32
As I said before, this course will cover all the material on the AP Calc BC test.
bwu19:43:42
what are the units we cover in this class?
DPatrick19:43:47
Here's the tentative syllabus:
DPatrick19:44:04
Week 1: Precalculus review
Week 2: Trig functions, logarithms, and exponentials
Week 3: Limits and continuity
Weeks 4-6: Derivative basics
Weeks 7-9: Applications of the derivative
Weeks 10-11: Antidifferentiation (indefinite intgerals)
Weeks 12-14: Definite integrals
DPatrick19:44:08
Weeks 15-16: Infinity
Weeks 17-18: Sequences and series
Week 19: Plane curves
Week 20: Polar coordinates
Weeks 21-23: Differential equations
Week 24: Review, harder problems, and/or AP Exam discussion
DPatrick19:44:35
(Don't let Week 2 fool you: we'll be covering those topics more rigorously than you've probably seen them before.)
undefined11719:44:39
No vector-valued functions?
DPatrick19:44:44
No, this is a single-variable calculus class only.
wordnerd19:45:13
How tentative is the syllabus? What would cause it to be altered?
DPatrick19:45:33
This is the first time that AoPS is offering calculus, so we're more or less guessing at the pace that we can go.
DPatrick19:46:00
That's also why there's some "wiggle room" in the syllabus; for example, why "Derivative basics" is Weeks 4-6.
DPatrick19:46:16
It might turn out we only need 2 or 2.5 weeks to do everything that I want to do.
sbk2017119:46:23
What do you mean by single-variable? Is there a solid definition for it?
chenhsi19:46:23
what does single-variable calculus mean? how is it different from regular calculus?
DPatrick19:46:37
"Single-variable" is "regular" calculus as far as the AP exam is concerned.
DPatrick19:46:58
It basically means we'll be studying functions of one variable, like f(x) = x^2 + e^x - sin(3x).
DPatrick19:47:39
The next step up would be either "multivariable" or "vector-valued" functions, but that's usually a second-year undergradate course.
sonny19:47:42
what kinds of stuff would we be doing in Precaculus review? Basic algebra, geo and trig?
DPatrick19:48:11
No, more like set theory, functions, real numbers, basic proof techniques, that sort of thing.
DPatrick19:48:21
I'm going to assume you know basic algebra, geometry, and trig.
tommy9319:48:34
So is this how the class will be taught? Will there be any visuals or audio?
DPatrick19:48:42
This is essentially what the class will look like.
DPatrick19:48:56
DPatrick19:49:23
DPatrick19:49:42
(If you don't know what this means, don't worry, we'll cover it pretty early in the course!)
bwu19:49:50
are we just answering questions today, or are we doing math too?
DPatrick19:50:02
I think what I just posted is about the extent of the math today. :)
sbk2017119:50:07
do we need latex
undefined11719:50:07
How do we input LaTeX?
DPatrick19:50:42
You don't need to learn LaTeX (which is what I just used to display the math above) for the course. If you do know it, we'll explain how to use it in the classroom when the course starts.
DPatrick19:51:13
I'm not going to bother to explain it now, because we expect to have a new version of the virtual classroom up and running by then, and the LaTeX functionality might work a bit differently than it does now.
Ruirui19:51:18
is any of the material covered in the calculus course going to appear on the AMC10?
DPatrick19:51:26
Definitely no.
DPatrick19:51:46
AMC 10 is for students in grades 10 and under. Calculus is typically for high school seniors or college freshmen.
DPatrick19:52:21
Any other questions?
sonny19:53:45
is the calculus we learn stuff that can be used to solve physics olympiad problems or is it above that level (or below)?
DPatrick19:54:14
I'm not sure. Calculus is definitely heavily used in physics.
DPatrick19:54:25
I don't know about the Physics Olympiad specifically.
tommy9319:54:38
Is there a multi-variable calculus course?
DPatrick19:55:02
We don't have one, no.
wordnerd19:55:06
I read somewhere that grades can be given if we inform you before the start of the class... how soon do you need to know?
DPatrick19:55:27
Just anytime before the start of class, so that we can make clear what work you'll have to do to earn a grade.
DPatrick19:55:48
Important: we cannot guarantee that your school will accept our grade, as we are not an accredited institution.
DPatrick19:55:58
You will have to make the appropriate arrangements with your school.
DPatrick19:56:12
However, we can certainly talk to someone at your school (if you set up the contact) if need be.
DPatrick19:57:35
The class doesn't start for another 5 weeks, so if you have any questions between now and then, you can post them on our "Classes Information" message board, or you can email classes@artofproblemsolving.com
DPatrick19:57:49
Any other questions right now?
miss30919:58:53
I came in late but are you planning to offer the Calculus class next fall and when do you expect the Calculus book to come out?
DPatrick19:59:04
We are planning to offer it again next year
DPatrick19:59:38
And as you mention, we are also working on our own textbook...ideally it will be available next fall too (so that in 2009-10, we'll be using our own textbook in conjunction with the class).
mathworm20:00:36
How much time is required to be spent on the challenge sets?
DPatrick20:00:53
It's hard to say.
DPatrick20:01:09
I would suggest that the class as a whole is a 10-15 hour/week commitment.
DPatrick20:01:37
For some it may be less, for others it may be slightly more. (It shouldn't be too much more.)
DPatrick20:02:14
When I used to teach calculus to college students at the University of Washington, we would tell them that calculus is a 15-20 hour/week commitment.
DPatrick20:04:04
For many students, calculus is their first "adult" math class: the concepts and techniques involved are more sophisticated than what you've seen before. But "more sophisticated" doesn't necessarily mean "harder".
mathworm20:04:09
If we can't manage to solve all the probems, is it ok if part solutions are provided?
DPatrick20:04:13
Certainly.
DPatrick20:04:28
In fact, we don't expect that many students, if any, will be able to solve all of the problems.
DPatrick20:05:09
Some of the problems will be very challenging.
DPatrick20:05:23
We feel that if you can solve all of the problems, then this means that the problems are too easy!
undefined11720:05:29
We'll be able to work together on the classes forum, right?
DPatrick20:05:33
Absolutely!
chenhsi20:05:44
How many students do you expect there to be?
DPatrick20:05:56
The enrollment in this course will be capped at 48 students.
DPatrick20:06:26
I expect it will fill to capacity but I don't know for sure as this is the first time we've offered it.
halfandhalf_220:06:28
How many students have already enrolled?
DPatrick20:06:30
About 20.
DPatrick20:07:07
It's a pretty substantial time commitment (as I said, 10-15 hours/week for 24 weeks).
corey20:07:25
Is learning calculus in a class better than just teaching oneself from a textbook and/or the internet?
DPatrick20:07:34
That depends on the student.
DPatrick20:08:08
It also depends what you want to get out of calculus, and what subsequent classes (math, physics, engineering, etc.) you're planning on taking.
DPatrick20:08:25
If you goal is solely to do well on the AP Calculus exam, then self-study will probably work for you.
Smartguy20:08:40
are we going to use calculators?
DPatrick20:08:59
Not a lot. I recommend having one, but it's not required.
adamdeb_220:09:53
If we don't want a grade, what are the passing requirments? Are there any tests, quizzes, or homeworks we have to pass?
DPatrick20:10:18
If you don't want a grade, then there is no "passing requirement", since we don't think in terms of "passing" or "failing".
DPatrick20:10:53
We'll give you written feedback on your assignments, but we won't give you a numeric score.
corey20:11:09
If I'm interested in learning calculus because I like learning math, would this course likely be better for me than the course offered by my high school/community college?
DPatrick20:11:28
Yes, for two reasons (I said this at the beginning, but it's worth repeating):
DPatrick20:11:39
First, our primary focus will be to understand the concepts of calculus, and not just to learn a bunch of algorithms in order to compute things. In particular, we will not spend a large amount of time doing "real-world applications" of calculus; rather, we will be focusing on the mathematical content of calculus.
DPatrick20:11:52
Second, we will be tackling much more difficult problems than those in a typical calculus course or on the AP exam. We will routinely discuss Putnam-level calculus problems (the Putnam is a college undergraduate-level math contest). Rather than do the same basic exercises over and over, we will stretch our understanding with difficult, challenging problems.
DPatrick20:12:56
Typical high-school courses are driven by the AP Calculus exam. This exam by and large has boring, one-step, uninteresting problems.
DPatrick20:13:29
Community college courses are generally even worse, in large part because their students often don't have a solid math background to begin with.
DPatrick20:13:42
(There are exceptions, or course; I'm broadly generalizing.)
DPatrick20:14:37
Again, I recommend our article "The Calculus Trap" in the Resources section of our website. This is the "trap" that our calculus course is trying to avoid.
DPatrick20:15:28
College-level calculus courses often suffer from a different problem:
DPatrick20:15:42
They are driven by the needs of their college's physics and engineering courses.
DPatrick20:16:10
Which means that they focus on the dry, applied, "real-world", algorithmic aspects of calculus, and tend to ignore the more interesting mathematical aspects of calculus.
DPatrick20:16:32
For engineering students, that's perfectly fine.
DPatrick20:16:42
But for students interested in math or problem solving, it's not so good.
DPatrick20:16:58
(I'm really getting up on my soapbox now! :) )
DPatrick20:17:45
Yeah, I feel like maybe I'm getting too opinionate or preachy now...are there any other questions about the class?
Aylsero20:18:32
Would piggybacking Trigonometry be okay? Or should I wait for next class?
DPatrick20:18:53
No, we would definitely recommend mastering trigonometry completely, before starting calculus.
Canton20:19:03
Do u plan to add video to your classes?
DPatrick20:19:08
Not in the short term.
Aylsero20:19:44
Would Calculus be useful for USAMO?
DPatrick20:19:52
Not even a little bit. :)
Canton20:20:14
How about audio
DPatrick20:20:22
No audio either.
DPatrick20:20:48
See http://www.artofproblemsolving.com/Classes/classroom.php for a discussion of our classroom and why we believe in our current setup.
DPatrick20:21:11
Having said that, we should have a new version of the classroom software up by the time the class starts.
DPatrick20:21:41
It may have a few extra bells and whistles (I don't know for sure...I'm not involved in setting it up).
karatemagic720:21:53
hi - sorry - I arrived late - will this whole transcript be online tonight?
DPatrick20:22:05
Yes: the transcript of this (and every other) Math Jam will be available on the website.
Ruirui20:22:17
so why should people be taking this class?
DPatrick20:23:00
Because we will be studying calculus at a deeper level than most high-school calculus classes, and we will be working to solve harder problems than most any other calculus class.
karatemagic720:23:05
WHY did you say that about Calculus and the USAMO??
DPatrick20:23:10
Because there is no calculus on the USAMO.
chenhsi20:23:19
What about for USAMTS?
DPatrick20:23:24
No calculus on the USAMTS either.
corey20:23:30
How does this course compare in difficulty with a college level calculus course?
DPatrick20:24:24
It varies. The "difficulty" in terms of the material is probably about the same (after all, calculus is calculus), and in fact our calculus class is probably "easier" in terms of "diffculty" than a good college-level Honors Calculus class.
DPatrick20:24:41
However, we will definitely be doing harder problems in our class than just about any other calculus class.
Smartguy20:24:45
This class will be helpful for the Putnam(for when we are in college), right?
DPatrick20:24:59
Definitely...we will be working on a lot of Putnam-level calculus problems in the class.
halfandhalf20:25:08
Can calculaus help for the AIMEs?
DPatrick20:25:13
No.
Canton20:25:36
Do all your classes have challenge sets and feedback mechanism?
DPatrick20:25:44
All of our subject classes do.
DPatrick20:25:49
The Mathcounts, AMC, AIME classes do not.
karatemagic720:26:04
If someone found the qualifying test quite easy and completed all in just a few minutes - does that most likely indicate the class material will be "too easy" or just right for that person? Usually, your site says if person gets more than 85% or 90% correct (forget the exact %) that they already masterd the class - but is the calc class qualifying test different?
DPatrick20:26:19
It means you're prepared to take the class, nothing more and nothing less.
DPatrick20:27:10
What you mention for our other classes is their "post-tests" (or "Do you need this?" tests). We don't have one of those tests for calculus.
karatemagic720:27:17
Oh, so how can someone know if they already understand most of the concepts taught in this class?
DPatrick20:27:42
If you know single-variable calculus and can solve most "easy" Putnam-level calculus problems, then our class wouldn't add much.
karatemagic720:28:27
one more question, pls? You listed a lot of competitions that DON'T apparently use a lot or Any calculus - can you name the ones that DO? thanks
DPatrick20:28:57
The Putnam and the Harvard-MIT Math Tournament are the two major ones (in the US at least).
DPatrick20:29:13
We'll be doing a lot of problems from past years of both of those contests.
DPatrick20:30:11
In fact, I suppose that you can use the HMMT Calculus Tests as a good measure for whether our calculus class would be redundant for you.
DPatrick20:30:15
For example, the 2008 test is at:
DPatrick20:30:55
If you can do, say, the first 5 problems on that test, then you won't gain much from our course.
DPatrick20:31:07
(If you can do the last 5 problems, you might be able to teach the course!)
prophet88620:32:05
(everyone starts doing the last 5 problems)
DPatrick20:32:09
Yeah, good luck!
DPatrick20:32:13
:)
DPatrick20:32:56
Any more questions?..I think I'm about to wrap things up.
karatemagic720:33:24
Wait .. if I can do the first 5 - (don't know how many are on test) but if I can do first 5 but NOT next ones - will this class show us how or will it stop at number 5 (on the test) difficulty level?
DPatrick20:34:11
The class will definitely contain really hard problems (like 6-10 on the HMMT Calculus Tests), but I guess my point is that the vast majority of the calc class will just be review if you are already at a level where you can do 1-5 on most HMMT Calculus Tests.
karatemagic720:34:38
ohhhh.... I see -- thanks!!
DPatrick20:35:51
I think I'll end it here...as I said before, the class doesn't start until October 14 (5 weeks from today), so there's still plenty of time to ask questions on our Forum or at classes@artofproblemsolving.com if you want.
DPatrick20:36:08
Thanks for coming tonight and for your interest in our classes!
