YankeeMagic24

Hey all,

I'm currently taking multivariable calc as a junior, and I was wondering what math courses or topics there are beyond this level that I could take next year.

cujoe

same here, but out of reference our school doesn't offer that, so i have to i/s a multivariable calc course at rutgers

violinperson2000

What do you mean Multivariable, is the the course designed for AP Calc AB or BC?

texas137

Take linear algebra next, then choose from differential equations, real analysis, or abstract algebra. For a good explanation of this, look at EPGY's guidelines for which courses to take after calculus at:
http://www-epgy.stanford.edu/courses/math/univ.html

(Violin - multivariable comes after AP calculus and is almost never available at a high school)

averagemathgeek

For "lower level" courses, try statistics (calculus-based) and discrete mathematics.

If you want to look at more rigorous courses, I recommend complex variables or introduction to analysis.

hsmomstef

texas137...did/do you take classes through EPGY? my youngest son is taking pre-algebra (and maybe algebra) this year through them in 5th grade. I was wondering where he would be in a few years if he keeps on track and if EPGY was a good way to go.

TheStonedPandas

yeah, after multivariable you should definitely go into linear algebra. after that you have some choice.

zogoto

Why does everyone say linear algebra after multivariable? What's so special about it? I mean, I'll probably take it, but I like number theory wayyy more.

Btw, texas is a dad, and a poster on AoPS I believe?

YankeeMagic24

I've already finished linear algebra, so that's not an option. I was looking at those courses on the EPGY website (thanks texas137) and I came across Modern Algebra. The course description contained concepts that are completely foreign to me, so I was wondering if anyone could explain some of the applications of Modern Algebra.

tokenadult

"texas137...did/do you take classes through EPGY?"

I'm not Texas137, but I hope she thinks I am a friend of hers, as I am much in her debt for many useful posts. It was over on the AoPS site that I learned about this College Confidential site from her. (I used to think Texas137 was a dad, because most parents on AoPS are dads, but here on CC I have seen her refer to her husband, so I think she is a mom.)

We have used EPGY here for our oldest son, who started the EPGY course sequence in math at the fifth-grade level, right after the end of his fourth-grade "school year." (We homeschool.) He got through the EPGY beginning algebra course by a year later. Since then, he has been in a classroom-based accelerated math program in our town, but has also taken the EPGY geometry course (which is VERY good). We have been very pleased with EPGY. He is just about to start the C programming course, and I expect he will be in the physics course before the end of this school year. He has also taken the EG20 Grammar of the English Sentence course, which is also very good.

Our son is about to start a precalculus course that compresses the whole content into one semester. Next year he starts a calculus I course at eighth-grade age. One can get a lot of extra speed through the standard math curriculum by starting out with EPGY. But for various reasons more fully explained elsewhere,

http://www.artofproblemsolving.com/R...A_Calculus.php

our goal here is not just to speed through the standard curriculum, but to go beyond it to a deep understanding of precalculus topics that are only treated cursorily in most United States school mathematics curricula.

The Art of Problem Solving (AoPS) Web site is a great resource for math-eager young people and their parents.

texas137

hsmomstef - thanks to Tokenadult (who has more than reciprocated with useful posts both here and on the aops forum) for stepping in. I've been aware of EPGY for years, but my son never actually used it. I provided the link because I like their guide to typical course sequences, not necessarily because I am recommending taking courses from them. My son self studied using materials we selected ourselves until after calc BC, then did distance learning thru http://www.utexas.edu/cee/dec/ for multivariable and linear algebra (much cheaper than EPGY but minimal "instruction"). Then he started taking courses on campus at the local university. He has also done a lot of specialized math summer programs.

Zogoto - in most programs, linear algebra is where students are first introduced to writing serious mathematical proofs (not the kind you do in geometry). So it's a prereq for most upper division college math courses. If you have an interest in number theory, by all means consider taking it or studying it on your own. Some number theory courses assume you already have exposure to proof-writing at the level of linear algebra, but other don't.

im_blue

Modern Algebra is also called abstract algebra at some schools. As the name implies, it deals with very abstract concepts. For example, instead of working with real numbers, we generalize operations to a set of objects called a group, in which the elements are closed under an "addition" operation (that is, the "addition" of any two elements in the set produces another element in the set), there exists an identity element, and for each element in the group there exists a "negative" of that element. After defining sets of objects like groups, rings, and fields, you then learn how to prove dozens of theorems and corollaries about them. Modern algebra and real analysis (in which you prove all the theorems from calculus) are very rigorous classes, and I wouldn't recommend them right after multivariable calculus. Modern algebra has a few esoteric applications, such as theoretical physics, and it's usually only taken by math majors. I think you should look at differential equations, since that's what most people take after multivariable and linear algebra. DiffEq is also applicable to a wide variety of fields, such as biology, chemistry, physics, and engineering.

EllenF

My son is also taking EPGY courses. I'd like to second tokenadult's comment about the EPGY geometry course. It is not only excellent, but lots of fun. It teaches students the logic rather than the tedium of proofs. Kudos for the team who developed this course!

For those who are taking EPGY math, the tutors at EPGY are most helpful in advising which course to take next. Contact one who has tutored your child and who knows his/her abilities.

The only EPGY course my son didn't like was precalc. It was a review of algebra he had already taken (Lial), with trig thrown on the end. If your child has a good grounding in algebra, you may want to teach the trig yourself. You will save money and your child several weeks of boredom.

tokenadult

A lot of math majors, and a few non-math majors, take a "transitions" course just after taking their multivariable calculus course to prepare for RIGOROUS treatment of linear algebra, real analysis, abstract algebra, and other higher math topics. You can find many textbooks for those subjects by browsing around Amazon.com (which is how I've discovered most of them over the years) and one list of those books

http://www.amazon.com/exec/obidos/tg.../31B4QV24TPSZ/

will lead you to other books of the same kind, so you can see what is appealing to you for self-study.

TonyLTH12

has anyone enter the 3D world of calculus yet?
Startin Calc III in Jan., so wonder if anyone of y'all got any advice.

From the college I attend, some people usually take Linear Algebra and calc II at the same time and Calc III and D.E. at the same time