College Classes: What to Expect as a Freshman Math Major

[devious_]

What classes did you take in college, and when did you take them (as a freshman, sophomore, etc.)?

I'm finishing up my senior high school year and I'm wondering what awaits me. I'd appreciate any replies, especially from math majors.

 

[mathwonk]

In high school I took plane geometry, 2 years of algebra, and as a senior a little solid geometry, but not trig.

then in college I began with a Spivak type calculus course that was unbelievably exciting and hard. I did very poorly, and in college in general and withdrew for a year.

Upon returning I took differential equations, which started out very difficult after a year off, and finally became very easy by studying hard. The summer before I returned I took linear algebra.

As a junior I took honors advanced calculus from Loomis and Sternberg, and then as a senior, abstract real analysis, similar to the treatment in Halmos' book.

I had no complex analysis, or topology, and little algebra, but in the summer after my senior year I read about half of Kelley's general topology.

Aftyer an unsuccessful run at grad school, I went to work and taught calculus from Thomas and Lang and Spivak, algebra from Herstein and Lang, topology and differential geometry from Spivak and Chern, and sheaf theory, to prepare for another shot.

When I went back to grad school, I was able to finish.

I recommend a more sane program to others. If you have had calculus in high school, and want to major in math, I recommend finding a good school that offers a Spivak type course at an honors level and taking it from the beginning.

One thing you need to elarn is how to prove thigns and to understand proofs. Hopefully you have ahd a traditional plane geometry course in high school with proofs. If not you need to learn that as soon as possible in college. That will be a side effect of a Spivak calculus course.

At some point soon after that, take linear algebra, and an advanced calculus course that uses linear algebra.

then take some abstract algebra, and some topology. and some differential equations.

as a career move, it is useful also to learn something about computers and/or statistics.

 

[xorbie]

I'm still in college now, so I can only give you info on the first couple years.

In high school, I took our AP math sequence, which covered basic set theory, probability, trig, algebra and ended in a full year of calculus, which was pretty advanced for a high school class (covered epsilon delta defiition of continuity).

My first semester in college I took an advanced multivariable calc class, which covered through line/surface integrals and the GGS theorems.

Semester two: differential equations and probability

First semester this year: linear algebra, differential equations II (which covered systems of linear and non-linear equations, phase plane analysis, and the such) and real analysis.

This semester: complex analysis, abstract algebra (rings, groups etc) and optimization by vector space methods.

In the future I am planning on taking a lot of graduate level classes in linear and non-linear analysis, dynamic systems, etc

All of this is at the same time as taking a lot of science classes though, last year I was a physics major and though I dropped that, I am now basically going through a pretty rigorous bio minor because I want to study dynamic biological systems when I grow up.

 

[xorbie]

I recommend a more sane program to others. If you have had calculus in high school, and want to major in math, I recommend finding a good school that offers a Spivak type course at an honors level and taking it from the beginning.

One thing you need to elarn is how to prove thigns and to understand proofs. Hopefully you have ahd a traditional plane geometry course in high school with proofs. If not you need to learn that as soon as possible in college. That will be a side effect of a Spivak calculus course.

Can't recommend this enough myself. Try to take as many classes that emphasize and utilize proofs, both the lecturer him (or her) self, as well as in homework assignments.

 

[devious_]

Wow, mathwonk, that's pretty hectic.