When should I take Linear Algebra?

[DarrenM]

Hello there,

The short version of the thread is just as the title states: When is the optimal time to take Linear Algebra?

I'll elaborate to provide the context of the question.

I'm leaning towards a B.S. in Mathematics; I'm currently taking as many courses as possible out of Georgia Perimeter College (a 2-year community college) before transferring to either Georgia State University or trying to transfer to Georgia Tech. There are a number of other factors influencing that particular decision (such as the fact that Tech seems to heavily favor an applied approach) but the one that is relevant to this thread is the fact that they kind of lump Linera Algebra in with Calculus II, and require transfer students in math to have Calculus II, with Linear Algebra strongly recommended.

I thought this was kind of SOP until I looked around a bit and realized that wasn't the case. For example, GSU has Linear Algebra as a bit of a higher level class, with an additional prerequisite consisting of a class called "Bridge to Higher Mathematics," whose course description states that the class covers "topics from set theory, real numbers, analysis, and algebra, which illustrate a formal approach to the presentation and development of mathematical concepts and proofs."

I mean, that class sounds awesome; what confuses me a bit is how one school has a class like that as a prereq. for Linear Algebra, while another school has Linear Algebra lumped in with Calc II (Calculus of One Variable II).

My initial reaction is that it would be wiser to take the Bridge course prior to taking Linear Algebra; however, as I stated before, I'm trying to take as many courses out of GPC as possible (largely due to cost difference between a 2-year and 4-year university; I'm a non-traditional student with a previous B.A., so financial aid is very limited). If it's not really necessary to have a class like the Bridge course before Linear Algebra, then it might be better for me to take it at the community college before transferring.

 

[Gear300]

Its a good idea to get a good feel for it when you take it under Calc II, but you'll only be touching the subject matter. Once you've covered a good amount of modern/higher algebra and some analysis, you can look over it again.

 

[Monocles]

I go to Georgia Tech so I can answer this question pretty well.

GT has not one, not two, not three, but FOUR undergraduate courses that cover linear algebra topics. The first one, Calc 2, covers basic applied topics, such as matrix decomposition, row reduction, finding eigenvalues/eigenvectors, etc. and only briefly touches on more theoretical aspects such as span and vector spaces. For students who transfer in that have already taken Calc 2, there is a course that I think is only 2 credit hours that basically covers these topics as a standalone course. Of course, it also covers typical Calc 2 topics such as infinite series, L'hopital's rule, etc.

Then, there is abstract vector spaces, which is basically our transition to higher math equivalent course. It is a very rigorous proof based course on linear algebra, though my prof also covered some set theory and infinite dimensional spaces. It is the first major weed-out course for math majors, with test scores regularly ranging around the 20's and 30's (depending on the prof of course, mine wasn't nearly that bad).

Finally, there is an old relic of a course called Topics in Linear Algebra, which is basically an extension of the material covered in Calc 2. It isn't very rigorous from what I hear, but it gets into topics such as singular value decomposition, convexity, difference equations, and Perron-Frobenius theory. I haven't taken this course, but math majors I talk to make it sound like a joke of a class. I think it is intended for engineering students. Ironically, it's a 4000 level class, while abstract vector spaces is a 2000 level class.

Finally, while GT doesn't have a pure math major, it still has all the courses you'd take in a typical pure math major, such as topology, number theory, modern algebra, etc. The only real difference as far as I can tell is that you're required to take things like applied combinatorics, numerical analysis, differential equations, and the intro physics sequence.

 

[DarrenM]

Thanks for the information.

Now, I've read that one's undergraduate institution does not necessarily have a significant impact when it comes time to apply to graduate programs. At least not as much as things like research experience, recommendation letters, test scores, and GPA. Is that actually the case? Is there likely to be a significant difference between how an applicant from GSU versus an applicant from Ga. Tech would be perceived by graduate admissions?

Also, I'm trying to assess how the two schools compare, particularly in regard to undergraduate mathematics programs, but I'm having a bit of difficulty. I can go to RateMyProfessor.com, but not all of the faculty members are to be found on sites like that, and I'm rather skeptical as to how much trust one can put in those sites anyway.

Any advice on how to evaluate which school would be more suitable?

 

[twofish-quant]

Now, I've read that one's undergraduate institution does not necessarily have a significant impact when it comes time to apply to graduate programs. At least not as much as things like research experience, recommendation letters, test scores, and GPA. Is that actually the case? Is there likely to be a significant difference between how an applicant from GSU versus an applicant from Ga. Tech would be perceived by graduate admissions?

Undergraduate institution only matters to the degree that it affects things that graduate schools do care about. If you go to a school with better research opportunities and more supportive professors, then that will matter, but the institution itself really doesn't make that much of a difference.

One thing that you do need to be aware of is that the main "brand" is the professors that supervise your research and write recommendation letters for you. When it comes to research, you can think of universities sort of as flea markets where professors set up booths.

Any advice on how to evaluate which school would be more suitable?

Yes. Go to the web sites of both universities and look at their course notes and research programs of the professors there. You can see for yourself the quality of the courses and the research. The other thing to do is to look up the professors in research databases to see whether they are doing something you are interested in. One other thing to look at is the events calendar. A good research university should have people coming in and giving talks.

The other thing is to see if the university has a organized system for undergraduate research. It helps a lot if there is something that handles the administrative aspects.