jmora13

Hello, I'm currently a Junior in high school and can't decide on whether I should take applied calculus 1-2 or go down the road of Caluclus with analytical geometry. I plan to major in Computer Science and have a background of Physics, and I have no idea which mathematics course would aid me the most for this major. At my CC, it says that the prereq for say Linear Algebra is calc analy geo 1-3, yet my worry is that the college I would like to go to as a freshman may not need this prereq, as I see some people moving into Linear Algebra with only a background of applied calc 1-2. I'm not sure whether i'll be wasting my time doing calc analy geo, when i could take applied calc 1-2 and possibly move into linear algebra once im in college. Can anybody give me some suggestions?

Shiyayo

I'd say take the Calculus with Analytic Geometry sequence. The coursework is probably more rigorous, which would help with the Physics classes you plan to take, and will probably transfer more easily, and you could probably take the BC Calculus exam, for colleges that don't accept CC credit, with the content you learned.

ucbalumnus

CS majors typically need to take the more rigorous lower division math courses for math, physics, and engineering majors, not the less rigorous versions for biology or business majors.

GLOBALTRAVELER

The main reason why schools require engineers and other applied scientists/mathematicians to take the more rigorous foundational math is to prepare them for as many POSSIBLE career options and interests. Some engineers/scientists MAY go into research so it is better to be prepared for that option, whether or not one selects that path. It is better to go from courses that include theory TO applied courses than the other way.

Besides, in the traditional Calc & Analytic Geometry sequences, you will still do applied problems like volume, flow of fluids, speed/velocity/acceleration, vector problems that will be the same of what you see in physics, and area coverage problems.

jmora13

Thanks for the reply, and with that being said, can you tell me what comes after differential equations? I just want to plan for my future classes in college.

GLOBALTRAVELER

A very-generalized undergraduate math program is of the following:

--starting foundation--
Calculus & Analytical Geometry I
Calculus & Analytical Geometry II
Calculus & Analytical Geometry III
Linear Algebra
Differential Equations

After that, the aim is to give you a background on doing proofs of higher mathematics with...

Analysis I,II or Real Analysis I,II or Advanced Calculus I,II
Abstract Algebra I, II

Now depending on your "emphasis", the number of Analysis and Abstract Algebra courses will vary. If you are planning to go into pure math and/or graduate study in math, then more likely you will have to take Analysis/Real Analysis I & II AND Abstract Algebra I & II. If you plan on doing applied math or math/CS then you will only take Analysis/Real Analysis I and Abstract Algebra I or just one ONE of those courses. Just about NO math department will let you out of there without at least one course in either Analysis or Algebra...regardless of your emphasis.

Note: because of the intensity of these theoretical courses, more and more schools are NOW offering a "Transition to Higher Math & Proofs" course to take after Diff Eq to prep you for the rigors or Analysis/Real Analysis and Abstract Algebra. I would suggest taking that course so that you know how to do good proofs without having to "learn it on the fly" while trying to digest Analysis/Real Analysis/Abstract Algebra at the same time (like us old math majors had to do).

After those courses, then you will get into your math electives that will form your emphasis. Here are some examples....

Applied Math
- Partial Diff Eqs
- Numerical Analysis
- Advanced Vector/Tensor analysis

Computational Math
- Numerical Analysis
- Numerical Linear Algebra
- Combinatorics (jr/sr level class...more advanced than discrete math as sophomore)
- Graph Theory (jr/sr level class...more advanced than discrete math as sophomore)
- Selected CS courses

Optimization/Operations Research
- Optimization/Mathematical Programming
- Operations Research
- Stochastic Processes

Statistics
- Probability (separate class...not the combined Prob & Stats course for engineers)
- Statistics (separate class...not the combined Prob & Stats course for engineers)
- Regression
- Experimental Design
- etc, etc

ucbalumnus

Applies math major example: Course Requirements: Applied Mathematics | Department of Mathematics at University of California Berkeley
Pure math major example: Course Requirements: Pure Mathematics | Department of Mathematics at University of California Berkeley

(Note: the lower division courses would typically be taken at CC for those students who start at CC and transfer in as juniors.)

Other majors, like statistics, physics, and engineering may not require additional math courses beyond the lower division courses listed for math majors above (though some upper division math courses may be optional or recommended for those intending graduate study in the subjects). They will, of course, have their own math-intensive courses that make use of the math you learn.

jmora13

Ah, I see. If I continue to take the calculus with analytical geometry sequence at my CC in conjunction with my high school classes, I should in theory be able to finish differential equations by the end of my senior year, thus also finishing all of the "lower division" courses as stated by "ucbalumnus". Well thanks again for the replies, you guys are really helpful .

ucbalumnus

If you do want to be a math major in college, note that some upper division courses, like real analysis, complex analysis, and abstract algebra, are heavily proof-oriented. This can be somewhat different from the lower division courses that are usually more computational (unless you can take honors courses). Some colleges have an additional lower division course that teaches proof techniques (Berkeley includes that in the discrete math course).