Math courses

[akoaysigod]

I just saw my advisor today and he gave me a ton of options on classes to choose for next semester, however, the descriptions for the courses are similar to examples in math books; they both assume you understand math, his descriptions were much the same. I have to take 4 classes out of these categories which are: algebra, analysis, and geometry/topology plus more math classes which I can choose; there is a good chance I will end up taking classes in all of them, eventually, maybe. Anyway, if someone could give me more detail into my current options that'd be much appreciated.

A MAT 312/312Z Basic Analysis (3)
Theoretical aspects of calculus including construction of the real numbers, differentiation and integration of functions in one variable, continuity, convergence, sequences and series of functions. Only one version of A MAT 312 may be taken for credit. Prerequisite(s): A MAT 214.

A MAT 314 Analysis for Applications I (3)
Introduction to topics in mathematical analysis which traditionally have been applied to the physical sciences, including vector analysis, Fourier series, ordinary differential equations, and the calculus of variations. Prerequisite(s): A MAT 214 and 220. Offered Fall semester only.

A MAT 326/326Z Classical Algebra (3)
Elementary number theory. Elementary theory of equations over rational, real, and complex fields. Only one version of A MAT 326 may be taken for credit. Prerequisite(s): A MAT 113.

A MAT 342/342Z Elementary Topology (3)
Networks, map coloring problems, surfaces, topological equivalence, the Euler number, the polygonal Jordan curve theorem, homotopy, the index of a transformation, and the Brouwer Fixed Point Theorem. Only one version of A MAT 342 may be taken for credit. Prerequisite(s): A MAT 214 and 220. Usually offered Fall semester only.

I could take one analysis and Classical algebra but I think I want to Differential Equations although I'm not entirely sure of that yet because I don't technically need to take it and 314 has ordinary differential equations in it. I have a bit of an idea of what I'm in for in analysis 312 but not so much for the 314 one. I have no idea what the last one is about. Can anyone give me a little more insight in what I'm getting myself into? There's really no turning back now; I'm in this whole math thing for the long haul, plus I really do like calculus even if it doesn't make sense. My calc teacher now is always like, if you take analysis this might make sense someday, or things to that effect, so I'm probably going to inquire about that with him.

Anyway, thanks for any feedback.

 

[Deleted member 4993]

What is your major field of study?

 

[daon]

Topology is quite abstract. I would take other classes like Real Analysis or Algebra before-hand (or even Complex Analysis where you should make great use of the Topology of the Complex Plane). You might see some tidbits of topology here and there, and more importantly, already have proof-writing down pat.

Real Analysis is basically "true calculus." What you probably know as The Calculus is moreso of an application of theorems (unless your professor went above and beyond)--most of which you will see/need to do the proofs of in Real Analysis.

Algebra is my favorite. You learn the innards of mathematical structures and why structures are needed. You will learn why Analysis is actually necessary if you want to work in the real (or complex/n-dimensional number systems). There is a touch of number theory involved, but not so much to make you dislike the class should you not like number theory. You will see that Polynomials are really numbers in their own right and why Pi is not a root of any polynomial with rational coefficients.

 

[Denis]

A good start would be to CHANGE this: "I'm probably going to fail all my math classes." :idea:

 

[akoaysigod]

A good start would be to CHANGE this: "I'm probably going to fail all my math classes." :idea:

haha, I thought I was going to last semester, I almost opted out of math but thanks to this board and a lot of studying I managed somehow, the ridiculous curve bringing me up, strangely, to an A was helpful as well; my math classes have become significantly easier this semester though, causing me to visit rather infrequently.

But thanks for the detailed response daon. Since I've posted this I've spoked with a few people and its been very highly suggested that I take classical algebra, especially since I'm not going the stats route. Eventually I'm going to take a good portion of these courses or their higher level equivalence but I wanted to know specifically what I might be getting into next semester. Since I'm taking differential equations over the summer now I'll have a bit of extra room to figure things out.

And my field of study is math with a bit of physics, although I think I'm going to get into physics more, double major perhaps. I do like math a lot but I'd also like to be able to apply it to something; I was thinking electrical engineering because I want to learn to design synthesizers. Who knows though.