Is a Proof Writing Course Necessary for Advanced Math Courses?

[mlarson9000]

I plan on studying math through real analysis. I am taking calc 3, and linear algebra at the moment. Calc 3 is not a problem for me, but linear algebra is by far the most difficult class I've had in my entire life. I'm still hoping I can get a B, but I may have blown that with the test I took today. No matter what happens, I will keep on going, even if I need to retake it, but I worry about the road ahead. At the very minimum, I will be taking Advanced Calculus and Intro to Analysis. I expect these to be very difficult as well. I am wondering how beneficial it would be to take this proof writing class described below, as it is not required for the two previously mentioned.

5000 Fundamental Concepts of Mathematics and Proof Writing. Cr. 3
Prereq: MAT 2250 or 2860 or consent of instructor. Not considered a 5000+ level course for undergrad. degree requirements in mathematics; no credit towards graduate degree in mathematics. Fundamental concepts: basic logic, basic set theory, functions, equivalence relations. Proof: methods of proof, structures of proofs, proof-writing in a variety of mathematical subjects. (F,W)

Or I could just go straight into this:
5070 Advanced Calculus. Cr. 4
Prereq: MAT 2030, and 2250 or 2350. The real numbers; limits; continuity; sequences and series of functions; uniform convergence; power series; differentiation; integration. (T)
(I hear this starts over at calc 1, and is strictly proofs.)

 

[maverick_starstrider]

That would depend. Are you in math or physics?

 

[George Jones]

That would depend. Are you in math or physics?

Maybe I've missed something, but I don't understand why this would depend on whether mlarson9000 is in math or physics.

If mlarson9000 were asking "Should I study math through real analysis?", the answer possibly (but not necessarily) could depend on whether mlarson9000 is in math or physics. mlarson9000, however, is not asking this. mlarson9000 is asking "Given that I am going to study math through real analysis, and that I am going to take Advanced Calculus, would taking Fundamental Concepts of Mathematics and Proof Writing first be of substantial benefit in understanding the material in Advanced Calculus?"

I don't know the answer to this question. I think you (mlarson9000) should ask a few of the faculty members in the math department of your school. I took several real analysis courses, the first two of which redid Calc I and II in a rigourous manner. The results in the first real analysis course were often poor, and a prerequisite course, Logic, sets, relations, functions. Development of skills in theoretical mathematics, was introduced specifically to address this. Without more details, I can't compare this course with Math 5000.

 

[mlarson9000]

That would depend. Are you in math or physics?

I am in economics. I have a BA in econ, and am starting an MA program in the fall. I intend to apply to phd programs later. From what I hear, the math is pretty intense, so the more I know going in, the better off I will be.

 

[maverick_starstrider]

In which case I don't know how useful (in fact I don't know if it'd be remotely useful) to take a proof writing course centered on set theory and number theory. I can't see it having any use in an economic degree. I'd say it's better to just take another step up the calculus ladder. Or, if possible, take another linear algebra course. You may hate it and find it very difficult but it has a lot of use in things like econometrics.