Applicability of Intro To Algebra and Intro to Real Analysis to Physics

[evankiefl]

Applicability of "Intro To Algebra" and "Intro to Real Analysis" to Physics

Well, due to timetable complications I'm having to search for courses that aren't apart of my graduation requirements so I'm thinking about taking some math courses.

Which one of these courses do you think is more applicable to physics? Have you taken either of these and did you enjoy them? Thoughts on more or less what these courses will be like?

Intro To Algebra:

Definitions and examples of groups, rings, fields, and integral domains; rational numbers, real numbers, and complex numbers; polynomials and their factorization; permutations. Additional topics chosen from Boolean algebras and lattices, and transfinite arithmetic.

Intro To Real Analysis:

Axiomatic and metric properties of the real numbers. Sequences and limits. Completeness, compactness, Bolzano-Weierstrass and Heine-Borel theorems. Infinite series. Continuous and uniformly continuous functions.


Thanks for your help!

 

[gb7nash]

What is your math background?

 

[evankiefl]

I'm scheduling for Spring session so by that time I will have

Calculus I (96%)
Math Logic and Foundations (65%)
Calculus II (haven't taken yet)
Matrix Algebra (haven't taken yet)

Math Logic and Foundations had this course description:

Logic and quantifiers, basic set theory, mathematical induction and recursive definitions, divide and conquer recurrence relations, properties of integers, counting, functions and relations, countable and uncountable sets, asymptotic notation.

I got 65% in that class, but I feel if I put a decent amount of effort into that course I could have gotten in the 75-85%.

 

[anonymity]

As far as aplicability, I could not cite specfics, but in the broder sense "pure" math is not overly applicable to physics (or anything else for that matter). From what I have gathered, its aplicability depends highly on what your specialization is (in the general sense, highly theoretical specializations use proof based math a lot more, by defenition -- theyve got to prove their math, they can't observe).

A side note: Real Analysis will be a continuation of your "Foundations" class, in a sense (Assuming that it was an intro-to-proofs class). I think that you will want to take this, and know that if you do enroll, it will end up being a highly proof based, theoretical math class.

 

[gb7nash]

I only asked what your background is since algebra doesn't have any requirements (aside from knowing how to write proofs) and real analysis requires some level of mathematical maturity and higher level classes.

From looking at your classes, it looks like you've been exposed to writing proofs from your logic class, so that's good. However, you haven't finished calc II. Real analysis studies concepts such as continuity, differentiation, integration and sequences of functions. Since you haven't completely finished calculus and haven't been exposed to that many proof-based classes, you'll be in the dark for real analysis. I would strongly suggest not taking it.

Algebra looks like a good bet though. Algebra was one of the first proof-based classes that I took, and I learned a lot from it. You should do fine in that class.

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As far as what class is more applicable to physics, I would probably say real analysis. There are a lot of equations floating around for physics and if you ever need to utilize continuity, take a derivative, etc.. , you're taking advantage of real analysis concepts. It's good to have an understanding of why it all works.

 

[evankiefl]

I only asked what your background is since algebra doesn't have any requirements (aside from knowing how to write proofs) and real analysis requires some level of mathematical maturity and higher level classes.

From looking at your classes, it looks like you've been exposed to writing proofs from your logic class, so that's good. However, you haven't finished calc II. Real analysis studies concepts such as continuity, differentiation, integration and sequences of functions. Since you haven't completely finished calculus and haven't been exposed to that many proof-based classes, you'll be in the dark for real analysis. I would strongly suggest not taking it.

Algebra looks like a good bet though. Algebra was one of the first proof-based classes that I took, and I learned a lot from it. You should do fine in that class.

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As far as what class is more applicable to physics, I would probably say real analysis. There are a lot of equations floating around for physics and if you ever need to utilize continuity, take a derivative, etc.. , you're taking advantage of real analysis concepts. It's good to have an understanding of why it all works.

Intro to Algebra requires the Logic and Foundations course and Real Analysis requires Calculus II and Logic and Foundations. My Dad who is a physicist was very surprised that you only needed Calculus II to take Intro Real Analysis and thinks I should hold off until I've done Multivariable Calc and Differential Equations. What do you think about that?

 

[gb7nash]

Intro to Algebra requires the Logic and Foundations course and Real Analysis requires Calculus II and Logic and Foundations. My Dad who is a physicist was very surprised that you only needed Calculus II to take Intro Real Analysis and thinks I should hold off until I've done Multivariable Calc and Differential Equations. What do you think about that?

I would take your dad's advice. It's better to get more classes under your belt before you take real analysis.