What undergrad math courses are traditionally more proof intensive?

[Mhorton91]

Hey everyone, I'm just curious what undergrad mathematics courses are traditionally more proof intensive.

The reason why, is that although I'm a physics major currently, I (generally) really enjoy doing mathematics, just for the sake of mathematics... so I regularly have thoughts of "maybe I should do a math major"... now, I'm not saying I don't enjoy physics, because I do, a lot.

My issue is, I remember reading, or hearing, somewhere to not really even consider a major (or a future career) in mathematics until you've had exposure to proof based courses. I'm just trying to get that exposure...

My thought was if I like the higher level math classes, to try to double major.. I know it will take longer, but, being a 23 y/o sophomore, I'm already "behind" so to speak, so what's another couple semesters!Thanks for any input!
Marshall.

 

[axmls]

Usually the first exposure to writing proofs is in an "introduction to higher mathematics" course that many universities offer. Some higher-ranked universities don't. Then, the first "real" math courses that are proof-intensive are typically analysis and algebra.

 

[Mhorton91]

Usually the first exposure to writing proofs is in an "introduction to higher mathematics" course that many universities offer. Some higher-ranked universities don't. Then, the first "real" math courses that are proof-intensive are typically analysis and algebra.

Thank you! I looked through my university's mathematics department course listings, I think this is our version of "introduction to higher mathematics".. does it look like I'm on the right track?

Thanks again!

MTH 315 Algebraic Structures
Prerequisite: MTH 261.

Sets, logic, quantifiers, functions, relations, matrices, elementary number theory, induction, recursion, combinatorics, with emphasis on reading and writing proofs and the development of mathematical maturity

 

[MidgetDwarf]

Looks like a typical intro proof class. It looks like a discrete math course to me, I can be mistaken.

 

[PhotonSSBM]

Most first courses in proofs are from the perspective of real analysis using introductory set theory and single variable calculus. The class you just listed is more of a discrete mathematics class for people who are either computer science majors or mathematics students who already have some experience in proofs.

This is more of the kind of class you'd be taking first:
http://www.pitt.edu/~borisov/courses/Math0450Spring11.html

 

[QuantumCurt]

I'm currently in a course that revolves around proofs. It's called Fundamental Mathematics and it basically serves as an introduction to advanced math and specifically to writing proofs in advanced math. It should really be a cool class I think. Topics include mathematical objects like rings, fields, and orderings, the least upper bound axiom for real numbers, metric and Euclidean spaces, and the p-adic completion of the rationals. It sounds fairly similar to the course at your school that you found. Today was only the first day of class, but so far it looks like it's going to be a really cool class.

 

[BubblesAreUs]

Looks like a typical intro proof class. It looks like a discrete math course to me, I can be mistaken.

Discrete math units tend to use a lot of mathematical logic and that's essentially what proofs entail. I'd say proofs is quite important in dealing with Set Theory, mathematical statistics ( and probability), and theory of PDEs.

Now my issue is that I like physics, but I'd rather jump straight in astrophysics, theoretical physics without the intermediate units electromag, fluids, thermal statistics and quantum mechanics. It's not due to dislike but more to do with preferring pure maths, number theory ( and cryptography) and theoretical computer science a lot more. I would be more satisfied if math departments offered units with solely astronomy applications.