Highly proof-based math courses for undergrads

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In summary, the conversation discusses the idea of taking theory-based math courses as a physics major. The speaker is unsure if it is a good idea and is seeking advice on whether to take these courses early on or wait until after completing more typical courses. They mention their math background, including independent study and covering BC calculus over the summer. The speaker also mentions starting in a basic physics course for majors and potentially being placed in an honors course. The other speaker encourages trying the theoretical courses for better preparation and mentions that lower-level classes often use applications to motivate theory. They also suggest taking pure math courses for fun.
  • #1
JoeTrumpet
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Hello, everyone!

I am beginning college next fall, and I am unsure of where I will/should head in mathematics. My school offers several theory-based courses that are more rigorous and extremely focused on proofs, though this comes at the expense of some application. They tend to be geared toward math majors. Do you think it's a good idea to take a course like this as a physics major? I really enjoy math, and I think it'd be a great experience to try a course like this, but do you suggest trying these courses after I get my more typical courses that have a stronger balance of application and theory out of the way?

My math background is getting a 5 on the Calculus AB exam after independent study last year, and I've touched lightly on some BC topics. I am considering covering the rest of BC calc over the summer.

In case this is of any significance, I am definitely starting in a typical physics 101 course for physics majors, and after a few weeks they will decide if I should be placed in honors. My physics background is very basic.

Thanks!
 
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  • #2
By all means, try the theoretical course. If you can do it, you'll be much better prepared for classes down the road. In lower-level classes, the "applications" are usually designed to motivate the theory, not the other way round. For instance, you may learn how to calculate centers of mass, etc.
 
  • #3
take the pure math courses, if nothing else they'll be fun.
 

1. What are highly proof-based math courses for undergrads?

Highly proof-based math courses for undergrads are advanced mathematics courses that focus on developing students' ability to construct and understand mathematical proofs. These courses often cover topics such as real analysis, abstract algebra, and topology.

2. Why are highly proof-based math courses important for undergraduate students?

Highly proof-based math courses are important for undergraduate students because they provide a strong foundation in mathematical reasoning and critical thinking skills. These courses also prepare students for more advanced math courses and graduate studies in mathematics.

3. Are highly proof-based math courses only for math majors?

No, highly proof-based math courses are not exclusively for math majors. While these courses are typically taken by math majors, they can also be beneficial for students majoring in fields such as physics, computer science, and engineering.

4. What skills are needed to succeed in highly proof-based math courses?

To succeed in highly proof-based math courses, students should have a strong foundation in calculus and linear algebra. They should also possess strong critical thinking skills, the ability to think abstractly, and a willingness to work through challenging problems.

5. How can students prepare for highly proof-based math courses?

Students can prepare for highly proof-based math courses by reviewing their calculus and linear algebra knowledge, practicing with proof-based problems, and familiarizing themselves with basic concepts in real analysis and abstract algebra. It can also be helpful to discuss course expectations with the instructor beforehand.

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