Some advice/ book suggestions needed

[stunner5000pt]

I am a physics major but i do want to also major in analysis and calculus. But ihav always had difficulties with the proofs involved (not unlike many of my friends). Although i learn the threorems and axioms it is always so hard for me to really apply them, especially the delta epsilon proofs. I know a lot of proofs - convergence, limits, sup and inf - involve those kind of proofs. Is there a book(s) i can perhaps look into the helping me master the technique?
I have a strong interest in mathematics and i do want to perhaps do mathematical physics since many discoveries i have read of involve calculus theorems that are generally not taught in the undergrad level. (although my knowledge of course content in grad courses is minimal)

 

[2k5 yzf-r1]

If you did well in calc 1,2,3 then I would say to try and squeeze in an "intro to analysis class" if you can. You will learn a lot about proofs, some schools call it advanced calculus. As for books I would check out:

elementary analysis: the theory of calculus, by Ken Ross
foundations of mathematical analysis, by johnsonbaugh and pfaffenberger

If you really want a challenge check out
Principles of mathematical analysis, by walter rudin

If you find those books are still to easy get
Measure and Integral by Wheeden and Zygmund

If you get any of these book start from the beginning and learn the theorems. I mean learn them inside and out and know what they mean in regular words, don't just memorize the symbols.
When you think you know a theorem try to prove it without looking at the book, that's how I taught my self how to do analysis and now I am a beast.

 

[piercas]

First of all, congratulations on pursuing a double major in physics and analysis/calculus! It's certainly a challenging but rewarding combination. As for your difficulties with proofs, it's completely normal to struggle with them, especially in the beginning. Proofs require a lot of practice and a deep understanding of the underlying concepts, so don't get discouraged if you find them difficult.

One book that I highly recommend for mastering the technique of proofs is "How to Prove It: A Structured Approach" by Daniel J. Velleman. This book breaks down the process of proof writing into manageable steps and provides plenty of examples and exercises to help you practice. It also covers the basics of set theory and logic, which are essential for understanding proofs.

Additionally, I would suggest seeking out a study group or tutor who can help you work through proofs and provide feedback on your approach. Sometimes, having a different perspective can make all the difference in understanding a proof.

In terms of your interest in mathematical physics, I would recommend exploring advanced calculus and real analysis courses, as well as differential equations and complex analysis. These topics are essential for understanding the mathematical foundations of physics and will also help you with your proof-writing skills.

Overall, the key to mastering proofs is practice, practice, practice. Don't be afraid to make mistakes and ask for help when needed. With dedication and perseverance, you will definitely improve in this area. Best of luck in your studies!