Proof Practice

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Anonymous
Proof Practice 2017-06-12 05:03:31 Post No. 8971798
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Proof Practice Anonymous 2017-06-12 05:03:31 Post No. 8971798 [Report]

Hey /sci/

This book was a rude awakening for me. I was always good at math until I got to proof-based Mathematics and realized I was actually shit at math. The plan has always been Physics which I'm good at, but I miss being able to enthusiastically and confidentially signing up for more and more advanced math classes.

I got a B in real analysis and a B in abstract algebra and it discouraged me a lot. I never had any formal training in proofs and that's what fucking shafted me when I got to this. It's the only reason I haven't taken topology, number theory, graduate group theory, etc.

I'm taking complex analysis next fall as a last shot at pure math before I commit to physics the rest of my life.

Any suggestions, advice, books, etc? Anything helps!

Anonymous 2017-06-12 05:06:45 Post No.8971806
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Anonymous 2017-06-12 05:06:45 Post No.8971806 [Report]

Here are some books you might find useful:

How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
Mathematics: Its Content, Methods and Meaning - A.D. Aleksandrov, A.N. Kolmogorov, & M.A. Lavrent'ev (optional but still informative)
The Art and Craft of Problem Solving - Paul Zeitz (optional but still helpful)

Anonymous 2017-06-12 05:11:50 Post No.8971815
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Anonymous 2017-06-12 05:11:50 Post No.8971815 [Report]

>>8971798
Try going through the first few chapters of Tao's analysis I. It goes over basic material, but asks you to prove everything rigorously. Might be good for you

Anonymous 2017-06-12 05:12:26 Post No.8971817
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Anonymous 2017-06-12 05:12:26 Post No.8971817 [Report]

>>8971798
Real analysis is a rude awakening for everyone. And if you only like math as it pertains to physics, I wouldn't blame you for struggling with abstract algebra.

Anonymous 2017-06-12 05:16:30 Post No.8971825
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Anonymous 2017-06-12 05:16:30 Post No.8971825 [Report]

>>8971806
>>8971815
Thank you so much!

>>8971817
And I actually do really enjoy learning Pure math, evening if it doesnt directly pertain to physics (although I loved group theory specifically because it helped me understand quantum and particle physics better)

Even though my primary interest is physics, I still love knowing pure math for its own sake.

Anonymous 2017-06-12 08:13:47 Post No.8972052
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Anonymous 2017-06-12 08:13:47 Post No.8972052 [Report]

>>8971798

Boost your mathematical maturity by learning other fields.

A Primer of Abstract Mathematics by Ash
The Joy of Sets: Fundamentals of Contemporary Set Theory by Devlin
An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery
Linear Algebra by Shilov (Dover Books)
Introduction to Logic: and to the Methodology of Deductive Sciences (Dover Books) by Alfred Tarski
Introduction to Metamathematics by Kleene
Principles of Topology (Dover Books) by Croom

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