Anyone know of any good mathematical texts?

In summary, the conversation revolves around a graduating senior who has discovered a love for mathematics too late in their academic career. They have taken various courses in calculus, real analysis, abstract mathematics, and applied linear algebra but are unable to continue their studies due to graduation requirements. They are seeking recommendations for texts to further their understanding of theory and proofs in mathematics, specifically in areas such as functional analysis, topology, abstract algebra, and combinatorics. Some suggested books include "What is Mathematics" by Courant & Robbins, "Introductory Functional Analysis with Applications" by Kreyszig, "The Shape of Space" by Weeks, "Foundations of Applied Mathematics" by Greenberg, "Numerical Linear Algebra" by Trefethen &
  • #1
ascapoccia
21
0
I'm a graduating senior who found out much too late in my academic career that I absolutely love mathematics. I've taken all the basic calculus courses, a three quarter series on real analysis, abstract mathematics (essentially a proof course), and an applied linear algebra course. However, the university will not let me stay long enough to continue and get a major or even a minor in mathematics. Because of this, I would need to extend my study beyond coursework.

This leads me to ask : What texts anyone would recommend to read for someone like me, with a basic understanding of theory and proofs, in order to better understand mathematics? I'm much more interested in theory than application, especially since my major is economics and there isn't much application of mathematical theory in my field beyond the courses I've already taken. I was wondering if perhaps anyone knew of some interesting or foundational books I could use to further my study of mathematics. or if there happens to be anyone who knows of a text on the application of mathematical theory to economics beyond the introductory calculus series?

Thank you for your responses.
 
Physics news on Phys.org
  • #2
Mathematics is huge, and there are good books in every field. It's kind of hard to give recommendations without having an idea of what area of mathematics you want to learn about.

So I'm just going to throw out a few mathematics books that I really liked and maybe you could pick up one that sounds interesting.

What is Mathematics - Courant & Robbins

Introductory Functional Analysis with Applications - Kreyszig

The Shape of Space - Weeks

Foundations of Applied Mathematics - Greenberg

Numerical Linear Algebra - Trefethen & Bau

Calculus on Manifolds - Spivak
 
  • #3
Thanks, I'll look into some of those.
 
  • #4
Artin - Algebra. Abstract algebra and rigorous linear algebra will blow your mind.

Munkres - Topology. The cleaner version of real analysis.

As maze said, Spivak's manifolds.

Stillwell - Intro to topology and combinatorics (or something like that).
 

1. What are some good mathematical texts for beginners?

For beginners, "A First Course in Mathematical Analysis" by David Brannan and "How to Prove It: A Structured Approach" by Daniel J. Velleman are highly recommended texts.

2. Are there any mathematical texts that cover a wide range of topics?

Yes, "Mathematical Methods in the Physical Sciences" by Mary L. Boas and "The Princeton Companion to Mathematics" edited by Timothy Gowers are both comprehensive texts that cover a wide range of mathematical topics.

3. What is a good mathematical text for self-study?

"Calculus" by Michael Spivak is a rigorous and well-written text that is often used for self-study by advanced students.

4. Are there any mathematical texts that are suitable for non-mathematicians?

"Mathematics: A Very Short Introduction" by Timothy Gowers and "The Joy of x: A Guided Tour of Math, from One to Infinity" by Steven Strogatz are both accessible and engaging texts for non-mathematicians.

5. Are there any online resources for finding good mathematical texts?

Yes, websites such as Goodreads and Amazon have user reviews and ratings for mathematical texts, making it easy to find highly recommended books. Additionally, asking for recommendations on math forums or social media platforms can also be helpful.

Similar threads

  • STEM Academic Advising
Replies
6
Views
1K
Replies
7
Views
808
  • STEM Academic Advising
Replies
2
Views
931
  • STEM Academic Advising
Replies
11
Views
526
Replies
2
Views
634
  • STEM Academic Advising
Replies
14
Views
553
  • STEM Academic Advising
Replies
5
Views
678
  • STEM Academic Advising
Replies
1
Views
693
Replies
8
Views
1K
  • STEM Academic Advising
Replies
9
Views
1K
Back
Top