My Favorite Math Books: Analysis, Algebra & More

[_F_]

My favorite math books:

1. Linear Algebra by Friedberg, Insel, and Spence.
2. Principals of Mathematical Reasoning by Peter J. Eccles. (if you need to learn proofs, this book is the way to go).
3. Set Theory and Logic by Robert Stoll.
4. Handbook of Mathematics by Bronshtien, Semendyayev, Musiol, and Muehlig (published by Springer).


I'm looking for books in the following topics:
1. Analysis
2. Abstract Algebra
3. Differential Equations
4. Nonlinear Systems/Dynamic Systems/Chaos
5. Anything else!


Any recommendations out there? The books I am recommending I truly back 110%. They are the books that changed my mathematical abilities the most.

 

[Tac-Tics]

Real Analysis By Norman B. Haaser, Joseph A. Sullivan -
This book did wonders for me. It was really tough, since I only had calculus and some early linear algebra when I started it, but it goes every step of the way from basic set theory, to the definition of the reals via cauchy sequences, to metric spaces, it has a short intro to topology, linear spaces, lesbegue integarls... I loved it, and I still keep it open in the magazine rack in my bathroom.Introduction to Analysis By Maxwell Rosenlicht
I bought this one earlier this year. After Haaser, this one was MUCH easier. It focuses more on a stable foundation for single-variable calculus, going from limits of sequences to limits of functions, then directly to derivatives and later Reimann integrals.Introduction to Topology By Theodore W. Gamelin, Robert Everist Greene
I like this book for topology because, unlike any other math text I've ever come across, it tries to give *motivation* for what you're doing at the start of every chapter. (I wish more authors did this). The introduction isn't as nice as the other two books above, but if you're read either one, that should compensate.

 

[lurflurf]

Coments apply to above book

1. Analysis
Complex Analysis (Graduate Texts in Mathematics) by Serge Lang
assumes only calculus
Introduction to Analysis, by Maxwell Rosenlicht
Very easy
Elementary Real and Complex Analysis, by Georgi E. Shilov
Easy
Undergraduate Analysis (Undergraduate Texts in Mathematics) by Serge Lang
Real and Functional Analysis (Graduate Texts in Mathematics) (v. 142) by Serge Lang

2. Abstract Algebra
Linear Algebra by Georgi E. Shilov
Advanced Linear Algebra (Graduate Texts in Mathematics) by Steven Roman
3rd edition out, 2nd edition many error, uses modules
A First Course in Abstract Algebra, by John B. Fraleigh
very easy, too expensive
Undergraduate Algebra (Undergraduate Texts in Mathematics) by Serge Lang
Algebra (AMS/Chelsea Publication) by Saunders Mac Lane and Garret Birkhoff
Algebra by Serge Lang
hard
3. Differential Equations
Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard
easy, wordy
Ordinary Differential Equations by Edward L. Ince
Elementary Differential Equations by Earl D. Rainville
Avoid recent editions and brief version


4. Nonlinear Systems/Dynamic Systems/Chaos
?
5. Anything else!
Anything else by Serge Lang.

 

[DyslexicHobo]

I think I would really enjoy reading about mathematics. How advanced are the books you both recommended? I have had up to calc 3 and part of linear algebra. Are these books focused on teaching specific methods of using different maths, or is it more focused on building a mathematical foundation?

If the latter, I think I'll definitely enjoy reading some of those texts!

Thanks