Choosing good textbooks in linear algebra, analysis and graph theory

Question

I need some advices to choose good undergraduate textbooks in LINEAR ALGEBRA, ANALYSIS and GRAPH THEORY. I found:

Gilbert Strang // Introduction to Linear Algebra - Welleslay Cambridge Press (2009)

Igor Kriz, Ales Pultr // Introduction to Mathematical Analysis - Birkhäuser (2013) and

Ioan Tomescu, R. A. Melter // Problems in Combinatorics and Graph Theory - Wiley Interscience

John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff// Combinatorics and Graph theory - Springer

I did study some combinatorics and analysis while preparing for the mathematical olympiads.

What are your recommendations?

Thanks in advance.

Answer 1

Sheldon Axler - Linear Algebra Done Right is pretty amazing. No matrices or determinants, and quite rigorous.

Principles of Mathematical Analysis by Walter Rudin is a classic first-year text in analysis. Quite terse, and very thorough; it's a great text! (If you have specific questions, don't hesitate to ask!)

Answer 2

You can't go wrong with Doug West's Graph Theory text. It's got great breadth and depth. It hits on the basics really well, including both mathematical and computer science related applications. You'll get cycles, paths, trees, algorithms, cuts, flows, connectivity, planarity, topological graph theory, colorability, Ramsey theory, algebraic graph theory, Matroids, and NP-Completeness proofs. Plus, it's a very approachable text.

Answer 3

Gilbert Strang's Algebra book is great. There are also corresponding video lectures on OCW so if you get stuck you can see how he explains it. He draws a lot of pictures (both in the book and the lectures) which really help to understand Linear Algebra.

I am currently using Rudin's Principles of Mathematical Analysis for self-study but am not convinced it's ideal. It is rigorous and does not provide a lot of intuition. However if you google a theorem usually some explanation of the proof and / or theorem shows up.