Top products from r/puremathematics

I think someone doing graphs and combinatorics for the first time should check out Combinatorics and Graph Theory by Harris, Mossinghoff et. al. I found the book to fit my learning style very well and helped me get a 98 in my first C&O course.

Brief, well written explanations, good instructive exercises, and a lot of enrichment sections on interesting topics like Ramsey numbers in the graph theory section.

The third section also gives an introduction to infinite graph theory.

Its also very up to date and is thoroughly referenced which is nice if you want to learn more about a given topic.

http://www.amazon.com/Combinatorics-Graph-Theory-Undergraduate-Mathematics/dp/1441927239/ref=sr_1_1?ie=UTF8&s=books&qid=1293475064&sr=8-1

I have a pdf copy if someone can think of an easy way for me to share it.

You'd think someone in their late 30's would be beyond the point of jerking their ego off, but here we are.

So that something productive might come out of this, here: https://www.amazon.com/Musimathics-Mathematical-Foundations-Music-Press/dp/0262516551

Your local library might have it, your nearest University's library probably does. Some of the math is a little iffy, but he's an intelligent man and it's all really interesting. To answer what is basically your only question, yes, making music is a common hobby among those who are good with math (as well as being a common hobby among those who blink or breathe).

Gallian is a good intro:

https://www.amazon.com/Contemporary-Abstract-Algebra-Joseph-Gallian/dp/1133599702

Doesn't require to much background, but is a good intro to the subject. D&F is a great book, but feels more referency

IF you're intereste in Measure Theory in the setting of Probability this is a book I'm reading now which I find pretty good

https://www.amazon.com/First-Look-Rigorous-Probability-Theory/dp/9812703713

I have trouble getting motivated with books but this one is pretty To-The-Point and concise so it's good for me. Plus there is a solutions manual to the even-numbered excersies online.

I'm a big fan of
Strocchi's Introduction to the Mathematical Structure of Quantum Mechanics where the first couple of chapters give a very nice, concise introduction to (and derivation of!) the C*-algebraic background to quantum mechanics. If you really want to do things rigorously, you'll of course end up with the four volumes of Reed and Simon... of course, these sources are for quantum mechanics, not QFT per se, which is a different kettle of fish entirely.

If you want to carry on with the algebraic formalism in QFT you'll end up with local QFT which involves assigning an algebra of observables to regions of spacetime.

Look on page 80-81 of this book: http://www.amazon.com/dp/0486450015 . It's available in the book preview.

http://www.amazon.com/Berkeley-Problems-Mathematics-Paulo-Souza/dp/0387008926

You might dig this book:
http://www.amazon.com/gp/aw/d/0486406822/