I have finished my B.S degree in mathematics recently and I would like to continue to study on my own.

I'm looking for books in all subjects you can recommend. I want to start each subject from its beginning because I don't think that I've gained much knowledge from the degree. I feel like studying at the university wasn't right for me. I've never quite finished the material for any given course or felt like I understood it well enough before I had to jump off to the next course. The only thing I gained was the ability to study on my own.

So I would love for you to recommend books (It can be more than one book for each subject) that start from the beginning of each subject and go on to being advanced (I don't want to do the B.S again. I want to go much beyond the material for a B.S degree in each subject).

Another thing I wish to ask you is to tell me what is the prerequisite for each book or subject (For example if you recommend a typology book and it requires a certain level of calculus). Lastly it would be nice to hear some opinions on where I should begin.

Some of the topics I'm already interested in include Logic, Set theory, Calculus, Probability, Number theory, Combinatorics and Algebra. But the point is to try many more subjects.

I've found some threads asking this question but none for people who already studied math and got a B.S degree (The assumption here is that I can really learn advanced material on my own). Plus most were on a specific subject.

Thank you.

  • $\begingroup$ I'm not sure exactly what you already know, but I'd suggest Spivak's Calculus book, followed by his Calculus on Manifolds, and then perhaps his Differential Geometry series (5 books). Each book should give you enough to start the next. $\endgroup$ – Trurl Jul 7 '16 at 2:06
  • $\begingroup$ Study what you like. You like probability? Go for it. You like analysis? Go deeper, etc... $\endgroup$ – Masacroso Jul 7 '16 at 5:50

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