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I want to fill the holes in my knowledge and get to a masterful level at undergraduate material, so I am looking for books to help me with that. I recently took the GRE Math Subject test and I focused on calculus problems. I am not sure how I did and I will be happy getting into just one graduate school, but what I really want to do is get better. I do not have much to do for the next few months, so I want to become expertly proficient in calculus, linear algebra, ODE, abstract algebra, number theory, and any other core subject. I have taken classes on these subjects so I am looking for books that do the following:

  • Cover material in a concise and complete manner
  • Have advanced questions that help me prepare for future learning
  • Have answers to the questions

Thanks!

Pareod
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  • http://math.stackexchange.com/questions/1922417/gre-subject-test-in-mathematics-where-can-i-find-related-past-papers-solution/1922418#1922418 – BCLC Nov 01 '16 at 21:49
  • I'm not looking for GRE Math Subject test practice, but thanks. – Pareod Nov 01 '16 at 22:21
  • Pareod, there are books suggested in links in post... – BCLC Nov 01 '16 at 22:33
  • Ah I see some of them, but this post isn't about reviewing for the test. I'm looking for books that are good ways to refresh my knowledge and fill in gaps. Concise books on each core subject that I might use as a reference for years. – Pareod Nov 01 '16 at 22:57
  • Why doesn't it still apply? Ross - Analysis and Lay - Analysis for example are pretty good. Trench - Analysis not so much. – BCLC Nov 01 '16 at 23:00
  • Well I don't know that Ross and Lay are better than Trench for what I want, so I was hoping to get recommendations specific to what I am asking for instead of sifting through every book. – Pareod Nov 01 '16 at 23:38
  • 'Do Dummit upto field extensions, if you have time do Artin's Algebra too. Rudin Real Analysis, Munkres Topology, Insel Linear Algebra are also must. I suggest to go for Gamlin Complex Analysis, Brown's Complex Analysis is also sufficient but if you are good at Complex Analysis you can save time in the exam by simplifying integral using methods from Complex Analysis. (Do till Residues)' – BCLC Nov 02 '16 at 00:35
  • 'Apostol is a nice reference. The incredibly informative book by Hubbard, which uses much more modern and conventional notation than Apostol, integrates multivariable calculus with linear algebra, but it also discusses differential forms and manifolds, which you don't really need to know for the GRE. (Hubbard's book goes just a little more in depth than the book by Ted Shifrin, who frequently posts in this forum. But his book also includes differential forms.)' – BCLC Nov 02 '16 at 00:36

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