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I'm going to enter into my final year undergraduate degree in Applied Mathematics in a few months (the university doesn't have pure maths), I have some maths credit from the other university Calc I-III and Linear Algebra (where I was attempting to study pure maths, but personal life stuff happened). I covered a bit of Differential Equations, Integral Transforms, Group Theory, Stats, Complex Analysis, number theory, Discrete Maths, and of course real/complex analysis, but didn't cover those subjects into depth.

I only have one year left to finish off my undergrad degree in Applied Math before attempting to try to get into the Masters program in Pure Maths (at another university).

Anyways straight into my inquiry on this matter. I am planning to cover Real, Complex, and Functional Analysis in the first six months, then I'll try to cover Algebra, Geometry and Topology in the last six months... this will all be done in 2020. My undergrad applied maths program doesn't offer those subjects in great detail, but however I'll be taking a course on complex variables (minus conformal mapping) and Series/Transforms. I am of course planning to self-study and will try to dissect definitions/theorems/lemmas/propositions slowly. I am also planning to study 10 pages a day.

I need to know one text that combines real, complex, and functional analysis. Also another one text that combines algebra, geometry and topology. So I can give myself a good grounding before trying to do a masters in pure maths.

Thanks.

DarkVampiric AbstractArtist
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    Why should it be a single textbook? You can use multiple textbooks. – littleO Oct 19 '19 at 00:39
  • I feel like it would take too long to cover three textbooks instead of one, plus I would have to do my coursework. – DarkVampiric AbstractArtist Oct 19 '19 at 00:41
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    Why should the number of books affect how much time it takes if you want to learn the same material? – Trevor Gunn Oct 19 '19 at 00:42
  • If I were to cover three books instead of one book, it'd be over 1000+ pages and I don't want it to deter away from my coursework. – DarkVampiric AbstractArtist Oct 19 '19 at 00:49
  • It would be unusual for one book to combine these three subjects. Even if there were one book, it would be unlikely to be the most clearly written option available. I think you're better off reading parts of multiple textbooks. (The list of subjects you mentioned is quite difficult to cover in one year by the way.) – littleO Oct 19 '19 at 01:04
  • Rudin's book "Real and complex analysis" seem to go your way, except that it does not really include functional analysis as far as I can tell. – Suzet Oct 19 '19 at 01:08
  • TrevorGunn littleO Suzet Alright, thanks guys. I guess might as well cover three texts instead of one, I'll spend four months on each of them. I'll use understanding (real) analysis by Abbott, Complex Analysis by Snaff, and Functional Analysis (Analysis II) possibly by Tao or Kreyzig. Then the three month holiday after I finish my applied maths undergrad, I'll go balls to the wall with Algebra, Geometry and Topology. – DarkVampiric AbstractArtist Oct 19 '19 at 01:16
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    @DarkVampiricAbstractArtist the books I used for analysis were rudin's principles of mathematical analysis, stein shakarchi complex analysis, munkres point set topology (which was very helpful with rudin), folland's real analysis (which covers a good amount of functional analysis). i highly, highly suggest these books – mathworker21 Oct 19 '19 at 01:27

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