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.