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I've been teaching myself math for more than a year. My current aim is towards algebraic topology and differential geometry.

Apart from a messy (by which i mean some rigorous and some not) background in calculus and linear algebra my current background is this:

I have completed the first 6 chapters of topology by Munkres.

( 1. Set Theory and Logic. 2. Topological Spaces and Continuous Functions. 3. Connectedness and Compactness. 4. Countability and Separation Axioms. 5. The Tychonoff Theorem. 6. Metrization Theorems and Paracompactness.)

At the same time I was reading Munkres I read a mix of Herstein's "Topics in algebra" and "Dummit and Foote".

(Part I-III of Dummit And Foote and pretty much all of Herstein).

My background in analysis is lacking and I was thinking of starting with baby Rudin. I'd like to learn from another book about a different topic at the same time.

As I mentioned My real passion is towards algebraic topology and differential geometry/topology.

How much time is it reasonable to spend with baby Rudin?

What different topic do you recommend me to learn simultaneously?

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I'm no expert but if you're learning by yourself I would suggest to start reading about the topics that excite you! You can always go back and repair lacking foundations when needed. –  Saal Hardali Dec 18 '13 at 0:02
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I agree with @SaalHardali. Why don't you for example start reading Milnor's Topology from the Differentiable Viewpoint and see what prerequisites you are lacking? –  Carsten Schultz Dec 28 '13 at 18:06
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The amount of time needed to master Rudin depends on the individual. From your prior coursework it appears that your background is stronger in algebra/topology than real analysis. I would not put a time line on learning analysis from Rudin as it is both difficult and rewarding. –  Mustafa Said May 4 at 10:15

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