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comment (undergraduate) Algebraic Geometry Textbook Recommendations
@AlJebr If you approach AG from a purely commutative algebra perspective (say via Hartshorne) then you just need a very basic conceptual understanding of complex analysis. However Complex AG, e.g. all the classical results about algebraic curves and surfaces, and the modern study of complex varieties with interconnections with the differential geometry approach, then complex analysis is a BIG important thing. Even in arithmetic geometry, complex analysis of modular forms related to e.g. elliptic curves is fundamental, so "some" complex analysis is a basic conceptual requirement for AG.
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Jan
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comment (undergraduate) Algebraic Geometry Textbook Recommendations
@JKnecht if you need to review basic topology a very short but comprehensive text is Runde's "A taste of Topology", for more rigour and algebraic topology having Bredon's "Geometry and Topology" as a reference is more than enough. Once "basic algebra" is mastered, any good comprehensive reference for adv. commutative algebra is enough, like Eisenbud or Sigh texts.
Jan
14
comment (undergraduate) Algebraic Geometry Textbook Recommendations
@JKnecht since you probably need to catch up fast, I would recommend a book on complex analysis, other on commutative algebra. Follow the first links in this other answer of mine math.stackexchange.com/a/257528/4058 For basic algebra review the excellent free books abstract.ups.edu/download.html and homepage.math.uiowa.edu/~goodman/algebrabook.dir/download.htm Pick any good book on complex analysis, my favourite is Freitag & Busam, the 2nd vol. even introduces Riemann surfaces and modular forms, then follow my 1st link for Gathmann and Kerr as brief but great intros to AG
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Mar
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comment String Theory: What to do?
@AranKomatsuzaki: the books you mention, and many others are less mathematical and more "phenomenological/experimental". Before or along with learning QFT, you may get the basics of real particle physics with Griffiths' "Introduction to Elementary Particles" and then something like Halzen-Martin "Quarks & Leptos". The more you know the better, but few "pure physics" books are easy to digest by some mathematicians as they tend to be too prosaic or not rigorous enough (e.g. more heuristics than formalism). Anyway, the other books you mention are only needed for a particle physicist I think.
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