TITLE: Complete undergraduate bundle-pack
QUESTION [38 upvotes]: First of all I'm sorry if this is not the right place to post this. I like math a lot. But I'm not sure if i want to do a math major in college. My question is: Can you give me a list of books that will give me the knowledge of the subjects a person doing a math major would have? I think I know all the stuff a good high school student knows. Thanks.

REPLY [5 votes]: Chicago undergraduate mathematics bibliography


ELEMENTARY
This includes “high school topics” and first-year calculus. Contents


Algebra $(4)$


Gelfand/Shen, Algebra
Gelfand/Glagoleva/Shnol, Functions and graphs
Gelfand/Glagoleva/Kirillov, The method of coordinates
Cohen, Precalculus with unit circle trigonometry, and its content is here.

Geometry $(2)$


Euclid, The elements
Coxeter, Geometry revisited

Foundations $(1)$


Rucker, Infinity and the mind

Problem solving $(4)$


New Mathematical Library problem books
Larson, Problem solving through problems
Pólya, How to solve it
Pólya, Mathematics and plausible reasoning, I and II

Calculus $(6)$


Spivak, Calculus
Spivak, The hitchhiker's guide to calculus
Hardy, A course of pure mathematics
Courant, Differential and integral calculus
Apostol, Calculus
Janusz, Calculus

Bridges to intermediate topics $(2) $


Smith, Introduction to mathematics: algebra and analysis
Johnson, Introduction to logic via numbers and sets




INTERMEDIATE
Roughly, general rather than specialized texts in higher mathematics. I would not hesitate to recommend any book here to honors second-years, but they might not find easy going in some of them. 


Foundations $(5)$


Halmos, Naive set theory
Fraenkel, Abstract set theory
Ebbinghaus/Flum/Thomas, Mathematical logic
Enderton, A mathematical introduction to logic
Landau, Foundations of analysis

General abstract algebra $(7)$ (difficulty: $\color{orange}{\mathscr{m}}$oderate-$\color{red}{\mathscr{h}}$igher)


$\color{orange}{\mathscr{m}}$ - Dummit/Foote, Abstract algebra
$\color{orange}{\mathscr{m}}$ - Herstein, Topics in algebra
$\color{orange}{\mathscr{m}}$ - Artin, Algebra
$\color{red}{\mathscr{h}}$ - Jacobson, Basic algebra I
$\color{red}{\mathscr{h}}$ - Hungerford, Algebra
$\color{red}{\mathscr{h}}$ - Lang, Algebra
$\color{red}{\mathscr{h}}$ - Mac Lane/Birkhoff, Algebra

Linear algebra $(3)$


Halmos, Finite dimensional vector spaces
Curtis, Abstract linear algebra
Greub, Linear algebra and Multilinear algebra

Number theory $(5)$


Ireland/Rosen, A classical introduction to modern number theory
Burn, A pathway into number theory
- Hardy/Wright, Introduction to number theory
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Combinatorics and discrete mathematics $(1)$
Real analysis $(10)$
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Multivariable calculus $(2)$

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Complex analysis $(5)$
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Differential equations $(2)$

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Point-set topology $(5)$
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Differential geometry $(4)$
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Classical geometry $(3) $
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TO BE CONTINUED