A guide for how to navigate the math major and how to learn the main subjects. Recommendations for courses and books.

Comment below to tell me what you think. And check out my channel for conversation videos with guests on math and other topics:    / @danielrubin1  

Especially relevant, my conversation with Connor Mooney on The Right Way To Do a Math Major:    • The Right Way to Do a Math Major (Con...  

0:00 Intro
1:33 Calculus
4:06 Multivariable calculus
6:44 Ordinary differential equations
8:56 Linear algebra
12:46 Proof class (not recommended)
13:49 Real analysis
18:31 Partial differential equations
20:51 Fourier analysis
22:18 Complex analysis
25:19 Number theory
30:08 Algebra
36:38 Probability and statistics
39:41 Topology
43:58 Differential geometry
47:25 Algebraic geometry
51:48 Summary and general advice

Books mentioned:
Calculus:
Stewart, Calculus (Early Transcendentals) https://amzn.to/3qKsm36
Spivak, Calculus https://amzn.to/3xgfhB5
Toeplitz, The Calculus: A Genetic Approach https://amzn.to/3hakfKi

Multivariable calculus:
Stewart, Calculus (Early Transcendentals) https://amzn.to/3qKsm36
Edwards, Jr., Advanced Calculus of Several Variables https://amzn.to/2UYiHKB
Bressoud, Second Year Calculus: From Celestial Mechanics to Special Relativity https://amzn.to/3ArbYcj

Ordinary Differential Equations:
Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems https://amzn.to/2V3SPx5

Linear Algebra:
Hoffman and Kunze, Linear Algebra https://amzn.to/3hfljwx
Strang, Linear Algebra and Its Applications https://amzn.to/369znBf
Strang, Linear Algebra and Learning from Data https://amzn.to/3hqbdHU
Demmel, Applied Numerical Linear Algebra https://amzn.to/2UoFEGo

Real analysis:
Rudin, Principles of Mathematical Analysis https://amzn.to/3qJhgeW
Haaser and Sullivan, Real Analysis https://amzn.to/2Tzinl7
Bressoud, A Radical Approach to Real Analysis https://amzn.to/3jzTK2x
Davidson and Donsig, Real Analysis and Applications: Theory in Practice https://amzn.to/3ywDMKT

Partial differential equations:
Strauss, Partial Differential Equations: An Introduction https://amzn.to/3haHLqv

Fourier analysis:
Stein and Shakarchi, Fourier Analysis: An Introduction https://amzn.to/3yfnzta

Complex analysis:
Greene and Krantz, Function Theory of One Complex Variable https://amzn.to/2Tov8iE
Ahlfors, Complex Analysis https://amzn.to/367TboH
Ablowitz and Fokas, Complex Variables: Introduction and Applications https://amzn.to/3ApujGD
Henrici, Applied and Computational Complex Analysis, Vol. 1-3 https://amzn.to/3w9k0mN https://amzn.to/3jzUXH7 https://amzn.to/3ygmkKi
Akhiezer, Elements of the Theory of Elliptic Functions https://amzn.to/2UpaDT6

Number Theory:
Hardy and Wright, An Introduction to the Theory of Numbers https://amzn.to/2V24Bbg
Gauss, Disquisitiones Arithmeticae https://amzn.to/3ApWmWI
Edwards, Fermat's Last Theorem: A Genetic Approach to Algebraic Number Theory https://amzn.to/36b96mc
Stewart and Tall, Algebraic Number Theory and Fermat's Last Theorem https://amzn.to/36aX7VG
Silverman and Tate, Rational Points on Elliptic Curves https://amzn.to/2UhPyK4
Knapp, Elliptic Curves https://amzn.to/3wfiWha

Algebra:
Dummit and Foote, Abstract Algebra https://amzn.to/3dEe2Ea
Dickson, Introduction to the Theory of Algebraic Equations https://amzn.to/2SHv9xy
Edwards, Galois Theory https://amzn.to/3hvRc2H
Stahl, Introductory Modern Algebra: A Historical Approach https://amzn.to/3qIcpuo
Georgi, Lie Algebras in Particle Physics https://amzn.to/3qMYH9B
Fulton and Harris, Representation Theory: A First Course https://amzn.to/3hyfPM2

Probability and Statistics:
Gorroochurn, Classic Problems of Probability https://amzn.to/3jJqAhz
Wasserman, All of Statistics: A Concise Course in Statistical Inference https://amzn.to/3ydwR8U

Topology:
Hatcher, Algebraic Topology (not recommended) https://amzn.to/3wdEeMu

Differential geometry:
do Carmo, Differential Geometry of Curves and Surfaces https://amzn.to/3ArXTvw
do Carmo, Riemannian Geometry (only after a first course in differential geometry) https://amzn.to/3AnF5gC
Coxeter, Introduction to Geometry https://amzn.to/3yjNXCo

Algebraic geometry:
Markushevich, Introduction to the Classical Theory of Abelian Functions https://amzn.to/3jL8AmC
McKean and Moll, Elliptic Curves (forgot to mention, but very highly recommended) https://amzn.to/3huTHCj
Donaldson, Riemann Surfaces https://amzn.to/2Uo5gDl
Clemens, A Scrapbook of Complex Curve Theory https://amzn.to/2V2TcYJ
Stepanov, Codes on Algebraic Curves https://amzn.to/3Ai2ss9
Harris, Algebraic Geometry: A First Course https://amzn.to/3AkJeC6
Griffiths and Harris, Principles of Algebraic Geometry https://amzn.to/3xe8uYP
Hartshorne, Algebraic Geometry (emphatically not recommended) https://amzn.to/3xgDqaK


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