Рет қаралды 48,495
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 ...
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) amzn.to/3qKsm36
Spivak, Calculus amzn.to/3xgfhB5
Toeplitz, The Calculus: A Genetic Approach amzn.to/3hakfKi
Multivariable calculus:
Stewart, Calculus (Early Transcendentals) amzn.to/3qKsm36
Edwards, Jr., Advanced Calculus of Several Variables amzn.to/2UYiHKB
Bressoud, Second Year Calculus: From Celestial Mechanics to Special Relativity amzn.to/3ArbYcj
Ordinary Differential Equations:
Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems amzn.to/2V3SPx5
Linear Algebra:
Hoffman and Kunze, Linear Algebra amzn.to/3hfljwx
Strang, Linear Algebra and Its Applications amzn.to/369znBf
Strang, Linear Algebra and Learning from Data amzn.to/3hqbdHU
Demmel, Applied Numerical Linear Algebra amzn.to/2UoFEGo
Real analysis:
Rudin, Principles of Mathematical Analysis amzn.to/3qJhgeW
Haaser and Sullivan, Real Analysis amzn.to/2Tzinl7
Bressoud, A Radical Approach to Real Analysis amzn.to/3jzTK2x
Davidson and Donsig, Real Analysis and Applications: Theory in Practice amzn.to/3ywDMKT
Partial differential equations:
Strauss, Partial Differential Equations: An Introduction amzn.to/3haHLqv
Fourier analysis:
Stein and Shakarchi, Fourier Analysis: An Introduction amzn.to/3yfnzta
Complex analysis:
Greene and Krantz, Function Theory of One Complex Variable amzn.to/2Tov8iE
Ahlfors, Complex Analysis amzn.to/367TboH
Ablowitz and Fokas, Complex Variables: Introduction and Applications amzn.to/3ApujGD
Henrici, Applied and Computational Complex Analysis, Vol. 1-3 amzn.to/3w9k0mN amzn.to/3jzUXH7 amzn.to/3ygmkKi
Akhiezer, Elements of the Theory of Elliptic Functions amzn.to/2UpaDT6
Number Theory:
Hardy and Wright, An Introduction to the Theory of Numbers amzn.to/2V24Bbg
Gauss, Disquisitiones Arithmeticae amzn.to/3ApWmWI
Edwards, Fermat's Last Theorem: A Genetic Approach to Algebraic Number Theory amzn.to/36b96mc
Stewart and Tall, Algebraic Number Theory and Fermat's Last Theorem amzn.to/36aX7VG
Silverman and Tate, Rational Points on Elliptic Curves amzn.to/2UhPyK4
Knapp, Elliptic Curves amzn.to/3wfiWha
Algebra:
Dummit and Foote, Abstract Algebra amzn.to/3dEe2Ea
Dickson, Introduction to the Theory of Algebraic Equations amzn.to/2SHv9xy
Edwards, Galois Theory amzn.to/3hvRc2H
Stahl, Introductory Modern Algebra: A Historical Approach amzn.to/3qIcpuo
Georgi, Lie Algebras in Particle Physics amzn.to/3qMYH9B
Fulton and Harris, Representation Theory: A First Course amzn.to/3hyfPM2
Probability and Statistics:
Gorroochurn, Classic Problems of Probability amzn.to/3jJqAhz
Wasserman, All of Statistics: A Concise Course in Statistical Inference amzn.to/3ydwR8U
Topology:
Hatcher, Algebraic Topology (not recommended) amzn.to/3wdEeMu
Differential geometry:
do Carmo, Differential Geometry of Curves and Surfaces amzn.to/3ArXTvw
do Carmo, Riemannian Geometry (only after a first course in differential geometry) amzn.to/3AnF5gC
Coxeter, Introduction to Geometry amzn.to/3yjNXCo
Algebraic geometry:
Markushevich, Introduction to the Classical Theory of Abelian Functions amzn.to/3jL8AmC
McKean and Moll, Elliptic Curves (forgot to mention, but very highly recommended) amzn.to/3huTHCj
Donaldson, Riemann Surfaces amzn.to/2Uo5gDl
Clemens, A Scrapbook of Complex Curve Theory amzn.to/2V2TcYJ
Stepanov, Codes on Algebraic Curves amzn.to/3Ai2ss9
Harris, Algebraic Geometry: A First Course amzn.to/3AkJeC6
Griffiths and Harris, Principles of Algebraic Geometry amzn.to/3xe8uYP
Hartshorne, Algebraic Geometry (emphatically not recommended) amzn.to/3xgDqaK
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