Math Textbook Recommendations

A more thorough subject by subject list is on the Mathematics page.

Preschool (Arithmetic)

Feel free to skip Preschool if you can add and multiply with any amount of proficiency.

Quick Arithmetic by Robert Carman

• All the Math You'll Ever Need: A Self-Teaching Guide by Slavin (All the *Arithmetic* you'll ever need)
• Speed Mathematics Simplified (Dover Books) by Edward Stoddard
• Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks by Benjamin
• The Mental Calculator's Handbook by Fountain and Koningsveld (More depth than the above, basic to intermediate level)
• Dead Reckoning: Calculating Without Instruments by Doerfler (Warning: More advanced than the above, covers logarithms and trigonometric functions and their inverses, may require some calculus knowledge for maximum enjoyment)^[site]

Grade School

• Algebra by Gelfand and Shen
• Functions and Graphs by Gelfand, Glagoleva, and Shnol
• The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
• Trigonometry by Gelfand and Saul
• Kiselev's Geometry: Book I. Planimetry & Book II. Stereometry
• Basic Mathematics by Lang and/or Precalculus with Unit Circle Trigonometry by Cohen

High School

• Euclid's Elements
• Geometry Revisited by Coxeter
• Elementary Calculus: An Infinitesimal Approach by H. Jerome Keisler<ref>https://www.math.wisc.edu/~keisler/calc.html</ref>
• Calculus Vol I & II by Apostol or Calculus by Spivak
• Linear Algebra and Its Applications by Strang
• Ordinary Differential Equations by Tenenbaum and Pollard
• A Primer of Abstract Mathematics by Ash 
• Conjecture and Proof by Laczkovich
• Proofs from THE BOOK by Aigner and Ziegler

University

• Elements of Set Theory by Enderton
• A Mathematical Introduction to Logic by Enderton
• Generatingfunctionology by Wilf<ref>http://www.math.upenn.edu/~wilf/DownldGF.html</ref>
• Linear Algebra by Shilov
• Geometry by Brannan
• Complex Analysis by Bak
• Visual Complex Analysis by Needham
• Probability and Random Processes by Grimmett & Stirzaker
• Applied Partial Differential Equations by Haberman
• Partial Differential Equations by Strauss
• Numerical Analysis by Burden
• Matrix Computations by Golub and Van Loan
• Algebra by Artin
• Topics in Algebra by Herstein
• The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by Steele
• Inequalities by Hardy, Littlewood, and Polya
• Topology by Munkres<ref group="Errata">http://www.math.toronto.edu/drorbn/classes/0405/Topology/etc/MunkresErrata.html</ref> and Counterexamples in Topology by Steen & Seebach
• Principles of Mathematical Analysis by Rudin<ref group="Errata">http://www.jirka.org/rudin-errata.html</ref>
• Counterexamples in Analysis by Gelbaum and Olmsted
• A Course of Modern Analysis by Whittaker and Watson and Special Functions by Wang and Guo
• An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery<ref group="Errata">http://www-personal.umich.edu/~hlm/nzm/</ref>
• Differential Geometry of Curves and Surfaces by Do Carmo<ref group="Errata">http://www.math.umn.edu/~tlawson/5378/docarmo_errata.pdf</ref>
• Analysis on Manifolds by Munkres
• Ordinary Differential Equations by Arnold
• Algebraic Topology by Hatcher<ref>http://www.math.cornell.edu/~hatcher/AT/ATpage.html</ref>
• Fourier Analysis; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; Functional Analysis by Stein
• Theoretical Numerical Analysis: A Functional Analysis Framework by Atkinson and Han
• An Introduction to Probability Theory and Its Applications Vol. 1&2 by Feller
• Partial Differential Equations by Jost
• Basic Algebra I & II by Jacobson
• Modern Graph Theory by Bollobás
• A Classical Introduction to Modern Number Theory by Ireland and Rosen
• Introduction to Analytic Number Theory by Apostol
• Enumerative Combinatorics by Stanley

Historical

Light reading

• e: the Story of a Number by Maor
• Trigonometric Delights by Maor
• MY BRAIN IS OPEN: The Mathematical Journeys of Paul Erdos by Schechter
• A Mathematician Apology by Hardy
• I Want to be a Mathematician: An Automathography by Halmos
• The Apprenticeship of a Mathematician by Andre Weil
• The Man Who Knew Infinity: A Life of the Genius Ramanujan by Kanigel
• The Way I Remember It by Walter Rudin
• The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940 by Goodstein
• Hilbert - Courant by Reid
• The Honors Class: Hilbert's Problems and Their Solvers by Yandell
• Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Ronan
• Gauss: A Biographical Study by Bühler

Textbooks and heavier works

• A History of Mathematics by Katz
• A History of Mathematics by Boyer and Merzbach
• Mathematics and Its History by Stillwell
• A History of Vector Analysis: The Evolution of the Idea of a Vectorial System by Crowe
• Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Dover Books) by Gregory H. Moore
• A History of Algebraic and Differential Topology, 1900 - 1960 by Dieudonne
• History of Topology by James
• Emergence of the theory of Lie groups. An essay in the history of mathematics 1869 - 1926 by Hawkins
• From Error Correcting Codes Through Sphere Packings to Simple Groups by Thompson
• History of Banach spaces and Linear Operators by Pietch

Original influential works, papers, and books of interest

• A History of Greek Mathematics by Heath
• The Works of Archimedes by Heath
• Ptolemy's Almagest
• On the Revolutions of Heavenly Spheres by Nicolaus Copernicus
• The Principia: Mathematical Principles of Natural Philosophy by Isaac Newton, Cohen and Whitman (Translators)
• Elements of Algebra by Leonhard Euler; notes added by Johann Bernoulli, and additions by Joseph-Louis Lagrange
• Introductio in analysin infinitorum (Introduction to Analysis of the Infinite) by Leonhard Euler
• Institutiones calculi differentialis (Foundations of Differential Calculus), Institutionum calculi integralis (Foundations of Integral Calculus) by Leonhard Euler
• Disquisitiones Arithmeticae by Carl Gauss
• An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole
• The Mathematical Theory of Communication by Claude Shannon

Errata

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Public Domain Material

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