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Preschool (Arithmetic) Edit

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

  • 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 SchoolEdit

  • 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 SchoolEdit

  • Euclid's Elements
  • Geometry Revisited by Coxeter
  • Elementary Calculus: An Infinitesimal Approach by H. Jerome Keisler[1]
  • 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

UniversityEdit

  • Elements of Set Theory by Enderton
  • A Mathematical Introduction to Logic by Enderton
  • Generatingfunctionology by Wilf[2]
  • 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[Errata 1] and Counterexamples in Topology by Steen & Seebach
  • Principles of Mathematical Analysis by Rudin[Errata 2]
  • 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[Errata 3]
  • Differential Geometry of Curves and Surfaces by Do Carmo[Errata 4]
  • Analysis on Manifolds by Munkres
  • Ordinary Differential Equations by Arnold
  • Algebraic Topology by Hatcher[3]
  • 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 Edit

Light reading Edit

  • 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 Edit

  • 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 Edit

  • 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 Edit

  1. http://www.math.toronto.edu/drorbn/classes/0405/Topology/etc/MunkresErrata.html
  2. http://www.jirka.org/rudin-errata.html
  3. http://www-personal.umich.edu/~hlm/nzm/
  4. http://www.math.umn.edu/~tlawson/5378/docarmo_errata.pdf

Public Domain Material Edit

  1. https://www.math.wisc.edu/~keisler/calc.html
  2. http://www.math.upenn.edu/~wilf/DownldGF.html
  3. http://www.math.cornell.edu/~hatcher/AT/ATpage.html

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