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
^{[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

## University[]

- 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[]

### 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