On The List

Please take not that this is not a curriculum meant to be followed in any particular order. Rather it is a list of books grouped by category, that I believe are the best in their respective categories. I have tried to include a wide range of topics, from the most basic to those needng the most prerequisites.

Mathematical History

• Men of Mathematics by E. T. Bell (1937)
• The World of Mathematics edited by James R. Newman (1956; rev. ed. 1959)

Mathematics Puzzles

• The Moscow Puzzles by Boris A. Kordemsky (1962)
• Mathematical Puzzles: A Connoisseur’s Collection by Peter Winkler (2004)

Arithmetic, Prealgebra, and Algebra

• Basic Mathematics by Serge Lang (1971; 2nd ed. 1975)
• The Art of Problem Solving, Vol. 1: The Basics by Richard Rusczyk & Sandor Lehoczky (2006)

Geometry

• Euclid’s Elements by Euclid (c. 300 BCE; Heath trans. 1956)
• Kiselev’s Geometry: Book I. Planimetry by A. P. Kiselev (1951; Dover repr. 1969)

Trigonometry & Precalculus

• Precalculus: Mathematics for Calculus by James Stewart, Lothar Redlin & Saleem Watson (7th ed., 2015)
• Algebra and Trigonometry by Robert F. Blitzer (5th ed., 2018)

Differential & Integral Calculus

• Calculus, Vol. I: One-Variable Calculus with an Introduction to Linear Algebra by Tom M. Apostol (2nd ed., 1969)
• Calculus by Michael Spivak (4th ed., 2008)

Linear Algebra

• Introduction to Linear Algebra by Gilbert Strang (4th ed., 2009)
• Linear Algebra Done Right by Sheldon Axler (3rd ed., 2015)

Discrete Mathematics

• Discrete Mathematics and Its Applications by Kenneth H. Rosen (7th ed., 2011)
• Concrete Mathematics by Ronald L. Graham, Donald E. Knuth & Oren Patashnik (2nd ed., 1994)

Probability & Statistics

• A First Course in Probability by Sheldon M. Ross (8th ed., 2014)
• Introduction to Probability by Dimitri P. Bertsekas & John N. Tsitsiklis (2nd ed., 2008)

Number Theory

• An Introduction to the Theory of Numbers by G. H. Hardy & E. M. Wright (5th ed., 1979)
• Elementary Number Theory by David M. Burton (7th ed., 2010)

Mathematical Logic

• How to Prove It by Daniel J. Velleman (2nd ed., 2006)
• A Mathematical Introduction to Logic by Herbert B. Enderton (2nd ed., 2001)

Bridge to Higher Mathematics

• Book of Proof by Richard Hammack (2nd ed., 2013)
• Transition to Advanced Mathematics by Douglas Smith, Maurice Eggen & Richard St. Andre (7th ed., 2014)

Abstract Algebra

• Abstract Algebra by David S. Dummit & Richard M. Foote (3rd ed., 2003)
• A First Course in Abstract Algebra by John B. Fraleigh (7th ed., 2002)

Real Analysis

• Principles of Mathematical Analysis by Walter Rudin (3rd ed., 1976)
• Introduction to Real Analysis by Robert G. Bartle & Donald R. Sherbert (4th ed., 2011)

Complex Analysis

• Complex Analysis by Lars V. Ahlfors (3rd ed., 1978)
• Complex Variables and Applications by James W. Brown & Ruel V. Churchill (9th ed., 2013)

Topology

• Topology by James R. Munkres (2nd ed., 2000)
• Introduction to Topology: Pure and Applied by Colin Adams & Robert Franzosa (2nd ed., 2007)

Differential Equations

• Elementary Differential Equations and Boundary Value Problems by William E. Boyce & Richard C. DiPrima (10th ed., 2012)
• Ordinary Differential Equations by Vladimir I. Arnold (3rd ed., 1992)

Numerical Analysis

• Numerical Analysis by Richard L. Burden & J. Douglas Faires (9th ed., 2011)
• An Introduction to Numerical Analysis by Kendall E. Atkinson (2nd ed., 1989)

Functional Analysis

• Introductory Functional Analysis with Applications by Erwin Kreyszig (10th ed., 1978)
• Functional Analysis by Walter Rudin (2nd ed., 1991)

Mathematical Writing

• Mathematical Writing by Donald E. Knuth, Tracy Larrabee & Paul M. Roberts (1989)
• Handbook of Writing for the Mathematical Sciences by Nicholas J. Higham (2nd ed., 1998)