These Math books are Solving administrators and members of books are recommended by Art of Problem Solving administrators the AoPS-M AoPS-MathLinks athLinks Community Community.. Levels of of reading and math at h ability ability are loosely defined def ined as foll f ollows: ows: Elementary Eleme ntary is for elementary school students up through pos sibly early early middle middle school. Getting Getting Started is recomm recommende d for students grades 6 to 9. Intermediate Int ermediate is recom is recomm mende d for students grad es 9 to 12 . Olympiad Olymp iad is recomm recommende d for high high school stude nts w ho are a lread lread y studying studying math at an undergraduate undergraduate level. leve l. Collegiate is recommende recommende d for college college and university university students .
More advanced advanced topics are topics are often left with the above levels unassigned. Before adding adding any books to this page, please review the AoPS AoPSWiki Wiki:Link :Linking ing books books page. page.
Contents Con tents [hide [hide]] 1 Books by subject 1.1 Algebra 1.1.1 1.1 .1 Getting Started S tarted 1.1.2 Intermediate 1.2 Analysis 1.3 Calculus 1.3.1 1.3 .1 High School School 1.3.2 1.3 .2 Collegiate 1.4 Combinatorics Combinatorics 1.4.1 1.4 .1 Getting Started Started 1.4.2 1.4 .2 Intermediate 1.4.3 Olympiad Olym piad 1.4.4 Collegia Colle giate te 1.5 Geometry 1.5.1 Getting Started 1.5.2 Intermediate 1.5.3 Olympiad 1.5.4 Collegiate 1.6 Inequalities 1.6.1 Intermediate 1.6.2 Olympiad 1.6.3 Collegiate 1.7 Number 1.7 Number Theory 1.7.1 Introductory 1.7.2 Olympiad 1.8 Trigonometry 1.8.1 Getting Started 1.8.2 Intermediate 1.8.3 Olympiad 1.9 Problem Solving 1.9.1 Getting Started 1.9.2 Intermediate
1.9.3 Olympiad 2 General interest 3 Math contest problem books 3.1 Elementary School 3.2 Getting Started 3.3 Intermediate 3.4 Olympiad 3.5 Collegiate 4 See also
Books by subject Algebra Getting Getting Started AoPS publishes Ri AoPS publishes Richard chard Rusczyk Rusczyk's, 's, David Pa tric trick k's, and Ravi Boppa Boppa na na's 's Prealgebra which is recomm recommende d for advanced elementary and middle middle schoo l students . AoPS publishes Ri AoPS publishes Richard chard Rusczyk Rusczyk's 's Intr Introduction oduction to Al Algeb geb ra advanced elementary, elementary, middle, middle, and high school stude nts.
textbook,
textbo ok, which is recomm recommende d for
Intermediate Algebra
by I.M. I.M. Gelfand an d Alexand er Shen.
101 P roblems in Algebra from the Training of the US IMO Team Feng
by Titu Titu Andree scu an d Zuming Zuming
AoPS publishes Ri AoPS publishes Richard chard Rusczyk Rusczyk's 's and Mathew Craw for ford d 's Intermediate Algebra is recomm recommende d for advanced middle and high s chool studen ts. Com Co mplex Numbe rs from A to .. .... Z
textboo k, which which
by Titu Andreescu
Analysis Counte rexam rexamples ples in Analysis Analysis
by Berna rd R. Gelbaum and John M. H. Olmsted.
Calculus High School AoPS publishes Dr. David Pa tric AoPS publishes trick k's Calculus middle and high school students . Calculus
textboo k, which which is recommende recommende d for ad vanced
by Mic Michae hae l Spivak. Spivak. Top students s we ar by this this book.
The Hitchhiker's Hitchhiker's Guide to Ca Calcul lculus us
by Mi Michae chae l Spivak. Spivak.
AP Calculus Calculus P roblem roblems s a nd Solutions P art II AB and BC mastering the material required for the AP exam.
-- A fantas fantas tic reso reso urce urce for studen ts
Collegiate Calculus on Manif Calculus Manifolds: olds: A Modern Approa ch to C lassical Theorems Theorems o f Advanced Advanced Calculus by Mic Michae hae l Spivak. Spivak.
Combinatorics Getting Getting Started AoPS publishes Dr. David Pa tric AoPS publishes trick k's Intr Introduction oduction to Counting & Proba bil bility ity recomm recommende d for advanced middle middle and high school stude nts.
textbo ok, which is
Intermediate AoPS publishes Dr. David Pa tric AoPS publishes trick k's Interm Intermediate ediate Counting & Prob abili ability ty recomm recommende d for advanced middle middle and high school stude nts. Mathematics of Choice
textbook, which is
by Ivan Niven.
102 Combinatori Combinatorial al P roblem roblems s
by Titu Andreescu and Andreescu and Zum Zuming ing Fen g .
A Path to Combinatori Combinatorics cs for Undergraduate s: Counting Strategies Feng.. Feng
by Titu Andreescu and Andreescu and Zuming
Olympiad 102 Combinatori Combinatorial al P roblem roblems s
by Titu Andreescu and Andreescu and Zum Zuming ing Fen g .
Generatingfunctionology
Collegiate Enumerative Co mbinato ric rics, s, Volume Volume 1
by Richard Richard Stanley.
Enumerative Co mbinato ric rics, s, Volume Volume 2
by Richard Richard Stanley.
A First First Co urse in Proba bil bility ity
by Sheldon Ross
Geometry Getting Getting Started AoPS publishes Ri AoPS publishes Richard chard Rusczyk Rusczyk's 's Introduction to Geometry advanced middle middle and high schoo l students.
textbo ok, which is recomm recommende d for
Intermediate Challenging P roblem roblems s in Geometry Geometry on elementary geometry. geometry. Geometry Revisited
-- A good bo ok for students w ho already have a s olid handle
-- A class ic.
Olympiad Geometry Revisited
-- A class ic.
Geometry of Co mplex Numbers
by Hans Schwe Schwe rfdtfeger. rfdtfeger.
Geometry: Geom etry: A Comprehens Comprehens iv ive e Course Non-Euclidean Geometry Projective Geometry
by Dan Dan Pedo e.
by H.S H.S.M .M.. Co xeter .
by H.S H.S.M .M.. Co xete r.
Geometric Trans Trans form formation ation s I III by I. M. Yag Yag lom.
, Geometric Trans Trans form formations ations II
Collegiate Geometry of Co mplex Numbers
by Hans Schwe Schwe rfdtfeger. rfdtfeger.
Geometry: Geom etry: A Comprehens Comprehens iv ive e Course Non-Euclidean Geometry Projective Geometry
by Dan Dan Pedo e.
by H.S H.S.M .M.. Co xeter .
by H.S H.S.M .M.. Co xete r.
Inequalities Intermediate Introduction Intr oduction to Inequaliti Inequalities es Geometric Inequ alities
, and Geometric Trans Trans form formations ations
Olympiad The Ca uchyuchy-Sc Schwa hwa rz Maste r Class : An Introduction Introduction to the Ar Artt o f Mathematical Mathematical Inequalities Inequalities Michael Steele. Problem Solving Strategies
by J.
by Arthur Engel contains significant material on inequalities.
Titu Titu Andre es cu's Boo k on Geo metric metric Maxima Maxima a nd Minima Minima Topics in Inequalities Olympiad Inequalities
by Hojoo Lee by Thomas Mildorf
A
by Pham Kim Hung
Collegiate Inequalities
by G. H. Hard y, J. E. Littlew Littlew oo d , and G. Polya. Polya .
Number Number T heory Introductory The AoPS Introduction to Number Theory
by Mathew Craw for ford d.
Olympiad Numbe Num berr Theory: A Proble mm-Solvi Solving ng App roa roach ch
by Titu Andreescu and Andreescu and Dorin Andrica. Andrica.
104 Number Theo ry Problems from the Training Training o f the USA IMO IMO Team Andrica and Zuming Feng. Problems in Elementary Number Theory
by Titu Andreescu, Andreescu , Dorin
by Hojoo Hojoo Lee .
Trigonometry Getting Getting Started Trigonometry
by I.M. Gelfand a nd Ma rk Saul.
Intermediate Trigonometry
by I.M. Gelfand a nd Ma rk Saul.
103 Trigonometry Problems
by Titu Andreescu and Andreescu and Zum Zuming ing Fe ng ng..
Olympiad 103 Trigonometry Problems
by Titu Andreescu and Andreescu and Zum Zuming ing Fe ng ng..
Problem Solving Getting Getting Started the Art of Prob lem Solving Solving Volume 1 by Sand or Leh oczky and Richard Richard Rusczyk is is recomm recommende d for avid avid math students in grades 7-9. Mathe matic matical al C irc ircles les
-- A wond erful peak into Russ ian math training. training.
100 Great Problems of Elementary Mathematics
by Heinrich Heinrich Dorrie.
Intermediate the Art of Prob lem Solving Solving Volume 2 by Sand or Leh oczky and Richard Richard Rusczyk is is recomm recommende d for avid avid math students in grades 9-12. The Art and Cra ft of Problem Solving Solving
by Paul Zeitz, Zeitz , former former coa ch of the U.S. math tea m.
How to Solve It
by George Po ly lya a.
A Mathe Mathe matical Mosa ic
by Putna m Fellow Fellow Ravi Vakil. Vakil.
Proofs Without Words
, Proofs Without Words II
Sequences, Combinations, Limits 100 Great Problems of Elementary Mathematics
by Heinrich Heinrich Dorrie.
Olympiad Mathematical Olympiad Challenges Problem Solving Strategies
by Arthur Engel.
Problem Solving Through Problems
by Loren Loren Larso n.
General interest The Code Book Count Down
by Simon Simon Singh.
by Steve Olson.
Fermat's En igm igma a
by Simon Simon Singh Singh .
Gode l, Esche r, Bach Journey Through Genius
by W illi illiam am Dunha m.
A Mathematician's Apology The Music of the P rim rimes es
by G. H. Hard y.
by Marcus Marcus d u Sautoy.
Proofs Without Words
by Roger B. Nelse Nelse n.
Wha t is Mathematics? Mathematics?
by Richard Richard Courant, Herbert Robb Robb ins and Ian Stewa rt.
Math contest contest problem books Elementary School Mathematical Olympiads for Elementary and Middle Schools ( Schools (MOEMS MOEMS)) publishes publishes two excel excellent lent contest problem books .
Getting Getting Started Starte d MathCounts Math Counts books
-- Practice prob lems at a ll levels levels from the MathCounts competition.
Conte st Problem Books Books
from the AMC AMC..
More Mathematical Mathematical C hallenges by Tony Gardiner. Over 150 prob lems from from the UK Junior Mathe matic matical al O lym lympiad piad,, for for studen ts age s 11-15.
Intermediate The Mandelbrot C ompetiti ompetition on has has two problem boo ks for sale
at AoPS AoPS..
ARML books: ARML-NYSML 1989-1994
(see ARML ARML). ).
ARML AR ML 1995-200 4 Five Fi ve Hundred Mathemati Mathematical cal Challenges
-- An excellent collection collection o f problems (with so lutions).
The USSR Pro Problem blem Book Leningrad O lym lympiads (Published (Published by MathProP ress.com) ress.com)
Olympiad
USAMO 1972-1986
-- Problems from the United States of America America Mathe matical Olympiad Olympiad .
The IMO Co mpend ium ium:: A Collection Collection of P roblem roblems s Suggeste d for The International Mathematical Mathematical Olympiads: 1959-2004 Mathematical Olympiad Challenges Problem Solving Strategies
by Arthur Engel.
Problem Solving Through Problems
by Loren Loren Larso n.
Hungarian Prob lem Book Book III Mathe matic matical al Miniatu Miniatures res Mathematical Olympiad Treasures Collections Collections o f Olympiads Olympiads (APMO, (APMO, China, USSR USSR to na me the harder o nes ) published published by MathProPress.com.
Collegiate Three Putnam competition books competition books are available at AoPS
.
