Difference between revisions of "Math books"

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These '''Math books''' are recommended by [[Art of Problem Solving]] administrators and members of the [http://aops.com/community AoPS Community].
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#REDIRECT [[Mathematics books]]
 
 
Levels of reading and math ability are loosely defined as follows:
 
* Elementary is for elementary school students up through possibly early middle school.
 
* Getting Started is recommended for students grades who are participating in contests like AMC 8/10 and Mathcounts.
 
* Intermediate is recommended for students who can expect to pass the AMC 10/12.
 
* Olympiad is recommended for high school students who are already studying math at an undergraduate level.
 
* Collegiate is recommended for college and university students.
 
 
 
More advanced topics are often left with the above levels unassigned.
 
 
 
Before adding any books to this page, please review the [[AoPSWiki:Linking books]] page.
 
 
 
 
 
== Books By Subject ==
 
 
 
=== General Introduction / Multiple Topics ===
 
==== Getting Started ====
 
* [https://www.amazon.com/gp/product/B09PMLFHX2/ref=ox_sc_act_title_1?smid=ATVPDKIKX0DER&psc=1 Getting Started with Competition Math], a textbook meant for true beginners (on-target middle school students, or advanced elementary school students). It is written by AoPS Community Member [https://artofproblemsolving.com/community/user/243060 cargeek9], currently a junior in high school. It covers the basics of algebra, geometry, combinatorics, and number theory, along with sets of accompanying practice problems at the end of every section.
 
 
 
 
 
=== Algebra ===
 
 
 
====Getting Started====
 
* [https://www.amazon.com/After-School-Maths-100-Challenging-Problems-ebook/dp/B07QFWSTDD/ref=sr_1_2?crid=CB0XAM4P81WI&keywords=after+school+maths+kawasaki&qid=1581288606&sprefix=after+school+maths+%2Caps%2C268&sr=8-2 100 Challenging Maths Problems]
 
* [[AoPS]] publishes [[Richard Rusczyk]]'s, [[David Patrick]]'s, and [[Ravi Boppana]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=prealgebra Prealgebra] textbook, which is recommended for advanced elementary and middle school students.
 
* [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:algebra Introduction to Algebra] textbook, which is recommended for advanced elementary, middle, and high school students.
 
 
 
==== Intermediate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817636773/artofproblems-20 Algebra] by I.M. Gelfand and Alexander Shen.
 
* [http://www.amazon.com/Problems-Algebra-Training-Team-Enrichment/dp/187642012X/ref=sr_1_2?ie=UTF8&s=books&qid=1204029534&sr=8-2 101 Problems in Algebra from the Training of the US IMO Team] by Titu Andreescu and Zuming Feng
 
* [[AoPS]] publishes [[Richard Rusczyk]]'s and [[Mathew Crawford]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=interm:algebra Intermediate Algebra] textbook, which is recommended for advanced middle and high school students.
 
* [http://www.amazon.com/Complex-Numbers-Z-Titu-Andreescu/dp/0817643265/ref=sr_1_1?ie=UTF8&s=books&qid=1204029652&sr=1-1 Complex Numbers from A to... Z] by [[Titu Andreescu]]
 
 
 
 
 
 
 
===Abstract Algebra===
 
 
 
====Collegiate====
 
* [https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/0471433349/ref=sr_1_4dchild=1&keywords=abstract+algebra&qid=1634318876&s=books&sr=1-4 Abstract Algebra] by [[David S. Dummit]] and [[Richard M. Foote]].  This is a famous textbook, and is usually the go-to book for students wishing to learn about [[groups]], [[rings]], [[fields]] and their properties.
 
* [https://www.amazon.com/Undergraduate-Algebra-Texts-Mathematics/dp/1441919597 Undergraduate Algebra] by [[Serge Lang]].  Some compare it to being similar to Dummit and Foote with regards to rigor, although this text is slightly more terse. 
 
* [https://www.amazon.com/Abstract-Algebra-Applications-Thomas-Judson/dp/1944325131 Algebra: Theory and Applications] by [[Thomas Judson]].  One of the easiest books to get started with in the genre, and is very comprehensive.
 
* [https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-Serge/dp/038795385X Algebra] by [[Serge Lang]] -- Extends undergraduate Abstract Algebra to the graduate level by studying homological algebra and more.
 
 
 
 
 
===Calculus===
 
 
 
==== Getting Started ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0883858126/artofproblems-20 The Hitchhiker's Guide to Calculus] by [[Michael Spivak]].
 
* [https://www.amazon.com/Calculus-Made-Easy-Very-Simplest-Introduction/dp/1409724670 Calculus Made Easy] by [[Silvanus P. Thompson]].
 
 
 
==== Single Variable (Intermediate) ====
 
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus Calculus] textbook, which is recommended for advanced middle and high school students.
 
* [https://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051 Calculus: Volume I] by [[Tom M. Apostol]] -- Provides a good transition into linear algebra which is uncommon in single variable calculus texts.
 
* [https://www.amazon.com/Single-Variable-Calculus-James-Stewart-dp-1305266633/dp/1305266633/ref=mt_other?_encoding=UTF8&me=&qid= Single Variable Calculus] by [[James Stewart]] -- Contains plenty of exercises for practice and focuses on application rather than rigor.
 
* [http://www.amazon.com/exec/obidos/ASIN/0914098896/artofproblems-20 Calculus] by [[Michael Spivak]].  Top students swear by this book.
 
* [https://press.princeton.edu/books/hardcover/9780691125336/honors-calculus Honors Calculus] by [[Charles R. MacCluer]] -- Uses the topological definition of the limit rather than the traditional delta-epsilon approach.
 
 
 
==== Multivariable (Collegiate) ====
 
* [https://www.amazon.com/dp/1305266641/?_encoding=UTF8&pd_rd_w=dgDsf&pf_rd_p=f0565570-f67b-4783-ab26-5a1f2c0bb3fd&pf_rd_r=7Y23GMHWH3DGTT7ZYJQF&pd_rd_r=a9ba1496-356e-4cbd-8e81-6d00bf440a1e&pd_rd_wg=OeBPr&ref_=bd_tags_dp_rec Multivariable Calculus] by [[James Stewart]].
 
* [https://www.amazon.com/Advanced-calculus-Frederick-S-Woods/dp/B0006AMNBI Advanced Calculus] by [[Frederick S. Woods]].  Advanced Calculus an iconic textbook because of how [[Richard Feynman]] learned calculus from it.  Feynman later popularized a technique taught in the book in college, which is now called the "Feynman Integration Technique."
 
* [https://www.amazon.com/Calculus-Vol-Multi-Variable-Applications-Differential/dp/0471000078/ref=sr_1_1?dchild=1&keywords=apostol+calculus+volume+2&qid=1634316891&sr=8-1 Calculus: Volume II] by [[Tom M. Apostol]].
 
 
 
 
 
 
 
=== Analysis ===
 
 
 
==== Collegiate ====
 
* [https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics-ebook/dp/B00XWDQUH4/ref=reads_cwrtbar_4/141-5921801-5552153?pd_rd_w=qfNPT&pf_rd_p=0285128d-50e0-4388-acba-48a4a1f64720&pf_rd_r=KKVZB6CTYFYZZBXTX003&pd_rd_r=a64cf661-9db5-4d77-82ad-10b31b05dc41&pd_rd_wg=5WaBc&pd_rd_i=B00XWDQUH4&psc=1 Understanding Analysis] by [[Stephen Abbott]].
 
* [https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X Principles of Mathematical Analysis] by [[Walter Rudin]].  Affectionately called "Baby Rudin" by some, Principles of Mathematical Analysis is known to be very terse for the analysis layman.
 
* [https://www.amazon.com/Analysis-Third-Texts-Readings-Mathematics/dp/9380250649 Analysis I] by [[Terrence Tao]] -- An easier first read than Rudin, and provides plenty of examples with thorough explanations.
 
* [https://www.amazon.com/Analysis-II-Third-Readings-Mathematics/dp/9380250657/ref=pd_bxgy_img_1/141-5921801-5552153?pd_rd_w=uYcOn&pf_rd_p=c64372fa-c41c-422e-990d-9e034f73989b&pf_rd_r=G13XQBEGM3PWH1RT97BC&pd_rd_r=32b7fa0f-65e8-4d8c-ad45-9f1a1c3c592a&pd_rd_wg=cbkGA&pd_rd_i=9380250657&psc=1 Analysis II] by [[Terrence Tao]] -- Continues off from where Volume I ended and finishes at the Lebesgue Integral.
 
* [https://www.amazon.com/Real-Analysis-Integration-Princeton-Lectures-ebook/dp/B007BOK6PW Real Analysis] by [[Rami Shakarchi]] and [[Elias M. Stein]].
 
* [https://www.amazon.com/Complex-Analysis-Elias-M-Stein-ebook/dp/B007K1BYD4/ref=reads_cwrtbar_1/141-5921801-5552153?pd_rd_w=hTDD7&pf_rd_p=0285128d-50e0-4388-acba-48a4a1f64720&pf_rd_r=VCM2JFE523FGVQE2HZ85&pd_rd_r=67a8e84d-8c73-4f2b-a3f1-463517afb999&pd_rd_wg=zaS7Z&pd_rd_i=B007K1BYD4&psc=1 Complex Analysis] by [[Rami Shakarchi]] and [[Elias M. Stein]].
 
* [https://www.amazon.com/Real-Complex-Analysis-Higher-Mathematics/dp/0070542341/ref=pd_bxgy_img_1/141-5921801-5552153?pd_rd_w=bf70N&pf_rd_p=c64372fa-c41c-422e-990d-9e034f73989b&pf_rd_r=T14A8XPXYK2XY7TCTSAC&pd_rd_r=2c7958c3-a431-4714-a756-12927e7267f1&pd_rd_wg=hbV0A&pd_rd_i=0070542341&psc=1 Real and Complex Analysis] by [[Walter Rudin]].  Called "Papa Rudin" by some, Real and Complex Analysis is typically used at the graduate level.
 
* [https://www.amazon.com/gp/product/B005HDOLUK?notRedirectToSDP=1&ref_=dbs_mng_calw_2&storeType=ebooks Functional Analysis]  by [[Rami Shakarchi]] and [[Elias M. Stein]].
 
 
 
 
 
 
 
=== Combinatorics ===
 
 
 
==== Getting Started ====
 
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:counting Introduction to Counting & Probability] textbook, which is recommended for advanced middle and high school students.
 
 
 
==== Intermediate ====
 
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=interm:counting Intermediate Counting & Probability] textbook, which is recommended for advanced middle and high school students.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856158/artofproblems-20 Mathematics of Choice] by Ivan Niven.
 
* [http://www.amazon.com/exec/obidos/ASIN/0817643176/artofproblems-20 102 Combinatorial Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
 
* [http://www.amazon.com/Path-Combinatorics-Undergraduates-Counting-Strategies/dp/0817642889/ref=sr_1_2?ie=UTF8&s=books&qid=1219586040&sr=1-2 A Path to Combinatorics for Undergraduates: Counting Strategies] by [[Titu Andreescu]] and [[Zuming Feng]].
 
 
 
==== Olympiad ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817643176/artofproblems-20 102 Combinatorial Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
 
* [http://www.math.upenn.edu/~wilf/DownldGF.html Generatingfunctionology]
 
 
 
==== Collegiate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0521663512/artofproblems-20 Enumerative Combinatorics, Volume 1] by Richard Stanley.
 
* [http://www.amazon.com/exec/obidos/ASIN/0521789877/artofproblems-20 Enumerative Combinatorics, Volume 2] by Richard Stanley.
 
* [http://www.amazon.com/First-Course-Probability-Sheldon-Ross/dp/0131856626/ref=pd_bbs_sr_1/103-7161656-8805468?ie=UTF8&s=books&qid=1190719501&sr=8-1 A First Course in Probability] by Sheldon Ross
 
* [https://www.amazon.com/Introductory-Combinatorics-Kenneth-P-Bogart/dp/0121108309 Introductory Combinatorics] by [[Kenneth P. Bogart]]
 
 
 
 
 
 
 
=== Geometry ===
 
 
 
==== Getting Started ====
 
* [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:geometry Introduction to Geometry] textbook, which is recommended for advanced middle and high school students.
 
 
 
==== Intermediate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0486691543/artofproblems-20 Challenging Problems in Geometry] -- A good book for students who already have a solid handle on elementary geometry.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic.
 
*[http://www.amazon.com/Geometry-Problems-AwesomeMath-Summer-Program/dp/0979926947 106 Geometry Problems from the AwesomeMath Summer Program] by Titu Andreescu, Michal Rolinek, and Josef Tkadlec
 
 
 
==== Olympiad ====
 
* [https://www.amazon.com/gp/product/0883858398?%2AVersion%2A=1&%2Aentries%2A=0&pldnSite=1 Euclidean Geometry in Mathematical Olympiads] by Evan Chen
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic.
 
* [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerfdtfeger.
 
* [http://www.amazon.com/exec/obidos/ASIN/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]].
 
* [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]].
 
* [http://www.amazon.com/Geometric-Transformations-I-Number-8/dp/0883856085/ref=sr_1_6?ie=UTF8&s=books&qid=1199807141&sr=1-6 Geometric Transformations I], [http://www.amazon.com/Geometric-Transformations-New-Mathematical-Library/dp/0883856212/ref=sr_1_5?ie=UTF8&s=books&qid=1199807203&sr=1-5 Geometric Transformations II], and [http://www.amazon.com/Geometric-Transformations-III-Mathematical-Library/dp/0883856247/ref=sr_1_1?ie=UTF8&s=books&qid=1199807249&sr=1-1 Geometric Transformations III] by I. M. Yaglom.
 
*[http://www.amazon.com/Geometry-Problems-Awesomemath-Year-Round-Program/dp/0979926971/ref=sr_1_1?s=books&ie=UTF8&qid=1433093202&sr=1-1&keywords=107+geometry+problems 107 Geometry Problems from the AwesomeMath Year-Round Program] Titu Andreescu, Michal Rolinek, and Josef Tkadlec
 
 
 
==== Collegiate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerfdtfeger.
 
* [http://www.amazon.com/exec/obidos/ASIN/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]].
 
* [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]].
 
 
 
 
 
 
 
===Topology===
 
 
 
====Collegiate====
 
* [https://www.amazon.com/Topology-James-Munkres-January-2000/dp/B015X4YE2M/ref=pd_sbs_14/141-5921801-5552153?pd_rd_w=u2xlH&pf_rd_p=690958f6-2825-419e-9c16-73ffd4055b65&pf_rd_r=JK1FK4KKJ1DSRW3V75C5&pd_rd_r=4c987b1e-0d6e-43ae-90ab-4cf445052ae5&pd_rd_wg=o2PH5&pd_rd_i=B015X4YE2M&psc=1 Topology] by [[James Munkres]].  Topology is arguably the most renowned topology textbook of all time.  It also contains an excellent introduction to set theory and logic. 
 
 
 
 
 
 
 
=== Inequalities ===
 
 
 
==== Intermediate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856034/artofproblems-20 Introduction to Inequalities]
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856042/artofproblems-20 Geometric Inequalities]
 
 
 
==== Olympiad ==== 
 
* [https://www.amazon.co.uk/Advanced-Olympiad-Inequalities-Algebraic-Geometric/dp/1794193928/ref=sr_1_fkmrnull_1?crid=XVQYS8R7NOL9&keywords=advanced+olympiad+inequalities&qid=1555930111&s=gateway&sprefix=advanced+ol%2Caps%2C165&sr=8-1-fkmrnull Advanced Olympiad Inequalities] by Alijadallah Belabess. 
 
* [http://www.amazon.com/exec/obidos/ASIN/052154677X/artofproblems-20 The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities] by J. Michael Steele.
 
* [http://www.amazon.com/exec/obidos/ASIN/0387982191/artofproblems-20 Problem Solving Strategies] by Arthur Engel contains significant material on inequalities.
 
*Titu Andreescu's Book on Geometric Maxima and Minima
 
* [http://ultrametric.googlepages.com/tin2007.pdf Topics in Inequalities] by Hojoo Lee
 
* [http://www.artofproblemsolving.com/Resources/Papers/MildorfInequalities.pdf Olympiad Inequalities] by Thomas Mildorf
 
* [https://artofproblemsolving.com/articles/files/KedlayaInequalities.pdf A<B (A is less than B)] by Kiran S. Kedlaya
 
* [http://can-hang2007.blogspot.com/2009/12/secrets-in-inequalities-volume-1-basic.html Secrets in Inequalities vol 1 and 2] by Pham Kim Hung
 
 
 
==== Collegiate ====
 
 
 
* [http://www.amazon.com/exec/obidos/ASIN/0521358809/artofproblems-20 Inequalities] by [[G. H. Hardy]], [[J. E. Littlewood]], and [[G. Polya]].
 
 
 
 
 
 
 
=== Number Theory ===
 
 
 
==== Getting Started ====
 
* The AoPS [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:nt Introduction to Number Theory] by [[Mathew Crawford]].
 
*[https://www.amazon.com/Number-Theory-Dover-Books-Mathematics/dp/0486682528 Number Theory] by [[George E. Andrews]].
 
 
 
==== Olympiad ====
 
* [http://www.amazon.com/exec/obidos/ASIN/081763245X/artofproblems-20 Number Theory: A Problem-Solving Approach] by [[Titu Andreescu]] and Dorin Andrica.
 
* [http://www.amazon.com/104-Number-Theory-Problems-Training/dp/0817645276/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1199806669&sr=8-1 104 Number Theory Problems from the Training of the USA IMO Team] by [[Titu Andreescu]], Dorin Andrica and Zuming Feng.
 
* [http://www.problem-solving.be/pen/published/pen-20070711.pdf Problems in Elementary Number Theory] by Hojoo Lee.
 
* [https://numbertheoryguy.com/publications/olympiad-number-theory-book/ Olympiad Number Theory through Challenging Problems] by Justin Stevens.
 
*[https://www.amazon.in/Elementary-Number-Theory-David-Burton/dp/1259025764 Elementary Number theory] by David M. Burton
 
*[https://drive.google.com/file/d/1BcJTLjQaelZ4w_70oHKyImC2I8zLfyrt/view Modern Olympiad Number Theory] by [[Aditya Khurmi]].
 
 
 
==== Collegiate ====
 
* [https://www.amazon.com/Introduction-Theory-Numbers-G-Hardy/dp/0199219869 An Introduction to the Theory of Numbers] by [[G. H. Hardy]], [[Edward M. Wright]], and [[Andrew Wiles]] (6th Edition).
 
 
 
 
 
 
 
=== Trigonometry ===
 
==== Getting Started ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817639144/artofproblems-20 Trigonometry] by I.M. Gelfand and Mark Saul.
 
 
 
==== Intermediate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817639144/artofproblems-20 Trigonometry] by I.M. Gelfand and Mark Saul.
 
* [http://www.amazon.com/exec/obidos/ASIN/0817643346/artofproblems-20 103 Trigonometry Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
 
 
 
==== Olympiad ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817643346/artofproblems-20 103 Trigonometry Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
 
 
 
 
 
 
 
=== Problem Solving ===
 
 
 
==== Getting Started ====
 
* the [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=1 Art of Problem Solving Volume 1] by Sandor Lehoczky and Richard Rusczyk is recommended for avid math students in grades 7-9.
 
* [http://www.amazon.com/exec/obidos/ASIN/0821804308/artofproblems-20 Mathematical Circles] -- A wonderful peak into Russian math training.
 
* [http://www.amazon.com/exec/obidos/ASIN/0486613488/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
 
 
 
==== Intermediate ====
 
* the [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=2 Art of Problem Solving Volume 2] by Sandor Lehoczky and Richard Rusczyk is recommended for avid math students in grades 9-12.
 
* [http://www.amazon.com/exec/obidos/ASIN/0471135712/artofproblems-20 The Art and Craft of Problem Solving] by [[Paul Zeitz]], former coach of the U.S. math team.
 
* [https://www.amazon.com/How-Solve-Mathematical-Princeton-Science-dp-069111966X/dp/069111966X/ref=dp_ob_title_bk How to Solve It] by [[George Polya]].
 
* [http://www.amazon.com/exec/obidos/ASIN/1895997046/artofproblems-20 A Mathematical Mosaic] by [[Putnam Fellow]] [[Ravi Vakil]].
 
* [http://www.amazon.com/exec/obidos/ASIN/0883857006/artofproblems-20 Proofs Without Words], [http://www.amazon.com/exec/obidos/ASIN/0883857219/artofproblems-20 Proofs Without Words II]
 
* [http://www.amazon.com/exec/obidos/ASIN/0486425665/artofproblems-20 Sequences, Combinations, Limits]
 
* [http://www.amazon.com/exec/obidos/ASIN/0486613488/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
 
 
 
==== Olympiad ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817641556/artofproblems-20 Mathematical Olympiad Challenges]
 
* [http://www.amazon.com/exec/obidos/ASIN/0387982191/artofproblems-20 Problem Solving Strategies] by Arthur Engel.
 
* [http://www.amazon.com/exec/obidos/ASIN/0387961712/artofproblems-20 Problem Solving Through Problems] by Loren Larson.
 
 
 
== General Interest ==
 
* [http://www.amazon.com/exec/obidos/ASIN/0385495323/artofproblems-20 The Code Book] by Simon Singh.
 
* [http://www.amazon.com/exec/obidos/ASIN/0618251413/artofproblems-20 Count Down] by Steve Olson.
 
* [http://www.amazon.com/exec/obidos/ASIN/0385493622/artofproblems-20 Fermat's Enigma] by Simon Singh.
 
* [http://www.amazon.com/exec/obidos/ASIN/0465026567/artofproblems-20 Godel, Escher, Bach]
 
* [http://www.amazon.com/exec/obidos/ASIN/014014739X/artofproblems-20 Journey Through Genius] by William Dunham.
 
* [http://www.amazon.com/exec/obidos/ASIN/0521427061/artofproblems-20 A Mathematician's Apology] by [[G. H. Hardy]].
 
* [http://www.amazon.com/exec/obidos/ASIN/0066210704/artofproblems-20 The Music of the Primes] by Marcus du Sautoy.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883857006/artofproblems-20 Proofs Without Words] by Roger B. Nelsen.
 
* [http://www.amazon.com/exec/obidos/ASIN/0195105192/artofproblems-20 What is Mathematics?]by Richard Courant, Herbert Robbins and Ian Stewart.
 
 
 
== Math Contest Problem Books ==
 
=== Elementary School ===
 
* [[Mathematical Olympiads for Elementary and Middle Schools]] ([[MOEMS]]) publishes [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MOEMS.php two excellent contest problem books].
 
 
 
 
 
 
 
=== Getting Started ===
 
* [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MC.php MATHCOUNTS books] -- Practice problems at all levels from the [[MATHCOUNTS]] competition.
 
* [http://www.artofproblemsolving.com/Books/AoPS_B_CP_AMC.php Contest Problem Books] from the [[AMC]].
 
* [http://www.amazon.com/exec/obidos/ASIN/0521585686/artofproblems-20 More Mathematical Challenges] by Tony Gardiner.  Over 150 problems from the [[UK Junior Mathematical Olympiad]], for students ages 11-15.
 
 
 
 
 
=== Intermediate ===
 
* The [[Mandelbrot Competition]] has [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Mand.php two problem books for sale] at [[AoPS]].
 
* ARML books:
 
**[http://www.amazon.com/exec/obidos/ASIN/0962640166/artofproblems-20 ARML-NYSML 1989-1994] (see [[ARML]]).
 
** [http://www.arml.com/books.htm ARML 1995-2004]
 
* [http://www.amazon.com/exec/obidos/ASIN/0883855194/artofproblems-20 Five Hundred Mathematical Challenges] -- An excellent collection of problems (with solutions).
 
* [http://www.amazon.com/exec/obidos/ASIN/0486277097/artofproblems-20 The USSR Problem Book]
 
*Leningrad Olympiads (Published by MathProPress.com)
 
 
 
=== Olympiad ===
 
* [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=50 USAMO 1972-1986] -- Problems from the [[United States of America Mathematical Olympiad]].
 
* [http://www.amazon.com/exec/obidos/ASIN/0387242996/artofproblems-20 The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004]
 
* [http://www.amazon.com/exec/obidos/ASIN/0817641556/artofproblems-20 Mathematical Olympiad Challenges]
 
* [http://www.amazon.com/exec/obidos/ASIN/0387982191/artofproblems-20 Problem Solving Strategies] by Arthur Engel.
 
* [http://www.amazon.com/exec/obidos/ASIN/0387961712/artofproblems-20 Problem Solving Through Problems] by Loren Larson.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856441/artofproblems-20 Hungarian Problem Book III]
 
* [http://www.amazon.com/exec/obidos/ASIN/088385645X/artofproblems-20 Mathematical Miniatures]
 
*Mathematical Olympiad Treasures
 
*Collections of Olympiads (APMO, China, USSR to name the harder ones) published by MathProPress.com.
 
 
 
=== Collegiate ===
 
* Three [[Putnam competition]] books are [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Putnam.php available at AoPS].
 
 
 
== See also ==
 
* [[Math textbooks]]
 
* [[Resources for mathematics competitions]]
 
* [[Olympiad Books]]
 
[[Category:Books]]
 

Latest revision as of 16:36, 1 March 2025

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