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 <url>index.php AoPS-MathLinks Community</url>.
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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].
  
 
Levels of reading and math ability are loosely defined as follows:
 
Levels of reading and math ability are loosely defined as follows:
 
* Elementary is for elementary school students up through possibly early middle school.
 
* Elementary is for elementary school students up through possibly early middle school.
* Getting Started is recommended for students grades 6 to 9.
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* Getting Started is recommended for students grades who are participating in contests like AMC 8/10 and Mathcounts.
* Intermediate is recommended for students grades 9 to 12.
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* 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.
 
* Olympiad is recommended for high school students who are already studying math at an undergraduate level.
 
* Collegiate is recommended for college and university students.
 
* Collegiate is recommended for college and university students.
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More advanced topics are often left with the above levels unassigned.
 
More advanced topics are often left with the above levels unassigned.
  
Before adding any books to this page, please review the [[Linking books]] page.
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Before adding any books to this page, please review the [[AoPSWiki:Linking books]] page.
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== Books By Subject ==
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=== General Introduction / Multiple Topics ===
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==== Getting Started ====
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* [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.
  
  
== Books by subject ==
 
 
=== Algebra ===
 
=== Algebra ===
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====Getting Started====
 
====Getting Started====
* [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=11 Introduction to Algebra] textbook, which is recommended for advanced elementary, middle, and high school students.
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* [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]
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* [[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.
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* [[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.
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==== Intermediate ====
 
==== Intermediate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817636773/artofproblems-20 Algebra] by I.M. Gelfand and Alexander Shen.
 
* [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
 
* [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
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* [[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]]
 
* [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]]
  
=== Analysis ===
 
* [http://www.amazon.com/exec/obidos/ASIN/0486428753/artofproblems-20 Counterexamples in Analysis] by Bernard R. Gelbaum and John M. H. Olmsted.
 
  
  
=== Calculus ===
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===Abstract Algebra===
==== High School ====
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====Collegiate====
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* [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.
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* [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. 
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* [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.
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* [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.
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* [https://www.amazon.com/Basic-Algebra-Second-Dover-Mathematics/dp/0486471896 Basic Algebra I] by [[Nathan Jacobson ]] -- Contains harder and more interesting problems than Dummit and Foote. Assumes a decent coverage of Linear Algebra
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===Calculus===
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==== Getting Started ====
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* [http://www.amazon.com/exec/obidos/ASIN/0883858126/artofproblems-20 The Hitchhiker's Guide to Calculus] by [[Michael Spivak]].
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* [https://www.amazon.com/Calculus-Made-Easy-Very-Simplest-Introduction/dp/1409724670 Calculus Made Easy] by [[Silvanus P. Thompson]].
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==== Single Variable (Intermediate) ====
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* [[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.
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* [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.
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* [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.
 
* [http://www.amazon.com/exec/obidos/ASIN/0914098896/artofproblems-20 Calculus] by [[Michael Spivak]].  Top students swear by this book.
* [http://www.amazon.com/exec/obidos/ASIN/0883858126/artofproblems-20 The Hitchhiker's Guide to Calculus] by [[Michael Spivak]].
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* [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.
* [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=8 AP Calculus Problems and Solutions Part II AB and BC] -- A fantastic resource for students mastering the material required for the AP exam.
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==== Multivariable (Collegiate) ====
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* [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]].
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* [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."
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* [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]].
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=== Analysis ===
  
 
==== Collegiate ====
 
==== Collegiate ====
* [http://www.amazon.com/exec/obidos/ASIN/0805390219/artofproblems-20 Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus] by [[Michael Spivak]].
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* [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]].
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* [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.
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* [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.
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* [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.
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* [https://www.amazon.com/Real-Analysis-Integration-Princeton-Lectures-ebook/dp/B007BOK6PW Real Analysis] by [[Rami Shakarchi]] and [[Elias M. Stein]].
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* [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]].
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* [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.
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* [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 ===
 
=== Combinatorics ===
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==== Getting Started ====
 
==== Getting Started ====
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=3 Introduction to Counting & Probability] textbook, which is recommended for advanced middle and high school students.
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* [[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.
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https://www.awesomemath.org/product/112-combinatorial-problems-from-amsp/.112 problems is a great discrete math book covering topics ranging from permutations and combinations to using creativity to count to doing proofs and then gives exposure to advanced topics like probability theory.Great for AMC 8 /10/12
  
 
==== Intermediate ====
 
==== Intermediate ====
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=302 Intermediate Counting & Probability] textbook, which is recommended for advanced middle and high school students.
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* [[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/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/exec/obidos/ASIN/0817643176/artofproblems-20 102 Combinatorial Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
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* [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 ====
 
==== Olympiad ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0817643176/artofproblems-20 102 Combinatorial Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
 
* [http://www.amazon.com/exec/obidos/ASIN/0817643176/artofproblems-20 102 Combinatorial Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
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* [http://www.math.upenn.edu/~wilf/DownldGF.html Generatingfunctionology]
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==== Collegiate ====
 
==== 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/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/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
 
* [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
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* [https://www.amazon.com/Introductory-Combinatorics-Kenneth-P-Bogart/dp/0121108309 Introductory Combinatorics] by [[Kenneth P. Bogart]]
  
  
  
 
=== Geometry ===
 
=== Geometry ===
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==== Getting Started ====
 
==== Getting Started ====
* [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=9 Introduction to Geometry] textbook, which is recommended for advanced middle and high school students.
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* [[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 ====
 
==== 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/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/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic.
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*[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 ====
 
==== Olympiad ====
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* [https://www.amazon.com/gp/product/0883858398?%2AVersion%2A=1&%2Aentries%2A=0&pldnSite=1 Euclidean Geometry in Mathematical Olympiads] by Evan Chen
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* [https://www.amazon.com/Solving-Problems-Geometry-Mathematical-Competitions/dp/981458374X/ref=sr_1_1?crid=2ZR4GP9R2R7KG&keywords=Solving+Problems+in+Geometry&qid=1646794260&sprefix=solving+problems+in+g%2Caps%2C1809&sr=8-1 Solving Problems In Geometry: Insights And Strategies For Mathematical Olympiad And Competitions] by Kim Hoo Hang and Haibin Wang
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic.
 
* [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/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerfdtfeger.
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* [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective 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/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.
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*[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 ====
 
==== Collegiate ====
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* [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/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/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]].
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===Topology===
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====Collegiate====
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* [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 ===
 
=== Inequalities ===
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==== Intermediate ====
 
==== Intermediate ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856034/artofproblems-20 Introduction to Inequalities]
 
* [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]
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856042/artofproblems-20 Geometric Inequalities]
  
==== Olympiad ====
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==== 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/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.
 
* [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
 
*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 ====
 
==== Collegiate ====
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=== Number Theory ===
 
=== Number Theory ===
==== Introductory ====
+
 
* The AoPS [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=10 Introduction to Number Theory] by [[Mathew Crawford]].
+
==== 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 ====
 
==== 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/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.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.
=== Probability ===
+
* [https://numbertheoryguy.com/publications/olympiad-number-theory-book/ Olympiad Number Theory through Challenging Problems] by Justin Stevens.
==== Getting Started ====
+
*[https://www.amazon.in/Elementary-Number-Theory-David-Burton/dp/1259025764 Elementary Number theory] by David M. Burton
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=3 Introduction to Counting & Probability] textbook, which is recommended for advanced middle and high school students.
+
*[https://drive.google.com/file/d/1BcJTLjQaelZ4w_70oHKyImC2I8zLfyrt/view Modern Olympiad Number Theory] by [[Aditya Khurmi]].
 
 
==== Intermediate ====
 
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=302 Intermediate Counting & Probability] textbook, which is recommended for advanced middle and high school students.
 
  
 
==== Collegiate ====
 
==== Collegiate ====
* [http://www.amazon.com/First-Course-Probability-Sheldon-Ross/dp/0131856626/ref=pd_bbs_sr_1/103-7161656-8805468?ie=UTF8&s=books&qid=1191347841&sr=8-1 A First Course in Probability] by Sheldon Ross
+
* [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).
  
  
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=== Problem Solving ===
 
=== Problem Solving ===
 +
 
==== Getting Started ====
 
==== 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.
 
* 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/0821804308/artofproblems-20 Mathematical Circles] -- A wonderful peak into Russian math training.
* [http://www.amazon.com/exec/obidos/ASIN/0821804308/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
+
* [http://www.amazon.com/exec/obidos/ASIN/0486613488/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
  
 
==== Intermediate ====
 
==== 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.
 
* 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.
 
* [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.
* [http://www.amazon.com/exec/obidos/ASIN/0691023565/artofproblems-20 How to Solve It] by [[George Polya]].
+
* [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/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/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/0486425665/artofproblems-20 Sequences, Combinations, Limits]
* [http://www.amazon.com/exec/obidos/ASIN/0821804308/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
+
* [http://www.amazon.com/exec/obidos/ASIN/0486613488/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
  
 
==== Olympiad ====
 
==== Olympiad ====
Line 146: Line 216:
 
* [http://www.amazon.com/exec/obidos/ASIN/0387961712/artofproblems-20 Problem Solving Through Problems] by Loren Larson.
 
* [http://www.amazon.com/exec/obidos/ASIN/0387961712/artofproblems-20 Problem Solving Through Problems] by Loren Larson.
  
 
+
== General Interest ==
 
 
== 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/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/0618251413/artofproblems-20 Count Down] by Steve Olson.
Line 159: Line 227:
 
* [http://www.amazon.com/exec/obidos/ASIN/0195105192/artofproblems-20 What is Mathematics?]by Richard Courant, Herbert Robbins and Ian Stewart.
 
* [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 ==
+
== Math Contest Problem Books ==
 
=== Elementary School ===
 
=== 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].
 
* [[Mathematical Olympiads for Elementary and Middle Schools]] ([[MOEMS]]) publishes [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MOEMS.php two excellent contest problem books].
Line 166: Line 234:
  
 
=== Getting Started ===
 
=== 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_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.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.
 
* [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.
Line 193: Line 261:
 
=== Collegiate ===
 
=== Collegiate ===
 
* Three [[Putnam competition]] books are [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Putnam.php available at AoPS].
 
* Three [[Putnam competition]] books are [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Putnam.php available at AoPS].
 
  
 
== See also ==
 
== See also ==
 
* [[Math textbooks]]
 
* [[Math textbooks]]
 
* [[Resources for mathematics competitions]]
 
* [[Resources for mathematics competitions]]
 
+
* [[Olympiad Books]]
 
[[Category:Books]]
 
[[Category:Books]]

Revision as of 10:10, 31 August 2024

These math books are recommended by Art of Problem Solving administrators and members of the AoPS Community.

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

  • 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 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

Intermediate


Abstract Algebra

Collegiate

Calculus

Getting Started

Single Variable (Intermediate)

Multivariable (Collegiate)


Analysis

Collegiate


Combinatorics

Getting Started


https://www.awesomemath.org/product/112-combinatorial-problems-from-amsp/.112 problems is a great discrete math book covering topics ranging from permutations and combinations to using creativity to count to doing proofs and then gives exposure to advanced topics like probability theory.Great for AMC 8 /10/12

Intermediate

Olympiad

Collegiate


Geometry

Getting Started

Intermediate

Olympiad

Collegiate


Topology

Collegiate

  • 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

Olympiad

Collegiate


Number Theory

Getting Started

Olympiad

Collegiate


Trigonometry

Getting Started

Intermediate

Olympiad


Problem Solving

Getting Started

Intermediate

Olympiad

General Interest

Math Contest Problem Books

Elementary School


Getting Started


Intermediate

Olympiad

Collegiate

See also