Difference between revisions of "Math books"

(Books By Subject)
(I revamped the entire book page through multiple edits on 10/15/21. I updated the calculus page which had little to no recommendations, as well as other collegiate material such as Abstract Algebra, Topology and Analysis.)
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== Books By Subject ==
 
== Books By Subject ==
 
=== Algebra ===
 
=== Algebra ===
 +
 
====Getting Started====
 
====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]
 
* [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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* [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/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/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.
====Graduate====
 
* [https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-Serge/dp/038795385X Algebra] by [[Serge Lang]].
 
  
  
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==== Single Variable (Intermediate) ====
 
==== 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.
 
* [[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/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.
+
* [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. Requires a high level proofing ability for most problems
+
* [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.
+
* [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) ====
 
==== 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/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]].  Became 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/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]].
 
* [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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* [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/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/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-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 Integration.
+
* [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/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/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.  
====Graduate====
 
* [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, and 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]].
 
* [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]].
  
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=== Combinatorics ===
 
=== Combinatorics ===
 +
 
==== Getting Started ====
 
==== 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.
 
* [[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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* [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
 +
* [https://www.amazon.com/Introductory-Combinatorics-Kenneth-P-Bogart/dp/0121108309 Introductory Combinatorics] by [[Kenneth P. Bogart]]
  
  
  
 
=== Geometry ===
 
=== Geometry ===
 +
 
==== Getting Started ====
 
==== 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.
 
* [[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.
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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]].
 +
 +
 +
 +
===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 ===
 
=== Inequalities ===
 +
 
==== 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]
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=== Number Theory ===
 
=== Number Theory ===
 +
 
==== Getting Started ====
 
==== Getting Started ====
 
* The AoPS [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:nt Introduction to Number Theory] by [[Mathew Crawford]].
 
* The AoPS [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:nt Introduction to Number Theory] by [[Mathew Crawford]].
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* [https://numbertheoryguy.com/publications/olympiad-number-theory-book/ Olympiad Number Theory through Challenging Problems] by Justin Stevens.
 
* [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://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 ====
 
==== 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).
 
* [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.

Revision as of 13:07, 15 October 2021

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

Algebra

Getting Started

Intermediate


Abstract Algebra

Collegiate


Calculus

Getting Started

Single Variable (Intermediate)

Multivariable (Collegiate)


Analysis

Collegiate


Combinatorics

Getting Started

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