Difference between revisions of "Math books"

(Analysis)
(Books By Subject)
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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.
 
* [[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]]
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===Abstract Algebra===
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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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====Graduate====
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* [https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-Serge/dp/038795385X Algebra] by [[Serge Lang]].
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===Calculus===
 
===Calculus===
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==== Getting Started ====
 
==== Getting Started ====
 
* [http://www.amazon.com/exec/obidos/ASIN/0883858126/artofproblems-20 The Hitchhiker's Guide to Calculus] by [[Michael Spivak]].
 
* [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]].
 
* [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) ====
 
==== 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.
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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.
 
* [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 (Advanced) ====
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==== 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]].  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/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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=== Analysis ===
 
=== Analysis ===
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==== Collegiate ====
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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/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/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/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 Integration.
 
* [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]].
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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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====Graduate====
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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, and 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]].
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=== Combinatorics ===
 
=== Combinatorics ===
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==== 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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=== Trigonometry ===
 
=== Trigonometry ===

Revision as of 12:39, 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

Graduate


Calculus

Getting Started

Single Variable (Intermediate)

Multivariable (Collegiate)


Analysis

Collegiate

Graduate


Combinatorics

Getting Started

Intermediate

Olympiad

Collegiate


Geometry

Getting Started

Intermediate

Olympiad

Collegiate


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