Difference between revisions of "Math books"

(Books By Subject: Added General Introduction / Multiple Topics section, added Getting Started with Competition Math book)
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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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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:
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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.
 
* [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.
 
* [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
  
 
===Calculus===
 
===Calculus===
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==== 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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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 ====
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==== Olympiad ====
 
==== Olympiad ====
 
* [https://www.amazon.com/gp/product/0883858398?%2AVersion%2A=1&%2Aentries%2A=0&pldnSite=1 Euclidean Geometry in Mathematical Olympiads] by Evan Chen
 
* [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.

Latest 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