Difference between revisions of "Math books"
(AoPS has a calculus book now!) |
(updated links to AoPS textbooks, added Prealgebra text) |
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=== Algebra === | === Algebra === | ||
====Getting Started==== | ====Getting Started==== | ||
| + | * [[AoPS]] publishes [[Richard Rusczyk]]'s, [[David Patrick]]'s, and [[Ravi Boppana]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=prealgebra Prealgebar] 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. | * [[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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* [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 | ||
| − | * [[AoPS]] publishes [[Richard Rusczyk]]'s and [[Mathew Crawford]]'s [http://www.artofproblemsolving.com/ | + | * [[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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=== Combinatorics === | === Combinatorics === | ||
==== Getting Started ==== | ==== Getting Started ==== | ||
| − | * [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/ | + | * [[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 ==== | ==== Intermediate ==== | ||
| − | * [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/ | + | * [[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]]. | ||
| Line 62: | Line 63: | ||
=== Geometry === | === Geometry === | ||
==== Getting Started ==== | ==== Getting Started ==== | ||
| − | * [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/ | + | * [[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 ==== | ||
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=== Number Theory === | === Number Theory === | ||
==== Introductory ==== | ==== Introductory ==== | ||
| − | * The AoPS [http://www.artofproblemsolving.com/ | + | * The AoPS [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:nt Introduction to Number Theory] by [[Mathew Crawford]]. |
==== 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. | ||
Revision as of 12:26, 16 May 2012
These Math books are recommended by Art of Problem Solving administrators and members of the <url>index.php AoPS-MathLinks Community</url>.
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 6 to 9.
- Intermediate is recommended for students grades 9 to 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.
Contents
Books by subject
Algebra
Getting Started
- AoPS publishes Richard Rusczyk's, David Patrick's, and Ravi Boppana's Prealgebar textbook, which is recommended for advanced elementary and middle school students.
- AoPS publishes Richard Rusczyk's Introduction to Algebra textbook, which is recommended for advanced elementary, middle, and high school students.
Intermediate
- Algebra by I.M. Gelfand and Alexander Shen.
- 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 Intermediate Algebra textbook, which is recommended for advanced middle and high school students.
- Complex Numbers from A to... Z by Titu Andreescu
Analysis
- Counterexamples in Analysis by Bernard R. Gelbaum and John M. H. Olmsted.
Calculus
High School
- AoPS publishes Dr. David Patrick's Calculus textbook, which is recommended for advanced middle and high school students.
- Calculus by Michael Spivak. Top students swear by this book.
- The Hitchhiker's Guide to Calculus by Michael Spivak.
- AP Calculus Problems and Solutions Part II AB and BC -- A fantastic resource for students mastering the material required for the AP exam.
Collegiate
- Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus by Michael Spivak.
Combinatorics
Getting Started
- AoPS publishes Dr. David Patrick's Introduction to Counting & Probability textbook, which is recommended for advanced middle and high school students.
Intermediate
- AoPS publishes Dr. David Patrick's Intermediate Counting & Probability textbook, which is recommended for advanced middle and high school students.
- Mathematics of Choice by Ivan Niven.
- 102 Combinatorial Problems by Titu Andreescu and Zuming Feng.
- A Path to Combinatorics for Undergraduates: Counting Strategies by Titu Andreescu and Zuming Feng.
Olympiad
Collegiate
- Enumerative Combinatorics, Volume 1 by Richard Stanley.
- Enumerative Combinatorics, Volume 2 by Richard Stanley.
- A First Course in Probability by Sheldon Ross
Geometry
Getting Started
- AoPS publishes Richard Rusczyk's Introduction to Geometry textbook, which is recommended for advanced middle and high school students.
Intermediate
- Challenging Problems in Geometry -- A good book for students who already have a solid handle on elementary geometry.
- Geometry Revisited -- A classic.
Olympiad
- Geometry Revisited -- A classic.
- Geometry of Complex Numbers by Hans Schwerfdtfeger.
- Geometry: A Comprehensive Course by Dan Pedoe.
- Non-Euclidean Geometry by H.S.M. Coxeter.
- Projective Geometry by H.S.M. Coxeter.
- Geometric Transformations I, Geometric Transformations II, and Geometric Transformations III by I. M. Yaglom.
Collegiate
- Geometry of Complex Numbers by Hans Schwerfdtfeger.
- Geometry: A Comprehensive Course by Dan Pedoe.
- Non-Euclidean Geometry by H.S.M. Coxeter.
- Projective Geometry by H.S.M. Coxeter.
Inequalities
Intermediate
Olympiad
- The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele.
- Problem Solving Strategies by Arthur Engel contains significant material on inequalities.
- Titu Andreescu's Book on Geometric Maxima and Minima
- Topics in Inequalities by Hojoo Lee
- Olympiad Inequalities by Thomas Mildorf
- A<B (A is less than B) by Kiran S. Kedlaya
- Secrets in Inequalities vol 1 and 2 by Pham Kim Hung
Collegiate
- Inequalities by G. H. Hardy, J. E. Littlewood, and G. Polya.
Number Theory
Introductory
- The AoPS Introduction to Number Theory by Mathew Crawford.
Olympiad
- Number Theory: A Problem-Solving Approach by Titu Andreescu and Dorin Andrica.
- 104 Number Theory Problems from the Training of the USA IMO Team by Titu Andreescu, Dorin Andrica and Zuming Feng.
- Problems in Elementary Number Theory by Hojoo Lee.
Trigonometry
Getting Started
- Trigonometry by I.M. Gelfand and Mark Saul.
Intermediate
- Trigonometry by I.M. Gelfand and Mark Saul.
- 103 Trigonometry Problems by Titu Andreescu and Zuming Feng.
Olympiad
Problem Solving
Getting Started
- the Art of Problem Solving Volume 1 by Sandor Lehoczky and Richard Rusczyk is recommended for avid math students in grades 7-9.
- Mathematical Circles -- A wonderful peak into Russian math training.
- 100 Great Problems of Elementary Mathematics by Heinrich Dorrie.
Intermediate
- the Art of Problem Solving Volume 2 by Sandor Lehoczky and Richard Rusczyk is recommended for avid math students in grades 9-12.
- The Art and Craft of Problem Solving by Paul Zeitz, former coach of the U.S. math team.
- How to Solve It by George Polya.
- A Mathematical Mosaic by Putnam Fellow Ravi Vakil.
- Proofs Without Words, Proofs Without Words II
- Sequences, Combinations, Limits
- 100 Great Problems of Elementary Mathematics by Heinrich Dorrie.
Olympiad
- Mathematical Olympiad Challenges
- Problem Solving Strategies by Arthur Engel.
- Problem Solving Through Problems by Loren Larson.
General interest
- The Code Book by Simon Singh.
- Count Down by Steve Olson.
- Fermat's Enigma by Simon Singh.
- Godel, Escher, Bach
- Journey Through Genius by William Dunham.
- A Mathematician's Apology by G. H. Hardy.
- The Music of the Primes by Marcus du Sautoy.
- Proofs Without Words by Roger B. Nelsen.
- 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 two excellent contest problem books.
Getting Started
- MathCounts books -- Practice problems at all levels from the MathCounts competition.
- Contest Problem Books from the AMC.
- 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 two problem books for sale at AoPS.
- ARML books:
- Five Hundred Mathematical Challenges -- An excellent collection of problems (with solutions).
- The USSR Problem Book
- Leningrad Olympiads (Published by MathProPress.com)
Olympiad
- USAMO 1972-1986 -- Problems from the United States of America Mathematical Olympiad.
- The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004
- Mathematical Olympiad Challenges
- Problem Solving Strategies by Arthur Engel.
- Problem Solving Through Problems by Loren Larson.
- Hungarian Problem Book III
- 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 available at AoPS.
