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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].
| + | #REDIRECT [[Mathematics books]] |
| − | | |
| − | Levels of reading and math ability are loosely defined as follows:
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| − | * Elementary is for elementary school students up through possibly early middle school.
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| − | * Getting Started is recommended for students grades 6 to 9.
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| − | * Intermediate is recommended for students grades 9 to 12.
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| − | * Olympiad is recommended for high school students who are already studying math at an undergraduate level.
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| − | * Collegiate is recommended for college and university students.
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| − | | |
| − | More advanced topics are often left with the above levels unassigned.
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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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| − | === Algebra ===
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| − | ====Getting Started====
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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 ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0817636773/artofproblems-20 Algebra] by I.M. Gelfand and Alexander Shen.
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| − | * [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.
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| − | * [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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| − | | |
| − | === Analysis ===
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0486428753/artofproblems-20 Counterexamples in Analysis] by Bernard R. Gelbaum and John M. H. Olmsted.
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| − | | |
| − | | |
| − | === Calculus ===
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| − | ==== High School ====
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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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| − | * [http://www.amazon.com/exec/obidos/ASIN/0914098896/artofproblems-20 Calculus] by [[Michael Spivak]]. Top students swear by this book.
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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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| − | * [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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| − | | |
| − | ==== Collegiate ====
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| − | * [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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| − | | |
| − | | |
| − | === Combinatorics ===
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| − | ==== Getting Started ====
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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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| − | | |
| − | ==== Intermediate ====
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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.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883856158/artofproblems-20 Mathematics of Choice] by Ivan Niven.
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| − | * [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]].
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| − | | |
| − | ==== Olympiad ====
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| − | * [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 ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0521663512/artofproblems-20 Enumerative Combinatorics, Volume 1] by Richard Stanley.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0521789877/artofproblems-20 Enumerative Combinatorics, Volume 2] by Richard Stanley.
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| − | * [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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| − | | |
| − | | |
| − | === Geometry ===
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| − | ==== Getting Started ====
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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.
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| − | | |
| − | ==== Intermediate ====
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| − | * [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.
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| − | * [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
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| − | | |
| − | ==== Olympiad ====
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| − | * Euclidean Geometry in Math Olympiads by Evan Chen
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic.
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| − | * [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/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]].
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]].
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| − | * [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
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| − | | |
| − | ==== Collegiate ====
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| − | * [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/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]].
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]].
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| − | === Inequalities ===
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| − | ==== Intermediate ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883856034/artofproblems-20 Introduction to Inequalities]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883856042/artofproblems-20 Geometric Inequalities]
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| − | | |
| − | ==== Olympiad ====
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| − | * [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.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387982191/artofproblems-20 Problem Solving Strategies] by Arthur Engel contains significant material on inequalities.
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| − | *Titu Andreescu's Book on Geometric Maxima and Minima
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| − | * [http://ultrametric.googlepages.com/tin2007.pdf Topics in Inequalities] by Hojoo Lee
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| − | * [http://www.artofproblemsolving.com/Resources/Papers/MildorfInequalities.pdf Olympiad Inequalities] by Thomas Mildorf
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| − | * [http://www.artofproblemsolving.com/Resources/Papers/KedlayaInequalities.pdf A<B (A is less than B)] by Kiran S. Kedlaya
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| − | * [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
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| − | | |
| − | ==== Collegiate ====
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| − | | |
| − | * [http://www.amazon.com/exec/obidos/ASIN/0521358809/artofproblems-20 Inequalities] by [[G. H. Hardy]], [[J. E. Littlewood]], and [[G. Polya]].
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| − | === Number Theory ===
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| − | ==== Introductory ====
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| − | * The AoPS [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:nt Introduction to Number Theory] by [[Mathew Crawford]].
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| − | ==== Olympiad ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/081763245X/artofproblems-20 Number Theory: A Problem-Solving Approach] by [[Titu Andreescu]] and Dorin Andrica.
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| − | * [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.
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| − | * [http://www.problem-solving.be/pen/published/pen-20070711.pdf Problems in Elementary Number Theory] by Hojoo Lee.
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| − | | |
| − | | |
| − | === Trigonometry ===
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| − | ==== Getting Started ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0817639144/artofproblems-20 Trigonometry] by I.M. Gelfand and Mark Saul.
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| − | | |
| − | ==== Intermediate ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0817639144/artofproblems-20 Trigonometry] by I.M. Gelfand and Mark Saul.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0817643346/artofproblems-20 103 Trigonometry Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
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| − | | |
| − | ==== Olympiad ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0817643346/artofproblems-20 103 Trigonometry Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
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| − | | |
| − | === Problem Solving ===
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| − | ==== Getting Started ====
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| − | * 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.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0821804308/artofproblems-20 Mathematical Circles] -- A wonderful peak into Russian math training.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0486613488/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
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| − | ==== Intermediate ====
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| − | * 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.
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| − | * [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.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0691023565/artofproblems-20 How to Solve It] by [[George Polya]].
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| − | * [http://www.amazon.com/exec/obidos/ASIN/1895997046/artofproblems-20 A Mathematical Mosaic] by [[Putnam Fellow]] [[Ravi Vakil]].
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| − | * [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]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0486425665/artofproblems-20 Sequences, Combinations, Limits]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0486613488/artofproblems-20 100 Great Problems of Elementary Mathematics] by Heinrich Dorrie.
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| − | | |
| − | ==== Olympiad ====
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0817641556/artofproblems-20 Mathematical Olympiad Challenges]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387982191/artofproblems-20 Problem Solving Strategies] by Arthur Engel.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387961712/artofproblems-20 Problem Solving Through Problems] by Loren Larson.
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| − | == General interest ==
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0385495323/artofproblems-20 The Code Book] by Simon Singh.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0618251413/artofproblems-20 Count Down] by Steve Olson.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0385493622/artofproblems-20 Fermat's Enigma] by Simon Singh.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0465026567/artofproblems-20 Godel, Escher, Bach]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/014014739X/artofproblems-20 Journey Through Genius] by William Dunham.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0521427061/artofproblems-20 A Mathematician's Apology] by [[G. H. Hardy]].
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0066210704/artofproblems-20 The Music of the Primes] by Marcus du Sautoy.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883857006/artofproblems-20 Proofs Without Words] by Roger B. Nelsen.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0195105192/artofproblems-20 What is Mathematics?]by Richard Courant, Herbert Robbins and Ian Stewart.
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| − | | |
| − | == Math contest problem books ==
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| − | === Elementary School ===
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| − | * [[Mathematical Olympiads for Elementary and Middle Schools]] ([[MOEMS]]) publishes [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MOEMS.php two excellent contest problem books].
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| − | === Getting Started ===
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| − | * [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MC.php MathCounts books] -- Practice problems at all levels from the [[MathCounts]] competition.
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| − | * [http://www.artofproblemsolving.com/Books/AoPS_B_CP_AMC.php Contest Problem Books] from the [[AMC]].
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| − | * [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.
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| − | | |
| − | === Intermediate ===
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| − | * The [[Mandelbrot Competition]] has [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Mand.php two problem books for sale] at [[AoPS]].
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| − | * ARML books:
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| − | **[http://www.amazon.com/exec/obidos/ASIN/0962640166/artofproblems-20 ARML-NYSML 1989-1994] (see [[ARML]]).
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| − | ** [http://www.arml.com/books.htm ARML 1995-2004]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883855194/artofproblems-20 Five Hundred Mathematical Challenges] -- An excellent collection of problems (with solutions).
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0486277097/artofproblems-20 The USSR Problem Book]
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| − | *Leningrad Olympiads (Published by MathProPress.com)
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| − | | |
| − | === Olympiad ===
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| − | * [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=50 USAMO 1972-1986] -- Problems from the [[United States of America Mathematical Olympiad]].
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387242996/artofproblems-20 The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0817641556/artofproblems-20 Mathematical Olympiad Challenges]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387982191/artofproblems-20 Problem Solving Strategies] by Arthur Engel.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0387961712/artofproblems-20 Problem Solving Through Problems] by Loren Larson.
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| − | * [http://www.amazon.com/exec/obidos/ASIN/0883856441/artofproblems-20 Hungarian Problem Book III]
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| − | * [http://www.amazon.com/exec/obidos/ASIN/088385645X/artofproblems-20 Mathematical Miniatures]
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| − | *Mathematical Olympiad Treasures
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| − | *Collections of Olympiads (APMO, China, USSR to name the harder ones) published by MathProPress.com.
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| − | | |
| − | === Collegiate ===
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| − | * Three [[Putnam competition]] books are [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Putnam.php available at AoPS].
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| − | | |
| − | | |
| − | == See also ==
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| − | * [[Math textbooks]]
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| − | * [[Resources for mathematics competitions]]
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| − | * [[Olympiad Books]]
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| − | [[Category:Books]]
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