国外 奥数 课本
http://www.ebama.net/forum.php?mod=viewthread&tid=47899&fromuid=1936
一个不错的国外 中学奥数课本 网站
http://www.artofproblemsolving.com/
这些书是这个网站上推荐的中学奥数书
http://www.artofproblemsolving.com/Wiki/index.php/Math_books
These Math books are recommended by Art of Problem Solving administrators and members of the AoPS-MathLinks 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 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 [url=http://www.artofproblemsolving.com/Wiki/index.php/AoPSWikiinking_books]AoPSWikiinking books[/url] page.
Books by subject Algebra Getting Started• 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 • 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 • 102 Combinatorial Problems by Titu Andreescu and Zuming Feng.
• Generatingfunctionology
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 • Introduction to Inequalities
• Geometric Inequalities
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 • 103 Trigonometry Problems by Titu Andreescu and Zuming Feng.
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:
•ARML-NYSML 1989-1994 (see ARML).
• ARML 1995-2004
• 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.
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