Difference between revisions of "How should I prepare?"

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== Introduction ==
 
== Introduction ==
The best way to prepare for math contests is to do lots of practice problems. There are also many books and online handouts/lectures you can use to improve your problem solving skills.  Depending on your current abilities, you will want to start out with different practice problems, different books, and in different areas of the forums.  This guide is intended to help you get started.
+
The best way to prepare for math contests is to '''do lots of practice problems''' and learn the material necessary to solve the problems. There are also many books and online handouts/lectures you can use to improve your problem-solving skills.  Depending on your current abilities, you will want to start out with different practice problems, different books, and in different areas of the forums. You should also try to strengthen in the areas you are not as good at.  This guide is intended to help you get started.
  
 
== Books ==
 
== Books ==
AoPS has a list of books available through the website, separated by contest level,  [http://www.artofproblemsolving.com/Books/AoPS_B_CP.php here].
+
AoPS has a list of books available through the website, separated by contest level,  [http://www.artofproblemsolving.com/Books/AoPS_B_CP.php here].  
  
The '''Art of Problem Solving books''' are an excellent resource to help prepare for math contests.  They cover a broad range of topics, from algebra to geometry to number theory to combinatorics and much much more.
+
The '''Art of Problem Solving books''' are an excellent resource to help prepare for math contests.  They cover a broad range of topics, from algebra to geometry to number theory to combinatorics and much much more.  
  
 
* Art of Problem Solving Volume 1 - MathCounts, AMC 8, AMC 10, AMC 12
 
* Art of Problem Solving Volume 1 - MathCounts, AMC 8, AMC 10, AMC 12
 
 
* Art of Problem Solving Volume 2 - AMC 12, AIME, USAMO
 
* Art of Problem Solving Volume 2 - AMC 12, AIME, USAMO
  
 +
The '''AoPS textbooks''' break down specific areas of mathematics. These books are on 3 levels, Introductory, Intermediate, and Advanced.  The Advanced series, as well as part of the Intermediate series, has not yet been published.  These books are indexed [https://artofproblemsolving.com/store/recommendations.php#state/240 here].  Excerpts are provided, as well as pretests and posttests to see if the books are on the right level for you. '''Alcumus''' is a good resource even if you do not own any of the AoPS books.
  
The '''AoPS textbooks''' break down specific areas of mathematics.  These books are on 3 levels, Introductory, Intermediate, and Advanced.  The Advanced series, as well as part of the Intermediate series, has not yet been published.  These books are indexed [http://www.artofproblemsolving.com/Books/AoPS_B_Texts.php here].  Excerpts are provided, as well as pretests and posttests to see if the books are on the right level for you.
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* Prealgebra - [[Mathcounts]], [[AMC 8]]  
 
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* Introduction to Algebra - Mathcounts, AMC 8, [[AMC 10]], AIME
* Introduction to Algebra - [[Mathcounts]], [[AMC 8]], [[AMC 10]], [[AMC 12]]
+
* Introduction to Number Theory - Mathcounts, AMC 8, AMC 10, [[AMC 12]], AIME
 
+
* Introduction to Geometry - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
* Introduction to Number Theory - Mathcounts, AMC 8, AMC 10, AMC 12
+
* Introduction to Counting & Probability - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
 
 
* Introduction to Geometry - Mathcounts, AMC 8, AMC 10, AMC 12
 
 
 
* Introduction to Counting & Probability - Mathcounts, AMC 8, AMC 10, AMC 12
 
 
 
 
* Intermediate Algebra - AMC 10, AMC 12, [[AIME]], [[USAMO]]
 
* Intermediate Algebra - AMC 10, AMC 12, [[AIME]], [[USAMO]]
 
 
* Intermediate Counting & Probability - AMC 12, AIME, USAMO
 
* Intermediate Counting & Probability - AMC 12, AIME, USAMO
+
* Precalculus - AMC 12, AIME, USAMO
*Precalculus- AMC 12, AIME, USAMO
+
* Calculus - [[Putnam]]
 
 
*Calculus- [[Putnam]]
 
  
 +
Here are a few more '''books good for preparation for higher level contests''' such as AMC 12, AIME, and USAMO (though some can be found online):
  
Here are a few more '''books good for preparation for higher level contests''' such as AMC 12, AIME, and USAMO:
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* [https://www.amazon.com/Three-Year-MATHCOUNTS-Marathon-Karen-Ge/dp/098550689X The Three-Year MATHCOUNTS Marathon] by Karen Ge (It is intended for Mathcounts, but it could potentially help in AMC 10 and 12.)
  
* [http://www.amazon.com/Geometry-Revisited-New-Mathematical-Library/dp/0883856190 Art and Craft of Problem Solving] by Paul Zeitz
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* [http://www.amazon.com/The-Art-Craft-Problem-Solving/dp/0471135712 Art and Craft of Problem Solving] by Paul Zeitz
  
 
* [http://www.amazon.com/Problem-Solving-Strategies-Problem-Books-Mathematics/dp/0387982191/ref=pd_bxgy_b_text_b Problem-Solving Strategies] by Arthur Engel
 
* [http://www.amazon.com/Problem-Solving-Strategies-Problem-Books-Mathematics/dp/0387982191/ref=pd_bxgy_b_text_b Problem-Solving Strategies] by Arthur Engel
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* [http://www.amazon.com/104-Number-Theory-Problems-Training/dp/0817645276/ref=pd_bxgy_b_text_b 104 Number Theory Problems] by Titu Andreescu & Zuming Feng
 
* [http://www.amazon.com/104-Number-Theory-Problems-Training/dp/0817645276/ref=pd_bxgy_b_text_b 104 Number Theory Problems] by Titu Andreescu & Zuming Feng
 +
 +
* [http://www.maa.org/press/ebooks/euclidean-geometry-in-mathematical-olympiads Euclidean Geometry in Math Olympiads] by Evan Chen
  
 
== Practice Problems ==
 
== Practice Problems ==
Old practice problems (with solutions) sorted by contest and year are available on the Wiki and the Resources section.
+
Old practice problems (with solutions) sorted by contest and year are available on the Wiki and the Resources section. Many practice problems are also available on the forums.
  
Many practice problems are also available on the forums.
+
[https://www.clevermath.org/ Clevermath] provides weekly problems. (Currently, Clevermath is not available.)
  
 
Here are some old contest archives that may be useful for practicing with:
 
Here are some old contest archives that may be useful for practicing with:
  
* [[AMC 8 Problems and Solutions]] - [http://www.math.ksu.edu/main/handbook/ProblemSets AMC 8] is a national contest for grades 8 and younger.
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American Mathematics Competitions:
 +
* [[AMC 8 Problems and Solutions]] - [http://www.math.ksu.edu/main/handbook/ProblemSets AMC 8] is a national contest for grades 8 and younger.  
  
 
* [[AMC 10 Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=43 AMC 10] is a national contest for grades 10 and younger.
 
* [[AMC 10 Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=43 AMC 10] is a national contest for grades 10 and younger.
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* [[AMC 12 Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44 AMC 12] is a national contest for grades 12 and younger.
 
* [[AMC 12 Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44 AMC 12] is a national contest for grades 12 and younger.
  
 +
American Invitational Mathematical Examination:
 
* [[AIME Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45 AIME] is a contest administered to those who qualify with a high score on the AMC 10/12.
 
* [[AIME Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=45 AIME] is a contest administered to those who qualify with a high score on the AMC 10/12.
  
 +
United States of America Mathematical Olympiad:
 
* [[USAMO Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=27 USAMO] is a proof-based contest which must be qualified for through a combination of AMC & AIME scores.
 
* [[USAMO Problems and Solutions]] - [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=27 USAMO] is a proof-based contest which must be qualified for through a combination of AMC & AIME scores.
  
* [http://web.mit.edu/hmmt/www/datafiles/problems/ HMMT] is a nice contest on a hard AIME level.
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Harvard-MIT Mathematics Tournament:
 
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* [https://www.hmmt.co/archive/problems/ HMMT] is a nice contest on a hard AIME level.
* [http://www.math.sc.edu/contest/problems.html USC] is a contest with a lot of problems based on common concepts you will see over and over.
 
  
 +
* [http://www.artofproblemsolving.com/Forum/resources.php More Contests].
  
* [http://www.artofproblemsolving.com/Forum/resources.php More contests].
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* [http://www.artofproblemsolving.com/wiki/index.php?title=AoPS_Past_Contests User-Created Contests].
  
 
== Forums ==
 
== Forums ==
 
The forums are one of the best ways to find problems to solve, get help with problems you cannot solve, and collaborate with people of all levels and abilities.  The forum is divided into many subforums for problems of different difficulties.
 
The forums are one of the best ways to find problems to solve, get help with problems you cannot solve, and collaborate with people of all levels and abilities.  The forum is divided into many subforums for problems of different difficulties.
  
* The [http://www.artofproblemsolving.com/Forum/index.php?f=132 MathCounts] forum is for MathCounts-level problems.
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* The [https://artofproblemsolving.com/community/c3_middle_school_math Middle School] forum is for MathCounts and AMC 8/10-level problems.
  
* The [http://www.artofproblemsolving.com/Forum/index.php?f=149 High School Basics] forum is a good place to find AMC-level and easy AIME-level problems.
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* The [https://artofproblemsolving.com/community/c4_high_school_math High School] forum is a good place to find AMC10/12-level and AIME-level problems.
  
* [http://www.artofproblemsolving.com/Forum/index.php?f=150 Intermediate Topics] has hard AMC-level problems, as well as all levels of AIME topics.  There is not a clear line between Intermediate and High School basics, but Intermediate is generally harder.
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* The [https://artofproblemsolving.com/community/c6_high_school_olympiads Olympiad] forum is a forum for problems at the olympiad level.
  
* [http://www.artofproblemsolving.com/Forum/index.php?f=151 Pre-Olympiad] is a forum for problems just below olympiad level.  Here you will find a lot of easy USAMO-level proofs, and problems as tough as the last few AIME problems.
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* The [http://www.artofproblemsolving.com/community/c68_latex_and_asymptote LaTeX] forum is a place to get help with <math>\text{\LaTeX}</math>, which is what you use to type things like <math>2^3</math> on the forums.
 
 
* The [http://www.artofproblemsolving.com/Forum/index.php?f=123 LaTeX] forum is a place to get help with LaTeX, which is what you use to type things like <math>2^3</math> on the forums.
 
  
 
== Cheat Sheets ==
 
== Cheat Sheets ==
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*The Mandelbrot Competition maintains a nice list of topics you need to know for high school math competitions called [http://www.mandelbrot.org/resources/forms/indivtopics.pdf All of Math in 3 Pages].
 
*The Mandelbrot Competition maintains a nice list of topics you need to know for high school math competitions called [http://www.mandelbrot.org/resources/forms/indivtopics.pdf All of Math in 3 Pages].
* [http://staff.imsa.edu/math/journal/volume4/articles/NoahSheets.pdf The Noah Sheets]
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* [http://web.archive.org/web/20060518133620/http://staff.imsa.edu/math/journal/volume4/articles/NoahSheets.pdf The Noah Sheets]
  
 
== Classes ==
 
== Classes ==
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* [http://www.mathpath.org/ MathPath]
 
* [http://www.mathpath.org/ MathPath]
 
* [http://www.awesomemath.org/index.shtml AwesomeMath]
 
* [http://www.awesomemath.org/index.shtml AwesomeMath]
 +
* [http://ideamath.org IdeaMath]
  
 
== Past AoPS Topics ==
 
== Past AoPS Topics ==
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''' * [https://artofproblemsolving.com/community/c5h520900 Stop Looking for the "Right" Training]'''
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''' * [https://artofproblemsolving.com/community/c5h420845p2379622 MellowMellon]'''
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=== Mathcounts ===
 +
* '''[http://artofproblemsolving.com/community/q1h1217349p6066794 How to Prepare for Mathcounts]'''
 +
 
=== AMC ===
 
=== AMC ===
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=174272 Best Ways to Prepare]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=174272 Best Ways to Prepare]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=139495 AMC prep.]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=139495 AMC prep.]
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=155952 AoPS is too hard for me......]
 
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=210890 too late to prepare?]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=210890 too late to prepare?]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=209162 Preparing book questions]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=209162 Preparing book questions]
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* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=152170 how should I study for the AMC 12/AIME?]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=152170 how should I study for the AMC 12/AIME?]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=152414 Preparing for AMC12/AIME]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=152414 Preparing for AMC12/AIME]
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* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=1361994 attacking the later problems in the AMC 10/AMC 10 advice]
  
 
=== AIME ===
 
=== AIME ===
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* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=149393 Memorization]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=149393 Memorization]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=142476 USAMO Help!]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=142476 USAMO Help!]
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== See Also ==
 +
* [http://artofproblemsolving.com/wiki/index.php?title=Resources_for_mathematics_competitions Resources for Math Competitions]
 +
* [https://sites.google.com/site/wwphssmathclub/resources More Resources]
 +
* [https://sites.google.com/site/wwpnorthmathclub1/contest-prep Useful Handouts]
 +
* [http://www.andrew.cmu.edu/user/daltizio/mathstuff.html More Useful Handouts]

Revision as of 21:43, 12 April 2019

Introduction

The best way to prepare for math contests is to do lots of practice problems and learn the material necessary to solve the problems. There are also many books and online handouts/lectures you can use to improve your problem-solving skills. Depending on your current abilities, you will want to start out with different practice problems, different books, and in different areas of the forums. You should also try to strengthen in the areas you are not as good at. This guide is intended to help you get started.

Books

AoPS has a list of books available through the website, separated by contest level, here.

The Art of Problem Solving books are an excellent resource to help prepare for math contests. They cover a broad range of topics, from algebra to geometry to number theory to combinatorics and much much more.

  • Art of Problem Solving Volume 1 - MathCounts, AMC 8, AMC 10, AMC 12
  • Art of Problem Solving Volume 2 - AMC 12, AIME, USAMO

The AoPS textbooks break down specific areas of mathematics. These books are on 3 levels, Introductory, Intermediate, and Advanced. The Advanced series, as well as part of the Intermediate series, has not yet been published. These books are indexed here. Excerpts are provided, as well as pretests and posttests to see if the books are on the right level for you. Alcumus is a good resource even if you do not own any of the AoPS books.

  • Prealgebra - Mathcounts, AMC 8
  • Introduction to Algebra - Mathcounts, AMC 8, AMC 10, AIME
  • Introduction to Number Theory - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
  • Introduction to Geometry - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
  • Introduction to Counting & Probability - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
  • Intermediate Algebra - AMC 10, AMC 12, AIME, USAMO
  • Intermediate Counting & Probability - AMC 12, AIME, USAMO
  • Precalculus - AMC 12, AIME, USAMO
  • Calculus - Putnam

Here are a few more books good for preparation for higher level contests such as AMC 12, AIME, and USAMO (though some can be found online):

Practice Problems

Old practice problems (with solutions) sorted by contest and year are available on the Wiki and the Resources section. Many practice problems are also available on the forums.

Clevermath provides weekly problems. (Currently, Clevermath is not available.)

Here are some old contest archives that may be useful for practicing with:

American Mathematics Competitions:

American Invitational Mathematical Examination:

United States of America Mathematical Olympiad:

Harvard-MIT Mathematics Tournament:

  • HMMT is a nice contest on a hard AIME level.

Forums

The forums are one of the best ways to find problems to solve, get help with problems you cannot solve, and collaborate with people of all levels and abilities. The forum is divided into many subforums for problems of different difficulties.

  • The Middle School forum is for MathCounts and AMC 8/10-level problems.
  • The High School forum is a good place to find AMC10/12-level and AIME-level problems.
  • The Olympiad forum is a forum for problems at the olympiad level.
  • The LaTeX forum is a place to get help with $\text{\LaTeX}$, which is what you use to type things like $2^3$ on the forums.

Cheat Sheets

Many great reference guides are available for free on the internet.

  • Coach Monk's High School Playbook goes a little more in depth, and is useful for all levels of high school mathematics.

Classes

If you are serious about improving your problem-solving skills, AoPS offers several online classes, available here.

WOOT is an online class offered by AoPS for olympiad training. It has one of the best peer groups in the country, and is a great way to prepare for the USAMO.

Summer Camps

Summer programs are also a great way to improve problem-solving skills. Some of these include:

Past AoPS Topics

* Stop Looking for the "Right" Training

* MellowMellon

Mathcounts

AMC

AIME

USAMO

See Also