Difference between revisions of "Math books"

(Analysis)
(High School)
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=== Single Variable Calculus ===
 
=== Single Variable Calculus ===
==== High School ====
+
==== Getting Started ====
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* [http://www.amazon.com/exec/obidos/ASIN/0883858126/artofproblems-20 The Hitchhiker's Guide to Calculus] by [[Michael Spivak]].
 +
* [https://www.amazon.com/Calculus-Made-Easy-Very-Simplest-Introduction/dp/1409724670 Calculus Made Easy] by [[Silvanus P. Thompson]].
 +
==== Intermediate ====
 
* [[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.
 
* [[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.
* [http://www.amazon.com/exec/obidos/ASIN/0914098896/artofproblems-20 Calculus] by [[Michael Spivak]].  Top students swear by this book, and also provides an illuminating construction of the real numbers in later chapters. 
 
* [http://www.amazon.com/exec/obidos/ASIN/0883858126/artofproblems-20 The Hitchhiker's Guide to Calculus] by [[Michael Spivak]].
 
* [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.
 
 
* [https://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051 Calculus: Volume I] by [[Tom M. Apostol]].  Provides a good transition into linear algebra which is uncommon in single variable calculus texts.
 
* [https://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051 Calculus: Volume I] by [[Tom M. Apostol]].  Provides a good transition into linear algebra which is uncommon in single variable calculus texts.
 +
==== Advanced ====
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* [http://www.amazon.com/exec/obidos/ASIN/0914098896/artofproblems-20 Calculus] by [[Michael Spivak]].  Top students swear by this book.  Requires a high level proofing ability for most problems
  
 
==== Collegiate ====
 
==== Collegiate ====

Revision as of 11:30, 15 October 2021

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

Algebra

Getting Started

Intermediate

Single Variable Calculus

Getting Started

Intermediate

Advanced

  • Calculus by Michael Spivak. Top students swear by this book. Requires a high level proofing ability for most problems

Collegiate

Combinatorics

Getting Started

Intermediate

Olympiad

Collegiate


Geometry

Getting Started

Intermediate

Olympiad

Collegiate


Inequalities

Intermediate

Olympiad

Collegiate


Number Theory

Introductory

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