Difference between revisions of "Math textbooks"

(Math textbooks by subject: Added a section for general books that cover more than one topic, added Getting Started with Competition Math)
 
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This '''Math textbooks''' page is for compiling a list of [[textbooks]] for mathematics -- not problem books, contest books, or general interest books.
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This '''Math textbooks''' page is for compiling a list of [[textbook]]s for mathematics -- not problem books, contest books, or general interest books. See [[math books]] for more titles.
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Before adding any books to this page, please review the [[AoPSWiki:Linking books]] page.
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== Math textbooks by subject ==
 
== Math textbooks by subject ==
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* Getting Started is recommended for students grades 6 to 9.
 
* Getting Started is recommended for students grades 6 to 9.
 
* Intermediate is recommended for students grades 9 to 12.
 
* 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.
 
* Collegiate is recommended for college and university students.
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=== General Introduction / Multiple Topics ===
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==== Getting Started ====
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* [https://www.amazon.com/gp/product/B09PMLFHX2/ref=ox_sc_act_title_1?smid=ATVPDKIKX0DER&psc=1 Getting Started with Competition Math], a textbook meant for true beginners (on-target middle school students, or advanced elementary school students). It is written by AoPS Community Member [https://artofproblemsolving.com/community/user/243060 cargeek9], currently a junior in high school. It covers the basics of algebra, geometry, combinatorics, and number theory, along with sets of accompanying practice problems at the end of every section.
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=== Algebra ===
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==== Getting Started ====
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* [[AoPS]] publishes Dr. [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=200 Introduction to Algebra] textbook, which is recommended for advanced middle and high school students.
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* [http://www.amazon.com/exec/obidos/ASIN/0669431605/artofproblems-20 Algebra I: An Integrated Approach]
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==== Intermediate ====
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* [[AoPS]] publishes Dr. [[Richard Rusczyk]]'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/exec/obidos/ASIN/0133701492/artofproblems-20 Algebra and Trigonometry] by Michael Sullivan.
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=== Calculus ===
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==== High School ====
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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 ===
 
=== Combinatorics ===
 
==== Getting Started ====
 
==== Getting Started ====
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=3 Introduction to Counting & Probability] textbook, which is recommended for advanced middle and high school students.
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* [[AoPS]] publishes Dr. [[David Patrick]]'s [https://artofproblemsolving.com/store/item/intro-counting Introduction to Counting & Probability] textbook, which is recommended for advanced middle and high school students.
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==== Intermediate ====
 
==== Intermediate ====
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* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=302 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 Nevin.
 
* [http://www.amazon.com/exec/obidos/ASIN/0883856158/artofproblems-20 Mathematics of Choice] by Ivan Nevin.
* [http://www.amazon.com/exec/obidos/ASIN/0817643176/artofproblems-20 102 Combinatorial Problems] by [[Titu Andreescu]] and [[Zuming Feng]].
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==== Olympiad ====
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==== Collegiate ====
* [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/exec/obidos/ASIN/0817642889/artofproblems-20 A Path to Combinatorics for Undergraduates] by [[Titu Andreescu]] and [[Zuming Feng]].
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=== Geometry ===
 
=== Geometry ===
 
==== Getting Started ====
 
==== Getting Started ====
 
* [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=9 Introduction to Geometry] textbook, which is recommended for advanced middle and high school students.
 
* [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=9 Introduction to Geometry] textbook, which is recommended for advanced middle and high school students.
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* [http://www.amazon.com/exec/obidos/ASIN/0387966544/artofproblems-20 Geometry] by Serge Lang and Gene Murrow.
 
==== Intermediate ====
 
==== Intermediate ====
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* [http://www.amazon.com/exec/obidos/ASIN/1930190859/artofproblems-20 Advanced Euclidean Geometry] by Alfred S. Posamentier.
 
* [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.
 
* [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.
* [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/0883856190/artofproblems-20 Geometry Revisited] -- Not a traditional textbook, but close enough to list this classic.
==== Olympiad ====
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==== Collegiate ====
* [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/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe.
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=== Number Theory ===
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==== Getting Started ====
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* The AoPS [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=10 Introduction to Number Theory] by [[Mathew Crawford]].
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==== Collegiate ====
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* [http://www.amazon.com/exec/obidos/ASIN/0387351566/artofproblems-20 Quadratic Diophantine Equations] by [[Titu Andreescu]] and [[Dorin Andrica]].
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* [http://www.amazon.com/exec/obidos/ASIN/3540761977/artofproblems-20 Elementary Number Theory] by Gareth A. Jones and Josephine M. Jones.
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* [http://www.amazon.com/exec/obidos/ASIN/3540761977/artofproblems-20 An Introduction to the Theory of Numbers] by [[G. H. Hardy]] and E. M. Wright.
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===== Analytic Number Theory =====
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* [http://www.amazon.com/exec/obidos/ASIN/0387901639/artofproblems-20 Introduction to Analytic Number Theory] by Tom M. Apostol.
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* [http://www.amazon.com/exec/obidos/ASIN/0521012538/artofproblems-20 A Primer of Analytic Number Theory] by Jeffrey Stopple.
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===== Elliptic Curves =====
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* [http://www.amazon.com/exec/obidos/ASIN/0521658179/artofproblems-20 Elliptic Curves: Function Theory, Geometry, Arithmetic] by Henry McKean and Victor Moll.
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=== Probability ===
 
=== Probability ===
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==== Getting Started ====
 
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=3 Introduction to Counting & Probability] textbook, which is recommended for advanced middle and high school students.
 
* [[AoPS]] publishes Dr. [[David Patrick]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=3 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 [https://artofproblemsolving.com/store/item/intermediate-counting Intermediate Counting & Probability] textbook, which is recommended for advanced middle and high school students.
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==== Collegiate ====
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* [http://www.amazon.com/exec/obidos/ASIN/0824703790/artofproblems-20 Probability and Statistical Inference] by Nitis Mukhopadhyay.
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=== Statistics ===
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==== Collegiate ====
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* [http://www.amazon.com/exec/obidos/ASIN/0824703790/artofproblems-20 Probability and Statistical Inference] by Nitis Mukhopadhyay.
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* [http://www.amazon.com/exec/obidos/ASIN/0387960988/artofproblems-20 Statistical Theory and Bayesian Analysis] by James O. Berger.
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* [http://www.amazon.com/exec/obidos/ASIN/158488388X/artofproblems-20 Bayesian Data Analysis] by Andrew Gelman.
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* [http://www.amazon.com/exec/obidos/ASIN/0412055511/artofproblems-20 Markov Chain Monte Carlo in Practice] by W.R. Gilks.
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* [http://www.amazon.com/exec/obidos/ASIN/0387212396/artofproblems-20 Monte Carlo Statistical Methods]
  
 
== See also ==
 
== See also ==
 
* [[Math books]]
 
* [[Math books]]
* [[Online math classes]]
 
 
* [[Science books]]
 
* [[Science books]]
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[[Category:Books]]

Latest revision as of 13:11, 6 January 2022

This Math textbooks page is for compiling a list of textbooks for mathematics -- not problem books, contest books, or general interest books. See math books for more titles.

Before adding any books to this page, please review the AoPSWiki:Linking books page.


Math textbooks by subject

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.
  • Collegiate is recommended for college and university students.

General Introduction / Multiple Topics

Getting Started

  • Getting Started with Competition Math, a textbook meant for true beginners (on-target middle school students, or advanced elementary school students). It is written by AoPS Community Member cargeek9, currently a junior in high school. It covers the basics of algebra, geometry, combinatorics, and number theory, along with sets of accompanying practice problems at the end of every section.

Algebra

Getting Started

Intermediate

Calculus

High School

Collegiate


Combinatorics

Getting Started

Intermediate

Collegiate


Geometry

Getting Started

Intermediate

Collegiate


Number Theory

Getting Started

Collegiate

Analytic Number Theory
Elliptic Curves


Probability

Getting Started

Intermediate

Collegiate

Statistics

Collegiate

See also