View source for Math textbooks

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.

Before adding any books to this page, please review the [[AoPS Wiki: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 ====
* [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.

=== Algebra ===
==== Getting Started ====
* [[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.
* [http://www.amazon.com/exec/obidos/ASIN/0669431605/artofproblems-20 Algebra I: An Integrated Approach]

==== Intermediate ====
* [[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.
* [http://www.amazon.com/exec/obidos/ASIN/0133701492/artofproblems-20 Algebra and Trigonometry] by Michael Sullivan.

=== Calculus ===
==== High School ====
* [http://www.amazon.com/exec/obidos/ASIN/0914098896/artofproblems-20 Calculus] by [[Michael Spivak]].  Top students swear by this book.
* [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.
==== Collegiate ====
* [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]].


=== Combinatorics ===
==== Getting Started ====
* [[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.

==== Intermediate ====
* [[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.

* [http://www.amazon.com/exec/obidos/ASIN/0883856158/artofproblems-20 Mathematics of Choice] by Ivan Nevin.

==== Collegiate ====
* [http://www.amazon.com/exec/obidos/ASIN/0817642889/artofproblems-20 A Path to Combinatorics for Undergraduates] by [[Titu Andreescu]] and [[Zuming Feng]].



=== Geometry ===
==== 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.
* [http://www.amazon.com/exec/obidos/ASIN/0387966544/artofproblems-20 Geometry] by Serge Lang and Gene Murrow.
==== Intermediate ====
* [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/0883856190/artofproblems-20 Geometry Revisited] -- Not a traditional textbook, but close enough to list this classic.
==== Collegiate ====
* [http://www.amazon.com/exec/obidos/ASIN/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe.



=== Number Theory ===
==== Getting Started ====
* The AoPS [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=10 Introduction to Number Theory] by [[Mathew Crawford]].
==== Collegiate ====
* [http://www.amazon.com/exec/obidos/ASIN/0387351566/artofproblems-20 Quadratic Diophantine Equations] by [[Titu Andreescu]] and [[Dorin Andrica]].
* [http://www.amazon.com/exec/obidos/ASIN/3540761977/artofproblems-20 Elementary Number Theory] by Gareth A. Jones and Josephine M. Jones.
* [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.
===== Analytic Number Theory =====
* [http://www.amazon.com/exec/obidos/ASIN/0387901639/artofproblems-20 Introduction to Analytic Number Theory] by Tom M. Apostol.
* [http://www.amazon.com/exec/obidos/ASIN/0521012538/artofproblems-20 A Primer of Analytic Number Theory] by Jeffrey Stopple.
===== Elliptic Curves =====
* [http://www.amazon.com/exec/obidos/ASIN/0521658179/artofproblems-20 Elliptic Curves: Function Theory, Geometry, Arithmetic] by Henry McKean and Victor Moll.



=== Probability ===
==== 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.
====Intermediate====
* [[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.

==== Collegiate ====
* [http://www.amazon.com/exec/obidos/ASIN/0824703790/artofproblems-20 Probability and Statistical Inference] by Nitis Mukhopadhyay.

=== Statistics ===
==== Collegiate ====
* [http://www.amazon.com/exec/obidos/ASIN/0824703790/artofproblems-20 Probability and Statistical Inference] by Nitis Mukhopadhyay.
* [http://www.amazon.com/exec/obidos/ASIN/0387960988/artofproblems-20 Statistical Theory and Bayesian Analysis] by James O. Berger.
* [http://www.amazon.com/exec/obidos/ASIN/158488388X/artofproblems-20 Bayesian Data Analysis] by Andrew Gelman.
* [http://www.amazon.com/exec/obidos/ASIN/0412055511/artofproblems-20 Markov Chain Monte Carlo in Practice] by W.R. Gilks.
* [http://www.amazon.com/exec/obidos/ASIN/0387212396/artofproblems-20 Monte Carlo Statistical Methods]

== See also ==
* [[Math books]]
* [[Science books]]


[[Category:Books]]