Learn Math for Free

Curator's Note: This page serves as a central repository of links to various places where you can learn math and related topics (computer science, probability, statistics, etc.) for free online. These links lead to other sites that host the material. If you find a link that is outdated or otherwise inaccurate, please email the curator and it will be updated accordingly.

So you're interested in learning math on your own, but you don't want to spend a dime. You've come to the right place! Here at Math Majeure, I curate a list of free online classes, video tutorials, eBooks, and other resources that anyone can use to learn math (and the applied fields) or refresh their knowledge. The information is sorted by topic below, which will lead you to pages of resources specific to your desired field of study.

Under constant construction to add more sections... Last updated May 7, 2013.

Calculus (Last Update: Oct. 18, 2012)

Note: This section covers the material typically found in a two- or three-semester introductory calculus series (typically listed as Calculus I-III, or Single Variable and Multivariable).

• Khan Academy: Calculus - Video tutorials covering differential, integral, and multivariable calculus.
• MIT OpenCourseware - OCW has many free complete classes from MIT, including Single Variable, Calculus w/ Theory, Multivariable, Multivariable w/ Theory, and Calculus of Several Variables. I have bolded those courses which are the standard track for self-study (Single Variable and Multivariable).
• Paul's Online Math Notes: Calculus - Paul Dawkins of Lamar University also has detailed course notes on calculus: Calculus I, Calculus II, and Calculus III. He also provides practice/assignment problems for the first two courses.

Discrete Mathematics (Last Update: May 7, 2013)

Note: For general advice on good texts in Discrete Math, I suggest this thread over at MathExchange.

• UC Berkeley: Math 55 (2007) - A complete set of lectures available on iTunes U.
• e-booksdirectory.com - There are a handful of free e-texts focusing on Discrete Math over at e-booksdirectory.com. I haven't personally used any of them, but some focus on applications as well as theory.
• Lecture Notes in Discrete Mathematics by Marcel B. Finn, Arkansas Tech University
• Discrete Mathematics by WWL Chen

Linear Algebra (Last Update: Oct. 7, 2012)

• Khan Academy: Linear Algebra - Video tutorials covering the first two semesters of a typical college course.
• Paul's Online Math Notes: Linear Algebra - Paul Dawkins of Lamar University keeps a detailed list of class notes that he uses in his instruction. These notes are very in-depth and make a nice free replacement for a traditional text book. There's every reason that you could use just these to teach yourself the topic via independent study.
• MIT OCW: Linear Algebra - Prof. Gilbert Strang of MIT is well known for his research in Linear Algebra, and this free coverage of his entire introductory class on the field is one of the finest that you'll find online. While the traditional classroom format may turn off some who prefer a faster pace, the amount of knowledge and intuition that you can obtain is very high.
• Course of Linear Algebra and Multidimensional Geometry by R.A. Sharipov - A complete text book with an excellent focus on definitions and proofs.
• Wikibooks: Linear Algebra: An Introduction to Mathematical Discourse - This community-sourced eBook is designed to be rigorous, but has some flaws. A good free resource, but make sure you do some research into its weak points.

Real Analysis (Last Update: May 14, 2013)

• Analysis Yawp! - A complete series of recorded lectures as well as supporting materials from Professor Francis Su of Harvey Mudd College. If you enjoy the lecture style of teaching as well as "flipping the classroom," this is a great resource.