Paul's Online Math Notes

A huge well-organized collection of maths tutorials and notes by Paul Dawkins of Lamar University, Texas. It includes cheat sheets and tables and notes on algebra, calculus and differential equations. Very usefully, his assumptions about the reader's background are given with each set of notes

"..... a complete set of free online (and downloadable) notes and/or tutorials for classes that I teach at Lamar University. I've tried to write the notes/tutorials in such a way that they should be accessible to anyone wanting to learn the subject regardless of whether you are in my classes or not."

Street-Fighting Mathematics

This imaginative course from MIT OpenCourseWare by Sanjoy Mahajan is designed to teach a flexible attitude toward problem solving. In the form of an electronic textbook, the chapters should be accessible to anyone with some knowledge of algebra, trigonometry and single variable calculus. There are also 3 problem sets, a teacher's guide and video lectures.

"This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire and differential equations."

Basic Concepts of Mathematics

This book by Elias Zakon of the University of Windsor, Canada with many exercises and optional topics, aims to help in making the transition from purely manipulative to rigorous mathematics:

"..... covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces."

All uses of the text are subject to Terms and Conditions but free download is offered to students using it for self-study or lecturers evaluating it as a required or recommended text for a course.

Lecture notes of William Chen

Hundreds of pages from Macquarie University, Australia on the following topics:

First Year Calculus, Discrete Mathematics, Linear Algebra, Miscellaneous Topics in First Year Mathematics, Multivariable and Vector Analysis, Introduction to Complex Analysis, Fundamentals of Analysis, Linear Functional Analysis, Introduction to Lebesgue Integration, Elementary Number Theory, Distribution of Prime Numbers, Lectures on Irregularities of Point Distribution

Transforming Numerical Methods Education

Wolfram MathWorld

A well-organized resource provided by Wolfram Research, makers of Mathematica and assembled over more than a decade by Eric W. Weisstein with assistance from thousands of contributors. Topics include Algebra, Applied Mathematics, Calculus and Analysis, Discrete Mathematics, Foundations of Mathematics, Geometry, History and Terminology, Number Theory, Probability and Statistics, Recreational Mathematics and Topology.