Logic and proof: online resources
Introduction to Logic
A set of online tutorials for the study of elementary logic covering propositional and predicate calculus. Also an interactive Java applet with exercises.
An Elementary Introduction to Logic and Set Theory
An online tutorial including sentential logic, predicate logic and quantifiers, methods of proof, and naive set theory.
Logic for Mathematics by IMACS (Institute for Mathematics & Computer Science)
Choose "parents" or "students", then Mathematics & Logic from the submenu. This is an online course meant for mathematically precocious middle and high school students. This propositional calculus course introduces students to the propositional logic, a branch of modern mathematics which provides a rigorous mathematical analysis of the process of rational argument.
Logic & Proofs course from Open Learning Initiative (OLI)
Part of a full course that includes predicate logic and has been taught at Carnegie Mellon University. Click on the link "LOOK inside the free and open OLI Logic & Proofs Course" to see the course material.
How to Write Proofs
A 12-part tutorial on proof writing. Includes direct proof, proof by contradiction, proof by contrapositive, mathematical induction, if and only if, and proof strategies.
Let's Practice Geometry - Free Worksheets
Lots of free worksheets for high school geometry, including topics such as the Pythagorean Theorem, perimeter, area, volume, angle relationships, triangle theorems, similarity and congruence, logic, proofs, trig, polygons, and circles.
Cut The Knot
A site full of games, puzzles, illustrations, charts, paradoxes, illusions, mathematical droodles - often illustrated with interactive Java applets. You can learn a lot!
Real World Algebra by Edward Zaccaro
Algebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty.