The Book "A=B" by Marko Petkovsek, Herbert Wilf and Doron Zeilberger."A=B" is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks, and we intend to maintain the latest versions of the programs that carry out these algorithms on this page."
Basic Concepts of Mathematics by Elias Zakon. "This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition 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... In particular, it gives students the skills they need to succeed in the first courses in Real Analysis and Abstract Algebra/Modern Algebra."
Design of Comparative Experiments by R. A. Bailey.
Math Alive by Ingrid Daubechies, Princeton University. "How is life different from 25 or even 10 years ago? Mathematics has profoundly changed our world, from banking & computers to listening to music. This course is designed for those who haven't had college mathematics but would like to understand some of the mathematical concepts behind important modern applications. It will consist of largely independent 2-week units:
Error correction and compression
Probability and statistics
Birth, Growth, Death and Chaos
Geometry and Motion Control
Voting and Social Choice
You can navigate through the units using the navigation bar on the left. Each unit is divided into two parts. For each part you can download Lecture notes in PDF or PS format. Each part has its problem set and a corresponding on-line Lab. You can find the Lecture Notes,...