原始连接：
http://homepages.nyu.edu/~jmg336/html/mathematics.html
GENERAL MATHEMATICS
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:
Cryptography
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, On-Line Labs, and Problem Sets through corresponding links on the left. You can also find them (for each unit) through the corresponding unit links. The On-Line Labs review some of the material seen in class, and give you interactive windows to try out various things. The problem sets contain questions and assignments for you to answer or complete. To answer some of these questions you'll need the interactive pages from the On-Line Labs. "
ALGEBRA
Algebra and Analysis for Computer Science, by Jean Gallier. Book in progress, approx. 254 pages. Covers linear algebra, determinants, Gaussian elimination, LU- and Cholesky-factoring, affine geometry, polynomials, PID's, UFD's, basic topology, and differential calculus.
Abstract Algebra with GAP, Authored by By J. G. Rainbolt and J. A. Gallian. "This GAP Manual accompanies Contemporary Abstract Algebra, Fifth Edition, and provides instruction and exercises for students who use the GAP software program. You may choose either to download each chapter separately or download the entire manual at once. The subroutines and art figures needed for this GAP manual are saved in separate files. For your convenience, you will find a helpful Student Solutions Manual that provides the odd-numbered answers to the exercises found in this GAP Manual."
A Course In Algebraic Number Theory by Robert B. Ash. "We study fundamental algebraic structures, namely groups, rings, fields and modules, and maps between these structures. The techniques are used in many areas of mathematics, and there are applications to physics, engineering and computer science as well. In addition, I have attempted to communicate the intrinsic beauty of the subject.
Ideally, the reasoning underlying each step of a proof should be completely clear, but the overall argument should be as brief as possible, allowing a sharp overview of the result."
Mathematical Methods of Engineering Analysis, by Erhan
