This book was written to be a readable introduction to Algebraic Topology with rather broad coverage of the subject. Our viewpoint is quite classical in spirit, and stays largely within the confines of pure Algebraic Topology. In a sense, the book could have been written thirty years ago since virtually all its content is at least thatold. However, the passage of the intervening years has helped clarify what the most important results and techniques are.
Now back in print by the AMS, this is a significantly revised edition of a book originally published in 1987 by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes.
This classic book gives a thorough introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. It also provides a comprehensive look at recent research. For experimental number theoreticians, the authors developed new methods and obtained new results of great importance for them.
Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach
Algebraic geometry is often employed to encode and decode signals transmitted in communication systems. This book describes the fundamental principles of algebraic coding theory from the perspective of an engineer, discussing a number of applications in communications and signal processing. The principal concept is that of using algebraic curves over finite fields to construct error-correcting codes.
Computational Algebraic Geometry (London Mathematical Society Student Texts)
Recent advances in computing and algorithms make it easier to do many classical problems in algebra. Suitable for graduate students, this book brings advanced algebra to life with many examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The remainder of the book focuses on three active areas of contemporary algebra: homological algebra; algebraic combinatorics and algebraic topology; and algebraic geometry.
