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Abstract Algebra with Applications: In Two Volumes_ Vector Spaces and Groups

✍ Scribed by Karlheinz Spindler


Publisher
M. DEKKER, CRC PRESS
Year
1994
Tongue
English
Leaves
793
Edition
1
Category
Library

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✦ Synopsis


A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

✦ Table of Contents


TABLE OF CONTENTS

CHAPTER 1................................................ FIRST INTRODUCTION: AFFINE GEOMETRY

CHAPTER 2 .................................................SECOND INTRODUCTION: LINEAR EQUATIONS

CHAPTER 3 ................................................VECTOR SPACES

CHAPTER 4 ......................................................................LINEAR AND AFFINE MAPPINGS

CHAPTER 5........................................ ABSTRACT AFFINE GEOMETRY

CHAPTER 6................................................. DETERMINANTS

CHAPTER 8............................................................... VOLUME FUNCTIONS

CHAPTER 9.......................................................... EIGENVECTORS AND EIGENVALUES

CHAPTER 10 ..................................................CLASSIFICATION OF ENDOMORPHISMS UP TO SIMILARITY

CHAPTER 11............................................................ TENSOR PRODUCTS AND BASE-FIELD EXTENSIONS

CHAPTER 12............................................. METRIC GEOMETRY

CHAPTER 13 ........................................................EUCLIDEAN SPACES

CHAPTER 14 ........................................................LINEAR MAPPINGS BETWEEN EUCLIDEAN SPACES

CHAPTER 15 .......................................................BILINEAR FORMS

CHAPTER 16 .......................................................GROUPS OF AUTOMORPHISMS

CHAPTER 17 ..................................................APPLICATION: MARKOV CHAINS

CHAPTER 18 .......................................................APPLICATION: MATRIX CALCULUS AND DIFFERENTIAL EQUATIONS

CHAPTER 19......................................................INTRODUCTION: SYMMETRIES OF GEOMETRIC FIGURES

CHAPTER 20 .............................................GROUPS

CHAPTER 21........................................................... SUBGROUPS AND COSETS

CHAPTER 22 ..............................................................SYMMETRIC AND ALTERNATING GROUPS

CHAPTER 23 ......................................................................GROUP HOMOMORPHISMS

CHAPTER 24 ....................................................NORMAL SUBGROUPS AND FACTOR GROUPS

CHAPTER 25 ......................................................................FREE GROUPS; GENERATORS AND RELATIONS

CHAPTER 26......................................................................GROUP ACTIONS

CHAPTER 27 .............................................GROUP-THEORETICAL APPLICATIONS OF GROUP ACTIONS

CHAPTER 28.................................................... NILPOTENT AND SOLVABLE GROUPS

CHAPTER 29................................................. TOPOLOGICAL METHODS IN GROUP THEORY

CHAPTER 30............................................... ANALYTICAL METHODS IN GROUP THEORY

CHAPTER 31............................................... GROUPS IN TOPOLOGY

✦ Subjects


Vector Spaces, Groups


πŸ“œ SIMILAR VOLUMES


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✍ T. S. Blyth, E. F. Robertson (auth.) πŸ“‚ Library πŸ“… 1986 πŸ› Springer Netherlands 🌐 English

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