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

Description

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 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