E-Book, Englisch, 560 Seiten, Web PDF
Weiss First Course in Algebra and Number Theory
1. Auflage 2014
ISBN: 978-1-4832-7037-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 560 Seiten, Web PDF
ISBN: 978-1-4832-7037-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
First Course in Algebra and Number Theory presents the basic concepts, tools, and techniques of modern algebra and number theory. It is designed for a full year course at the freshman or sophomore college level. The text is organized into four chapters. The first chapter is concerned with the set of all integers - positive, negative, and zero. It investigates properties of Z such as division algorithm, Euclidean algorithm, unique factorization, greatest common divisor, least common multiple, congruence, and radix representation. In chapter 2, additional axioms about Z were introduced and some of their consequences are discussed. The third chapter sets up terminologies about polynomials, solutions or roots of polynomial equations, and factorization of polynomials. Finally, chapter 4 studies logically simpler algebraic systems, known as 'groups', algebraic objects with a single operation. The book is intended for students in the freshman and sophomore levels in college.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;First Course in Algebra and Number Theory;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;10
6;Chapter 1. Elementary Number Theory;14
6.1;1-1. DIVISIBILITY;15
6.2;1-2. THE DIVISION ALGORITHM;19
6.3;1-3. THE GREATEST COMMON DIVISOR;26
6.4;1-4. UNIQUE FACTORIZATION;34
6.5;1-5. A CONVENIENT NOTATION;41
6.6;1-6. LINEAR DIOPHANTINE EQUATIONS;55
6.7;1-7. CONGRUENCE;63
6.8;1-8. RADIX REPRESENTATION;77
6.9;MISCELLANEOUS PROBLEMS;96
7;Chapter 2. Rings and Domains;103
7.1;2-1. RINGS: ELEMENTARY PROPERTIES;104
7.2;2-2. EXAMPLES;117
7.3;2-3. ORDERED AND WELL-ORDERED DOMAINS;151
7.4;2-4. COMPUTATION RULES;173
7.5;2-5. CHARACTERIZATION OF THE INTEGERS;187
7.6;MISCELLANEOUS PROBLEMS;212
8;Chapter 3. Congruences and Polynomials;223
8.1;3-1. LINEAR CONGRUENCES;224
8.2;3-2. UNITS AND FIELDS;243
8.3;3-3. POLYNOMIALS AND POLYNOMIAL FUNCTIONS;266
8.4;3-4. FACTORIZATION IN F[X];287
8.5;3-5. ROOTS OF POLYNOMIALS;307
8.6;3-6. SOLVING POLYNOMIALS IN Z„,|X];335
8.7;3-7. QUADRATIC RECIPROCITY;353
8.8;MISCELLANEOUS PROBLEMS;378
9;Chapter 4. Groups;393
9.1;4-1. BASIC FACTS AND EXAMPLES;394
9.2;4-2. SUBGROUPS AND COSETS;414
9.3;4-3. CYCLIC GROUPS;434
9.4;4-4. NORMAL SUBGROUPS; FACTOR GROUPS; HOMOMORPHISMS;452
9.5;4-5. PERMUTATION GROUPS;473
9.6;4-6. THE GROUP Z*m;503
9.7;MISCELLANEOUS PROBLEMS;521
10;Selected Answers and Comments;534
11;Subject Index;556
