First Course in Algebra and Number Theory
- 1st Edition - May 10, 2014
- Imprint: Academic Press
- Author: Edwin Weiss
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 8 2 9 - 5
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 0 3 7 - 1
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… Read more
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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.
PrefaceI. Elementary Number Theory 1-1. Divisibility 1-2. The Division Algorithm 1-3. The Greatest Common Divisor 1-4. Unique Factorization 1-5. A Convenient Notation 1-6. Linear Diophantine Equations 1-7. Congruence 1-8. Radix Representation Miscellaneous ProblemsII. Rings and Domains 2-1. Rings: Elementary Properties 2-2. Examples 2-3. Ordered and Well-Ordered Domains 2-4. Computation Rules 2-5. Characterization of the Integers Miscellaneous ProblemsIII. Congruences and Polynomials 3-1. Linear Congruences 3-2. Units and Fields 3-3. Polynomials and Polynomial Functions 3-4. Factorization in F[X] 3-5. Roots Of Polynomials 3-6. Solving Polynomials In Zm[x] 3-7. Quadratic Reciprocity Miscellaneous ProblemsIV. Groups 4-1. Basic Facts And Examples 4-2. Subgroups and Cosets 4-3. Cyclic Groups 4-4. Normal Subgroups; Factor Groups; Homomorphisms 4-5. Permutation Groups 4-6. The Group Z*m Miscellaneous ProblemsSelected Answers and CommentsSubject Index
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- Language: English
EW
Edwin Weiss
Affiliations and expertise
Department of Mathematics, Boston UniversityRead First Course in Algebra and Number Theory on ScienceDirect