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Elsevier

First Course in Algebra and Number Theory

  • 1 Edición - 1 de enero de 1971
  • Última edición
  • Autor: Edwin Weiss
  • Idioma: Inglés

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… Leer más

Descripción

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.

Índice

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

Detalles del producto

  • Edición: 1
  • Última edición
  • Publicado: 10 de mayo de 2014
  • Idioma: Inglés

Sobre el autor

EW

Edwin Weiss

Afiliaciones y experiencia
Department of Mathematics, Boston University

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