From Natural Numbers to Quaternions / by Jürg Kramer, Anna-Maria von Pippich.

Format:

Book

Author/Creator:

Kramer, Jürg., Author.

von Pippich, Anna-Maria., Author.

Series:

Springer Undergraduate Mathematics Series, 1615-2085

Language:

English

Subjects (All):

Algebra.

Number theory.

Number Theory.

Local Subjects:

Algebra.

Number Theory.

Physical Description:

1 online resource (XVIII, 277 p. 10 illus., 6 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

Contents:

Introduction

I The Natural Numbers

II The Integers

III The Rational Numbers

IV The Real Numbers

V The Complex Numbers

VI Hamilton's Quaternions

Solutions to Exercises

Selected Literature

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-69429-4

OCLC:

1066178694