Number Systems: An Introduction to Algebra and Analysis (Pure and Applied Undergraduate Texts) - Hardcover

Ovchinnikov, Sergei

Hardcover

ISBN 10: 147042018X ISBN 13: 9781470420185

Publisher: American Mathematical Society, 2015

Synopsis

This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers.

The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.

About this title

About the Author

Sergei Ovchinnikov, San Francisco State University, CA, USA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2015
• Language: English
• ISBN 10: 147042018X
• ISBN 13: 9781470420185
• Binding: Hardcover
• Number of pages: 144