Table of Contents

Preface; 1. Real numbers; 2. Non-standard numbers; 3. Rational numbers; 4. Completion; 5. The p-adic numbers; 6. Appendix; Hints and solutions; Bibliography; Notation; Index.

Promotional Information

The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.

About the Author

Helmutt Salzmann is Full Professor of Mathematics at Mathematisches Institut, Universitat Tubingen, Germany. Theo Grundhofer is Full Professor of Mathematics at Institut fur Mathematik, Universitat Wurzburg, Germany. Hermann Hahl is Full Professor of Mathematics at Institut fur Geometrie und Topologie, Universitat Stuttgart, Germany. Rainer Lowen is Full Professor of Mathematics at Institut fur Analysis und Algebra, Universitat Braunschweig, Germany.

Reviews

"Each of these fields comprise several closely interwoven algebraic and topological structures. Salzmann (mathematics, U. Tubingen) and his fellow authors Grundhofer (mathematics, U. Wurzburg>, Hahl (mathematics, U. Stuttgart) and Lowen (mathematics, Technische U. Braunchwieg) explain the interaction and interdependencies of these fields. They begin with real numbers, describing real numbers as an ordered set and explaining the concept of real numbers as a field and as an ordered group and a topological group. They explain complex numbers and rational numbers, expanding on the latter as a field and describing rational numbers as a field, then work through the concept of completion, as chains, ordered groups, topological abelian groups, and topological rings and fields. They conclude by explaining the field of p-adic numbers, their squares, absolute values and valuations, the topologies of valuation type, local fields and locally compact fields. They provide exercises with hints and solutions." -- Book News