From Natural Numbers to Quaternions

Provides a self-contained introduction to the construction of integers, rationals, reals, complex numbers and Hamilton's quaternions Develops the basic prerequisites in group and ring theory as well as elementary number theory Contains appendices to each chapter highlighting the ubiquity of the material Includes more than 100 exercises with solutions Includes supplementary material: sn.pub/extras

Autorentext

Jürg Kramer is Professor of Mathematics at the Humboldt-Universität zu Berlin, Germany. His research focuses on arithmetic geometry, in particular on Arakelov geometry, and the theory of modular and automorphic forms. He is also interested in questions about the teaching of mathematics at university level.

Anna-Maria von Pippich is Junior Professor of Algebra and Number Theory at the Technische Universität Darmstadt, Germany. She is working in number theory, in particular in the theory of automorphic forms, and Arakelov geometry.

Inhalt
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.