Description

Book Synopsis

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.



Table of 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.

From Natural Numbers to Quaternions

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    A Paperback / softback by Jürg Kramer, Anna-Maria von Pippich

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      Publisher: Springer International Publishing AG
      Publication Date: Publication Date: 23/11/2017
      ISBN13: 9783319694276, 978-3319694276
      ISBN10: 3319694278

      Description

      Book Synopsis

      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.



      Table of 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.

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