From Natural Numbers to Quaternions
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Beschreibung
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.
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
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Jürg Kramer
Themen in »From Natural Numbers to Quaternions«
MSC (2010): 08–01, 11–01, 12–01, 20–01 integers construction rational numbers construction real numbers construction complex numbers construction Hamiltonian quaternions construction group theory elements ring theory elements complex numbers algebraicity proof transcendence Euler number e Associative Rings and Algebras Commutative Rings and Algebras Field Theory and Polynomials Group Theory and Generalizations Number Theory