Kramer, Jürg. From Natural Numbers to Quaternions [electronic resource] / / by Jürg Kramer, Anna-Maria von Pippich.. — 1st ed. 2017.. — XVIII, 277 p. 10 illus., 6 illus. in color. : online resource. — (Springer Undergraduate Mathematics Series,) 1615-2085. - Springer Undergraduate Mathematics Series, .
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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Анотація: 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.