From Natural Numbers to Quaternions

前表紙
Springer, 2017/11/15 - 277 ページ

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.

 

ページのサンプル

目次

Introduction
1
I The Natural Numbers
9
II The Integers
45
III The Rational Numbers
92
IV The Real Numbers
141
V The Complex Numbers
183
VI Hamiltons Quaternions
218
Solutions to Exercises
247
Selected Literature
279
Index
282
著作権

他の版 - すべて表示

From Natural Numbers to Quaternions
Jürg Kramer,Anna-Maria von Pippich
プレビュー不可 - 2017

多く使われている語句

abelian group absolute value addition and multiplication arbitrary assertion associative bijective calculate called Chapter commutative completes the proof complex numbers congruence conjecture construction cosets decimal expansion defined Definition denote det(A distributive laws elliptic curves encryption equality equation equivalence class example Exercise exists finite function fundamental theorem greatest common divisor group G group homomorphism group isomorphism identity element im(f Im(IH induction inequality injective integers integral domain inverse isomorphism ker(f Lemma Let G map(A mapping f modulo natural numbers nontrivial normal subgroup normed number systems number theory octonions operation prime factorization prime numbers principal ideal prove quadratic quaternions quotient quotient group R-algebra rational Cauchy sequence rational null sequence rational numbers rational points reader real numbers relatively prime Remark ring homomorphism satisfies semigroup solution Springer subring surjective thereby obtain uniquely determined unit element zero divisors

著者について (2017)

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.

書誌情報

書籍名From Natural Numbers to Quaternions
Springer Undergraduate Mathematics Series
著者Jürg Kramer, Anna-Maria von Pippich
出版社Springer, 2017
ISBN3319694294, 9783319694290
ページ数277 ページ
  
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