A Journey Through The Realm of Numbers : From Quadratic Equations to Quadratic Reciprocity. 1st ed. 2020

種類:

電子ブック

責任表示:

by Menny Aka, Manfred Einsiedler, Thomas Ward

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Aka, Menny.
• Einsiedler, Manfred.
• Ward, Thomas.
• SpringerLink (Online service)

シリーズ名:

SUMS Readings ;

ISBN:

9783030552336 [3030552330]    

注記:

1 Introduction: Polynomial Equations -- 2 Cantor's Paradise -- 3 Sums of Squares -- 4 Sums of Two Squares -- 5 Abstract Algebra: Ring Theory -- 6 Cubic and Quartic Diophantine Equations -- 7 The Structure of the Group Fp⨯ -- 8 Studying Squares Again -- Hints to Selected Exercises -- References and further reading -- Index.
This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are l

ローカル注記:

学内専用E-BOOKS (local access only)