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A journey through the realm of numbe...

Aka, Menny.

A journey through the realm of numbersfrom quadratic equations to quadratic reciprocity /

Record Type:	Electronic resources : Monograph/item
Title/Author:	A journey through the realm of numbersby Menny Aka, Manfred Einsiedler, Thomas Ward.
Reminder of title:	from quadratic equations to quadratic reciprocity /
Author:	Aka, Menny.
other author:	Einsiedler, Manfred.
Published:	Cham :Springer International Publishing :2020.
Description:	xix, 344 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Number theory.
Online resource:	https://doi.org/10.1007/978-3-030-55233-6
ISBN:	9783030552336$q(electronic bk.)

A journey through the realm of numbersfrom quadratic equations to quadratic reciprocity /
Aka, Menny.

A journey through the realm of numbersfrom quadratic equations to quadratic reciprocity /[electronic resource] :by Menny Aka, Manfred Einsiedler, Thomas Ward. - Cham :Springer International Publishing :2020. - xix, 344 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series: SUMS Readings. - Springer undergraduate mathematics series..

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 lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

ISBN: 9783030552336$q(electronic bk.)

Standard No.: 10.1007/978-3-030-55233-6doiSubjects--Topical Terms:

189521
Number theory.

LC Class. No.: QA241 / .A336 2020

Dewey Class. No.: 512.7

A journey through the realm of numbersfrom quadratic equations to quadratic reciprocity /
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520 $a 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 lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.
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