A journey through the realm of numbers : from quadratic equations to quadratic reciprocity / Menny Aka, Manfred Einsiedler, Thomas Ward.

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A journey through the realm of numbers : from quadratic equations to quadratic reciprocity / Menny Aka, Manfred Einsiedler, Thomas Ward.

9783030552336 (electronic book)
3030552330 (electronic book)
3030552322
9783030552329

Cham, Switzerland : Springer, [2020]

English

1 online resource

QA241 .A33 2020

512.7

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.

Includes bibliographical references and index.

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Description based on online resource; title from digital title page (viewed on November 16, 2020).

Springer undergraduate mathematics series.

Print version: 9783030552329

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