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A Journey Through The Realm of Numbers

From Quadratic Equations to Quadratic Reciprocity
BuchKartoniert, Paperback
344 Seiten
Englisch
Springererschienen am04.10.20201st ed. 2020
This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory.mehr
Verfügbare Formate
BuchKartoniert, Paperback
EUR19,25
E-BookPDF1 - PDF WatermarkE-Book
EUR37,44

Produkt

KlappentextThis book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory.
Zusammenfassung
Introduces foundational concepts in number theory, set theory, and algebra in an accessible and motivated way

Includes over 300 carefully structured exercises to aid understanding

Helps the reader develop basic programming skills for mathematical computations

Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-3-030-55232-9
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2020
Erscheinungsdatum04.10.2020
Auflage1st ed. 2020
ReiheSUMS Readings
Seiten344 Seiten
SpracheEnglisch
Gewicht552 g
IllustrationenXIX, 344 p.
Artikel-Nr.48791375

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
"This book offers a leisurely path to elementary number theory accessible to bright and motivated high-school students. ... There is also a section that introduces the readers to Sage, and lots of exercises with hints. There are thousands of books out there that popularize mathematics by removing the mathematics from the text; the present book is different: it popularizes number theory and keeps the mathematics in. It is clearly written, suitable for self study, and it deserves a wide readership." ( Franz Lemmermeyer, zbMATH 1462.00008, 2021)mehr

Autor


Menny Aka studied at the Hebrew University, with a Ph.D. in 2012 under Alexander Lubotzky. He held research positions at EPFL and ETH Zürich before becoming a senior scientist at ETH Zürich. He works on the interaction between number theory, ergodic theory and group theory. An enthusiastic and innovative lecturer, he is interested in making mathematics accessible, especially to younger audiences. He has initiated and taught in various programs for high school students, including projects aimed at gifted students and prospective undergraduates. He is interested in showcasing the beauty and simplicity underpinning complex mathematical ideas.

Manfred Einsiedler studied at the University of Vienna, with a Ph.D. in 1999 under Klaus Schmidt. He held research positions at the University of East Anglia, Penn State University, the University of Washington, and Princeton University as a Clay Research Scholar. After becoming a Professor at Ohio State University he joinedETH Zürich. In 2004 he won the Research Prize of the Austrian Mathematical Society, in 2008 he was an invited speaker at the European Mathematical Congress in Amsterdam, and in 2010 he was an invited speaker at the International Congress of Mathematicians in Hyderabad. He works on ergodic theory (especially dynamical and equidistribution problems on homogeneous spaces) and its applications to number theory. He has collaborated with Grigory Margulis and Akshay Venkatesh. With Elon Lindenstrauss and Anatole Katok, Einsiedler proved that a conjecture of Littlewood on Diophantine approximation is "almost always" true.

Thomas Ward studied at the University of Warwick, with a Ph.D. in 1989 under Klaus Schmidt. He held research positions at the University of Maryland, College Park and at Ohio State University before joining the University of East Anglia in 1992. Since 2008 he has served on university executives, as Pro-Vice-Chancellor for Education at the University of East Anglia and Durham University, and since 2016 as Deputy Vice-Chancellor (Student Education) at the University of Leeds. He worked on the ergodic theory of algebraic dynamical systems, compact group automorphisms, and number theory. A long collaboration with Graham Everest on links between number theory and dynamical systems included the book Heights of polynomials and entropy in algebraic dynamics and a paper on Diophantine equations that won the 2012 Lester Ford Prize for mathematical exposition. With Einsiedler he has written Ergodic theory with a view towards number theory in 2011 and Functional analysis, spectral theory, and applications in 2017.    







     
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