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Number Theory Revealed

A Masterclass

Häftad, Engelska, 2020

1 559 kr

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Number Theory Revealed: A Masterclass acquaints enthusiastic students with the ""Queen of Mathematics''. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves.This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials.

Produktinformation

Utgivningsdatum2020-09-30
Mått260 x 30 x 170 mm
Vikt1 100 g
FormatHäftad
SpråkEngelska
SerieMiscellaneous Books
Antal sidor587
FörlagAmerican Mathematical Society
ISBN9781470463700

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Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.

Preliminary chapter on inductionThe Eulidean algorithmCongruencesThe basic algebra of number theoryMultiplicative functionsThe distribution of prime numbersDiophantine problemsPower residuesQuadratic residuesQuadratic equationsSquare roots and factoringRational approximations to real numbersBinary quadratic formsThe anatomy of integersCounting integral and rational points on curves, modulo $p$Combinatorial number theoryThe $p$-adic numbersRational points on elliptic curveHints for exercisesRecommended further readingIndex

I strongly recommend the reading of Number Theory Revealed (the 'Masterclass' in particular) not only to all mathematicians but also to anybody scientifically inclined and curious about what mathematics is and how it is done. Not only are the topics well chosen and well presented, but this book is a real page-turner. How often can you say that about a mathematical textbook? Chapeau!"" —Marco Abate, The Mathematical Intelligencer""Andrew Granville has written many wonderful expository articles about number theory (especially patterns in primes), as well as dozens of research articles on many aspects of this field. It is, thus, highly appropriate that he turn all this knowledge into a series of textbooks for number theory. So if you are looking for enrichment in how the world of number theory connects together but formatted as a textbook with familiar topical arrangement, this is a great resource; I can't wait for the next two volumes to appear."" —Karl-Dieter Crisman, MAA Reviews