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• Base Product Code Keyword List: mbk; MBK; mbk/126; MBK/126; mbk-126; MBK-126
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Title (HTML): Number Theory Revealed: An Introduction
Author(s) (Product display): Andrew Granville
Affiliation(s) (HTML): University of Montreal, Quebec, Canada and University College London, London, England and (formerly) University of Georgia, Athens, GA
Custom URL: mbk-126
Abstract:

Number Theory Revealed: An Introduction presents a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations, as well as 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, Fermat's Last Theorem for polynomials, and modern twists on traditional questions. This book provides careful coverage of all core topics in a standard introductory number theory course with pointers to some exciting further directions.

An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach, adding additional material in further chapters and appendices. It is ideal for instructors who wish to tailor a class to their own interests and gives well-prepared students further opportunities to challenge themselves and push beyond core number theory concepts, serving as a springboard to many current themes in mathematics.

This book is part of Number Theory Revealed: The Series. Find full tables of contents, sample problems, hints, and appendices, as well as updates about forthcoming related volumes here.

About the Author:

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.

Publication Month and Year: 2019-11-12
Copyright Year: 2019
Page Count: 264
Cover Type: Hardcover
Print ISBN-13: 978-1-4704-4157-9
Online ISBN 13: 978-1-4704-5423-4
Online ISSN:
Primary MSC: 11
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Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/mbk-126
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Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-5423-4&pisbn=978-1-4704-4157-9&epc=MBK/126.E&ppc=MBK/126&title=Number%20Theory%20Revealed%3A%20An%20Introduction&author=Andrew%20Granville&type=DE
Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-5423-4&pisbn=978-1-4704-4157-9&epc=MBK/126.E&ppc=MBK/126&title=Number%20Theory%20Revealed%3A%20An%20Introduction&author=Andrew%20Granville&type=R
Readership:

Undergraduate and graduate students interested in introductory number theory.

Reviews:

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

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• Base Product Code Keyword List: mbk; MBK; mbk/127; MBK/127; mbk-127; MBK-127
Print Product Code: MBK/127.S
Online Product Code: MBK/127.E
Title (HTML): Number Theory Revealed: A Masterclass
Author(s) (Product display): Andrew Granville
Affiliation(s) (HTML): University of Montreal, Quebec, Canada and University College London, London, England and (formerly) University of Georgia, Athens, GA
Custom URL: mbk-127
Abstract:

Number Theory Revealed: A Masterclass presents 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, Fermat's Last Theorem for polynomials, and modern twists on traditional questions.

This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction. It is ideal for instructors who wish to tailor a class to their own interests and gives well-prepared students further opportunities to challenge themselves and push beyond core number theory concepts, serving as a springboard to many current themes in mathematics. Additional topics in A Masterclass include the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, magic squares of primes, a new proof of Mordell's Theorem for congruent elliptic curves, as well as links with algebra, analysis, cryptography, and dynamics.

This book is part of Number Theory Revealed: The Series. Find full tables of contents, sample problems, hints, and appendices, as well as updates about forthcoming related volumes here.

About the Author:

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.

Book Series Name: Miscellaneous Books
Volume: 127
Publication Month and Year: 2020-09-23
Copyright Year: 2019
Page Count: 587
Cover Type: Softcover
Print ISBN-13: 978-1-4704-6370-0
Online ISBN 13: 978-1-4704-5424-1
Online ISSN:
Primary MSC: 11
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Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/mbk-127
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Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-5424-1&pisbn=978-1-4704-6370-0&epc=MBK/127.E&ppc=MBK/127.S&title=Number%20Theory%20Revealed%3A%20A%20Masterclass&author=Andrew%20Granville&type=R
Readership:

Undergraduate and graduate students interested in introductory number theory.

Reviews:

Not just a list of results and definitions that were hopefully explained in class, this a book for sitting down and engaging with, pen in hand, ready for the exercises interlaced with the exposition. Students learn not just by seeing examples and special cases worked out in advance of a general statement, but by working things out for themselves...One striking feature of this book (and perhaps one argument for a stream of new books on old subjects) is its inclusion of current research in its additional topics...This book will surely address the precocious student.s desire to know what number theory is about now.

-- Patrick Ingram, York University, CMS Notes

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

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• Base Product Code Keyword List: crmp; CRMP; crmp/46; CRMP/46; crmp-46; CRMP-46
Print Product Code: CRMP/46
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Title (HTML): Anatomy of Integers
Author/Editor Label (optional): Edited by
Author(s) (Product display): Jean-Marie De Koninck; Andrew Granville; Florian Luca
Affiliation(s) (HTML): Université Laval, Québec, QC, Canada; Université de Montréal, Montréal, QC, Canada; Universidad Nacional Autonoma de México, Morelia, México
Publisher Blurb: A co-publication of the AMS and Centre de Recherches Mathématiques
Custom URL: crmp-46
Abstract:

The book is mostly devoted to the study of the prime factors of integers, their size and their quantity, to good bounds on the number of integers with different properties (for example, those with only large prime factors) and to the distribution of divisors of integers in a given interval. In particular, various estimates concerning smooth numbers are developed. A large emphasis is put on the study of additive and multiplicative functions as well as various arithmetic functions such as the partition function. More specific topics include the Erdős–Kac Theorem, cyclotomic polynomials, combinatorial methods, quadratic forms, zeta functions, Dirichlet series and $$L$$-functions. All these create an intimate understanding of the properties of integers and lead to fascinating and unexpected consequences. The volume includes contributions from leading participants in this active area of research, such as Kevin Ford, Carl Pomerance, Kannan Soundararajan and Gérald Tenenbaum.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Book Series Name: CRM Proceedings & Lecture Notes
Volume: 46
Publication Month and Year: 2008-07-18
Copyright Year: 2008
Page Count: 297
Cover Type: Softcover
Print ISBN-13: 978-0-8218-4406-9
Online ISBN 13: 978-1-4704-3960-6
Print ISSN: 1065-8580
Online ISSN: 1065-8580
Primary MSC: 11
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Publisher (non-AMS): A co-publication of the AMS and Centre de Recherches Mathématiques
SXG Subject: NT
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Readership:

Undergraduates and graduate students and research mathematicians interested in Erdős–type elementary number theory, smooth numbers, and distribution of prime factors of integers, partitions, etc.

Reviews:

[I]t is quite satisfying to read in these papers some pretty descriptions of the insights behind the methods of proof, so that the application of technical anatomical results seems natural rather than confounding.

-- Greg Martin, University of British Columbia

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• Base Product Code Keyword List: crmp; CRMP; crmp/43; CRMP/43; crmp-43; CRMP-43
Print Product Code: CRMP/43
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Title (HTML): Additive Combinatorics
Author/Editor Label (optional): Edited by
Author(s) (Product display): Andrew Granville; Melvyn B. Nathanson; József Solymosi
Affiliation(s) (HTML): Université de Montréal, Montréal, QC, Canada; City University of New York, Lehman College, Bronx, NY; University of British Columbia, Vancouver, BC, Canada
Publisher Blurb: A co-publication of the AMS and Centre de Recherches Mathématiques
Custom URL: crmp-43
Abstract:

One of the most active areas in mathematics today is the rapidly emerging new topic of “additive combinatorics”. Building on Gowers' use of the Freiman–Ruzsa theorem in harmonic analysis (in particular, his proof of Szemerédi's theorem), Green and Tao famously proved that there are arbitrarily long arithmetic progressions of primes, and Bourgain and his co-authors have given non-trivial estimates for hitherto untouchably short exponential sums. There are further important consequences in group theory and in complexity theory and compelling questions in ergodic theory, discrete geometry and many other disciplines. The basis of the subject is not too difficult: it can be best described as the theory of adding together sets of numbers; in particular, understanding the structure of the two original sets if their sum is small. This book brings together key researchers from all of these different areas, sharing their insights in articles meant to inspire mathematicians coming from all sorts of different backgrounds.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Book Series Name: CRM Proceedings & Lecture Notes
Volume: 43
Publication Month and Year: 2007-10-16
Copyright Year: 2007
Page Count: 335
Cover Type: Softcover
Print ISBN-13: 978-0-8218-4351-2
Online ISBN 13: 978-1-4704-3957-6
Print ISSN: 1065-8580
Online ISSN: 1065-8580
Primary MSC: 11
Secondary MSC: 05; 42; 28; 37
Textbook?: false
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Publisher (non-AMS): A co-publication of the AMS and Centre de Recherches Mathématiques
SXG Subject: DM
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Readership:

Undergraduates, graduate students, and research mathematicians interested in additive combinatorics.

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