Excursions In Multiplicative Number Theory
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Excursions In Multiplicative Number Theory
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Author : Olivier Ramaré
language : en
Publisher: Springer Nature
Release Date : 2022-03-03
Excursions In Multiplicative Number Theory written by Olivier Ramaré and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Mathematics categories.
This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided “walks” invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin–Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at “higher ground”, where they will find opportunities for extensions and applications, such as the Selberg formula, Brun’s sieve, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area.
Excursions In Number Theory Algebra And Analysis
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Author : Kenneth Ireland
language : en
Publisher: Springer Nature
Release Date : 2023-03-27
Excursions In Number Theory Algebra And Analysis written by Kenneth Ireland and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-27 with Mathematics categories.
This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland’s path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics. A pool of 200 ‘Dialing In’ problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way. Excursions in Number Theory, Algebra, and Analysis invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and do some mathematics.
Multiplicative Number Theory I
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Author : Hugh L. Montgomery
language : en
Publisher: Cambridge University Press
Release Date : 2007
Multiplicative Number Theory I written by Hugh L. Montgomery and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Computational Excursions In Analysis And Number Theory
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Author : Peter Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Excursions In Analysis And Number Theory written by Peter Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is designed for a topics course in computational number theory. It is based around a number of difficult old problems that live at the interface of analysis and number theory. Some of these problems are the following: The Integer Chebyshev Problem. Find a nonzero polynomial of degree n with integer eoeffieients that has smallest possible supremum norm on the unit interval. Littlewood's Problem. Find a polynomial of degree n with eoeffieients in the set { + 1, -I} that has smallest possible supremum norm on the unit disko The Prouhet-Tarry-Escott Problem. Find a polynomial with integer co effieients that is divisible by (z - l)n and has smallest possible 1 norm. (That 1 is, the sum of the absolute values of the eoeffieients is minimal.) Lehmer's Problem. Show that any monie polynomial p, p(O) i- 0, with in teger coefficients that is irreducible and that is not a cyclotomic polynomial has Mahler measure at least 1.1762 .... All of the above problems are at least forty years old; all are presumably very hard, certainly none are completely solved; and alllend themselves to extensive computational explorations. The techniques for tackling these problems are various and include proba bilistic methods, combinatorial methods, "the circle method," and Diophantine and analytic techniques. Computationally, the main tool is the LLL algorithm for finding small vectors in a lattice. The book is intended as an introduction to a diverse collection of techniques.
Excursions In The History Of Mathematics
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Author : Israel Kleiner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-02
Excursions In The History Of Mathematics written by Israel Kleiner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-02 with Mathematics categories.
This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.
Analytic And Probabilistic Methods In Number Theory
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Author : F. Schweiger
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Analytic And Probabilistic Methods In Number Theory written by F. Schweiger and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
No detailed description available for "Analytic and Probabilistic Methods in Number Theory".
Excursions In Harmonic Analysis Volume 6
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Author : Matthew Hirn
language : en
Publisher: Springer Nature
Release Date : 2021-09-01
Excursions In Harmonic Analysis Volume 6 written by Matthew Hirn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-01 with Mathematics categories.
John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Elementary Number Theory With Applications
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Author : Thomas Koshy
language : en
Publisher: Elsevier
Release Date : 2007-05-08
Elementary Number Theory With Applications written by Thomas Koshy and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-08 with Mathematics categories.
This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East
Fourier Analysis On Finite Groups And Applications
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Author : Audrey Terras
language : en
Publisher: Cambridge University Press
Release Date : 1999-03-28
Fourier Analysis On Finite Groups And Applications written by Audrey Terras and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-28 with Mathematics categories.
It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Analytic And Elementary Number Theory
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Author : Krishnaswami Alladi
language : en
Publisher: Springer
Release Date : 2013-12-21
Analytic And Elementary Number Theory written by Krishnaswami Alladi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Mathematics categories.
This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. Audience: Researchers and students of number theory, analysis, combinatorics and modular forms will find this volume to be stimulating.