De Gruyter, 2017. — 342 p. — (Textbook). — ISBN 978-3110515849. This two-volume set collects and presents the fundamentals of mathematics in an exciting and pedagogically sound way. The present volume examines the most important basic results in algebra and number theory, along with their proofs, and also their history. Preface The natural, integral and rational numbers...
Springer, 2021. — 342 p. — ISBN 978-3-030-83898-0. This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital...
2nd Edition. — World Scientific, 2021. — 444 p. — ISBN 978-981-123-350-0, 978-981-123-351-7, 978-981-123-352-4. This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking...
Springer, 2021. — 445 p. — ISBN 978-3-030-67995-8. This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The...
Birkhäuser, 2021. — 319 p. — ISBN 978-3-030-77262-8. This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field,...
Dover Publications, 2007 (first published in 1967). — 144 p. — eISBN-13 978-0-486-15494-7. The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's...
Springer, 2020. — 284 p. — (Mathematical Engineering). — ISBN13 978-3030613020. — ISBN10 303061302X. This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research. The contributions of this volume stem from the Workshop...
Oxford University Press. — 2020. — 176 p. — (Very Short Introductions). — ISBN13: 9780192519078. Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many...
Springer, 2018. — 286 p. — (Undergraduate Texts in Mathematics). — ISBN: 978-3-030-02603-5, 978-3-030-02604-2. This book came out of an attempt to explain to a class of motivated students at the University of Illinois at Chicago what sorts of problems I thought about in my research. In the course, we had just talked about the integral solutions to the Pythagorean Equation and...
Ivy Press, 2020. — 160 p. — ISBN: 9780711254664, 0711254664, 9781782408475, 1782408479. — Niamh Nic Daéid, Christian Cole (eds.). Full of fascinating facts about numbers and how they are used, 30-Second Numbers demystifies the world of counting, measuring, ordering, calculating and many other applications of numbers. We know that we use numbers pretty often, some of us...
2nd Edition. — Springer, 2012. — 464 p. — (Modern Birkhäuser Classics). — ISBN: 978-08176-8297-2. From the original hard cover edition: In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem....
Springer, 2015. — 282 p. — ISBN: 3319110349. The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory....
Springer, 2018. — 430 p. — ISBN: 978-3-319-77832-7, 3319778323. Считавшийся утерянным сборник заметок гениального индийского математика Раманужана. Для изучающих теорию чисел, теорию функций, историю математики, психологию математического творчества. In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to...
New York: Palgrave McMillan, 2011. — 272 p. — ISBN10: 0230113842; ISBN13: 978-0230113848 — (MacSci) Every time we download music, take a flight across the Atlantic or talk on our cell phones, we are relying on great mathematical inventions. In The Number Mysteries, one of our generation's foremost mathematicians Marcus du Sautoy offers a playful and accessible examination of...
Dover Publications, 2018. — 298 p. — (Dover Books on Mathematics). — ASIN 048682764X. Concise but thorough and systematic, this categorical discussion of the real number system presents a series of step-by-step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and...
Springer, 2015. — 232 p. — ISBN: 0387351566. This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and...
Springer, 2018. — 196 p. — ISBN: 978-3-319-92777-0. This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research...
М.: Изд-во МГУ, 1982. — 312 с. В монографии излагаются история решения седьмой проблемы Гильберта и основные результаты, полученные с помощью методов, примененных для ее решения. Значительная часть книги посвящена изложению найденного в 1966 г. А. Бейкером усиления метода А. О. Гельфонда и полученным в связи с этим эффективным решением ряда задач теории чисел. Большая часть...
Cambridge University Press, 2015. — 216 p. — ISBN: 1107427746 Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book provides, for the first time, a comprehensive collection of their properties and applications in combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. After an...
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