Number Theory Through Exercises

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Number Theory Through Exercises

Author : Nairi Sedrakyan
Publisher :
ISBN 13 : 9781090987891
Total Pages : 259 pages
Book Rating : 4.9/5 (878 download)

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Book Synopsis Number Theory Through Exercises by : Nairi Sedrakyan

Download or read book Number Theory Through Exercises written by Nairi Sedrakyan and published by . This book was released on 2019-03-19 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a teacher's manual of Number Theory and a self-study handbook for high-school or college students, and mathematical competitors. The book teaches new and classical proof techniques of Number Theory through practical and challenging problems. It is arranged by topics and difficulty level.It mainly consists of new problems created by authors with author-prepared-solutions, some of these problems were proposed in different national and international Mathematical Olympiads from 1984 to 2018.The book gives a broad view of Number Theory and goes beyond the typical elementary mathematics by providing deeper treatment of the topics.About the authors.Hayk Sedrakyan is an IMO medal winner, Professor of mathematics in Paris, France and a professional Math Olympiad Coach in Greater Boston area, Massachusetts, USA. Having served as a Team Leader at Harvard-MIT Mathematics Tournament (HMMT) and as a scientific researcher at the European Commission. He has defended his PhD thesis in mathematics in UPMC-Sorbonne University, Paris, France.Nairi Sedrakyan is involved in national and international Olympiads of mathematics, having been the President of Armenian Mathematics Olympiads and IMO jury member. He is the author of one of the hardest problems ever proposed in the history of IMO (5th problem of 37th IMO). Students of Nairi Sedrakyan have obtained 20 Gold, Silver and Bronze medals in IMO, providing more than half of the medals that Armenia received in the history of its participation in IMO (till that year). For his outstanding teaching Nairi Sedrakyan received the title of the best teacher of the Republic of Armenia and has been awarded with a special gift from the Prime Minister.

Number Theory Through Exercises

Author : Nairi Sedrakyan
Publisher :
ISBN 13 : 9781090868138
Total Pages : 259 pages
Book Rating : 4.8/5 (681 download)

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Book Synopsis Number Theory Through Exercises by : Nairi Sedrakyan

Download or read book Number Theory Through Exercises written by Nairi Sedrakyan and published by . This book was released on 2019-03-18 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a teacher's manual of Number Theory and a self-study handbook for high-school or college students, and mathematical competitors. The book teaches new and classical proof techniques of Number Theory through practical and challenging problems. It is arranged by topics and difficulty level.It mainly consists of new problems created by authors with author-prepared-solutions, some of these problems were proposed in different national and international Mathematical Olympiads from 1984 to 2018.The book gives a broad view of Number Theory and goes beyond the typical elementary mathematics by providing deeper treatment of the topics.This book consists of two parts. Part 1 is a separate book consisting of Chapter 1, Chapter 2 and Chapter 3.Part 2 is a separate book consisting of Chapter 4, Chapter 5 and Chapter 6.

Galois Theory Through Exercises

Author : Juliusz Brzeziński
Publisher : Springer
ISBN 13 : 331972326X
Total Pages : 296 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Galois Theory Through Exercises by : Juliusz Brzeziński

Download or read book Galois Theory Through Exercises written by Juliusz Brzeziński and published by Springer. This book was released on 2018-03-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.

Number Theory and Geometry: An Introduction to Arithmetic Geometry

Author : Álvaro Lozano-Robledo
Publisher : American Mathematical Soc.
ISBN 13 : 147045016X
Total Pages : 488 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Number Theory and Geometry: An Introduction to Arithmetic Geometry by : Álvaro Lozano-Robledo

Download or read book Number Theory and Geometry: An Introduction to Arithmetic Geometry written by Álvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on 2019-03-21 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.

Introduction to Number Theory

Author : Anthony Vazzana
Publisher : CRC Press
ISBN 13 : 1584889381
Total Pages : 530 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Introduction to Number Theory by : Anthony Vazzana

Download or read book Introduction to Number Theory written by Anthony Vazzana and published by CRC Press. This book was released on 2007-10-30 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi

Steps into Analytic Number Theory

Author : Paul Pollack
Publisher : Springer Nature
ISBN 13 : 3030650774
Total Pages : 191 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Steps into Analytic Number Theory by : Paul Pollack

Download or read book Steps into Analytic Number Theory written by Paul Pollack and published by Springer Nature. This book was released on 2021-02-08 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.

Elements of Number Theory

Author : I. M. Vinogradov
Publisher : Courier Dover Publications
ISBN 13 : 0486160351
Total Pages : 244 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Elements of Number Theory by : I. M. Vinogradov

Download or read book Elements of Number Theory written by I. M. Vinogradov and published by Courier Dover Publications. This book was released on 2016-01-14 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, detailed exposition that can be understood by readers with no background in advanced mathematics. More than 200 problems and full solutions, plus 100 numerical exercises. 1949 edition.

Number Theory

Author : Róbert Freud
Publisher : American Mathematical Soc.
ISBN 13 : 1470452758
Total Pages : 549 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Number Theory by : Róbert Freud

Download or read book Number Theory written by Róbert Freud and published by American Mathematical Soc.. This book was released on 2020-10-08 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.

Number Theory

Author : George E. Andrews
Publisher : Courier Corporation
ISBN 13 : 0486135101
Total Pages : 292 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Number Theory by : George E. Andrews

Download or read book Number Theory written by George E. Andrews and published by Courier Corporation. This book was released on 2012-04-30 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Exercises in Number Theory

Author : D.P. Parent
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 326 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Exercises in Number Theory by : D.P. Parent

Download or read book Exercises in Number Theory written by D.P. Parent and published by Springer Science & Business Media. This book was released on 1984-09-12 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy of its distinguished past. More 'and more researchers have been attracted by problems which, though it is possible to express in simple statements, whose solutions require all their ingenuity and talent. In so doing, their work enriches the whole of mathematics with new and fertile methods. To be in a position to tackle these problems, it is neces sary to be familiar with many specific aspects of number theory. These are very different from those encountered in analysis or geometry. The necessary know-how can only be acquired by study ing and solving numerous problems. Now it is very easy to form ulate problems whose solutions, while sometimes obvious, more often go beyond current methods. Moreover, there is no doubt that, even more than in other disciplines, in mathematics one must have exercises available whose solutions are accessible. This is the objective realised by this work. It is the collab orative work of several successful young number theorists. They have drawn these exercises from their own work, from the work of their associated research groups as well as from published work.

An Illustrated Theory of Numbers

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
ISBN 13 : 1470463717
Total Pages : 341 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Illustrated Theory of Numbers by : Martin H. Weissman

Download or read book An Illustrated Theory of Numbers written by Martin H. Weissman and published by American Mathematical Soc.. This book was released on 2020-09-15 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.

An Adventurer's Guide to Number Theory

Author : Richard Friedberg
Publisher : Courier Corporation
ISBN 13 : 0486152693
Total Pages : 241 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Adventurer's Guide to Number Theory by : Richard Friedberg

Download or read book An Adventurer's Guide to Number Theory written by Richard Friedberg and published by Courier Corporation. This book was released on 2012-07-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.

Solved and Unsolved Problems in Number Theory

Author : Daniel Shanks
Publisher : American Mathematical Society
ISBN 13 : 1470476452
Total Pages : 321 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Solved and Unsolved Problems in Number Theory by : Daniel Shanks

Download or read book Solved and Unsolved Problems in Number Theory written by Daniel Shanks and published by American Mathematical Society. This book was released on 2024-01-24 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.

A Course in Algebraic Number Theory

Author : Robert B. Ash
Publisher : Courier Corporation
ISBN 13 : 0486477541
Total Pages : 130 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Course in Algebraic Number Theory by : Robert B. Ash

Download or read book A Course in Algebraic Number Theory written by Robert B. Ash and published by Courier Corporation. This book was released on 2010-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.

Exercises in Group Theory

Author : E. Lyapin
Publisher : Springer Science & Business Media
ISBN 13 : 1461345898
Total Pages : 245 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Exercises in Group Theory by : E. Lyapin

Download or read book Exercises in Group Theory written by E. Lyapin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is a translation of E. S. Lyapin, A. Va. Aizenshtat, and M. M. Lesokhin's Uprazhneniya po teorii grupp. I have departed somewhat from the original text in the following respects. I) I have used Roman letters to indicate sets and their elements, and Greek letters to indicate mappings of sets. The Russian text frequently adopts the opposite usage. 2) I have changed some of the terminology slightly in order to conform with present English usage (e.g., "inverses" instead of "regular conjugates"). 3) I have corrected a number of misprints which appeared in the original in addition to those corrections supplied by Professor Lesokhin. 4) The bibliography has been adapted for readers of English. 5) An index of all defined terms has been compiled (by Anita Zitarelli). 6) I have included a multiplication table for the symmetric group on four elements, which is a frequent source of examples andcounterex::Imples both in this book and in all of group theory. I would like to take this opportunity to thank the authors for their permission to publish this translation. Special thanks are extended to Professor Lesokhin for his errata list and for writing the Foreword to the English Edition. I am particularly indebted to Leo F. Boron, who read the entire manuscript and offered many valuable comments. Finally, to my unerring typists Sandra Rossman and Anita Zitarelli, I am sincerely grateful.

A Brief Guide to Algebraic Number Theory

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
ISBN 13 : 9780521004237
Total Pages : 164 pages
Book Rating : 4.0/5 (42 download)

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Book Synopsis A Brief Guide to Algebraic Number Theory by : H. P. F. Swinnerton-Dyer

Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Explorations in Number Theory

Author : Cam McLeman
Publisher : Springer Nature
ISBN 13 : 3030989313
Total Pages : 380 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Explorations in Number Theory by : Cam McLeman

Download or read book Explorations in Number Theory written by Cam McLeman and published by Springer Nature. This book was released on 2022-12-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics. The text is organized around three core themes: the notion of what a “number” is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems. Other aspects of modern number theory – including the study of elliptic curves, the analogs between integer and polynomial arithmetic, p-adic arithmetic, and relationships between the spectra of primes in various rings – are included in smaller but persistent threads woven through chapters and exercise sets. Each chapter concludes with exercises organized in four categories: Calculations and Informal Proofs, Formal Proofs, Computation and Experimentation, and General Number Theory Awareness. IBL “Exploration” worksheets appear in many sections, some of which involve numerical investigations. To assist students who may not have experience with programming languages, Python worksheets are available on the book’s website. The final chapter provides five additional IBL explorations that reinforce and expand what students have learned, and can be used as starting points for independent projects. The topics covered in these explorations are public key cryptography, Lagrange’s four-square theorem, units and Pell’s Equation, various cases of the solution to Fermat’s Last Theorem, and a peek into other deeper mysteries of algebraic number theory. Students should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the “numberverse.”