Elementary Methods In Number Theory
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Elementary Methods In Number Theory
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Elementary Methods In Number Theory written by Melvyn B. Nathanson 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 2000 with Mathematics categories.
This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion.
Topics In The Theory Of Numbers
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Author : Janos Suranyi
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-14
Topics In The Theory Of Numbers written by Janos Suranyi 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 2003-01-14 with Mathematics categories.
Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.
Methods Of Solving Number Theory Problems
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Author : Ellina Grigorieva
language : en
Publisher: Birkhäuser
Release Date : 2018-07-06
Methods Of Solving Number Theory Problems written by Ellina Grigorieva and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Mathematics categories.
Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence. The next chapter begins with the Euclidean algorithm, explores therepresentations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.
Number Theory For Elementary School Teachers
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Author : Edward Wall
language : en
Publisher: McGraw-Hill Humanities/Social Sciences/Languages
Release Date : 2009-02-13
Number Theory For Elementary School Teachers written by Edward Wall and has been published by McGraw-Hill Humanities/Social Sciences/Languages this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-13 with Education categories.
In response to concerns about teacher retention, especially among teachers in their first to fourth year in the classroom, we offer future teachers a series of brief guides full of practical advice that they can refer to in both their student teaching and in their first years on the job. Number Theory for Elementary School Teachers is designed for preservice candidates in early and/or elementary education. The text complements traditional Math Methods courses and provides deep content knowledge for prospective and first year teachers.
Excursions In Number Theory
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Author : Charles Stanley Ogilvy
language : en
Publisher: Courier Corporation
Release Date : 1988-01-01
Excursions In Number Theory written by Charles Stanley Ogilvy and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.
Analytic Number Theory An Introductory Course
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Author : Paul Trevier Bateman
language : en
Publisher: World Scientific
Release Date : 2004-09-07
Analytic Number Theory An Introductory Course written by Paul Trevier Bateman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Mathematics categories.
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
Elementary Number Theory Primes Congruences And Secrets
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Author : William Stein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Elementary Number Theory Primes Congruences And Secrets written by William Stein 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 2008-10-28 with Mathematics categories.
This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predeterminedsecret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
An Introductory Course In Elementary Number Theory
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Author : Wissam Raji
language : en
Publisher: Lulu.com
Release Date : 2016-08-18
An Introductory Course In Elementary Number Theory written by Wissam Raji and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-18 with Education categories.
These notes serve as course notes for an undergraduate course in number theory. Most if not all universities worldwide offer introductory courses in numbertheory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be addressedin a course in number theory. Proofs of basic theorems are presented inan interesting and comprehensive way that can be read and understood even bynon-majors with the exception in the last three chapters where a background inanalysis, measure theory and abstract algebra is required. The exercises are carefullychosen to broaden the understanding of the concepts. Moreover, these notesshed light on analytic number theory, a subject that is rarely seen or approachedby undergraduate students. One of the unique characteristics of these notes is thecareful choice of topics and its importance in the theory of numbers. The freedomis given in the last two chapters because of the advanced nature of the topics thatare presented. Thanks to professor Pavel Guerzhoy from University of Hawaii for his contributionin chapter six on continued fraction and to Professor Ramez Maalouf fromNotre Dame University, Lebanon for his contribution to chapter eight.
Number Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 1986-05-05
Number Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-05-05 with Mathematics categories.
This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.
Elementary Theory Of Numbers
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Author : C Y Hsiung
language : en
Publisher: World Scientific Publishing Company
Release Date : 1992-10-20
Elementary Theory Of Numbers written by C Y Hsiung and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-20 with Mathematics categories.
This book explains clearly and in detail the basic concepts and methods of calculations of the elementary theory of numbers. It consists of 7 chapters illustrated by numerous examples and exercises. Answers together with some hints to the exercises are given at the end of the book. It may be used as a textbook for undergraduate students.