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| elementary number theory underwood dudley: Elementary Number Theory Underwood Dudley, 2012-06-04 Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition. |
| elementary number theory underwood dudley: A Guide to Elementary Number Theory Underwood Dudley, 2009-12-31 An introductory guide to elementary number theory for advanced undergraduates and graduates. |
| elementary number theory underwood dudley: Elementary Number Theory Gareth A. Jones, Josephine M. Jones, 2012-12-06 An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles. |
| elementary number theory underwood dudley: Elementary Number Theory in Nine Chapters James J. Tattersall, 1999-10-14 This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject. |
| elementary number theory underwood dudley: Elementary Number Theory Underwood Dudley, 1978 With almost a thousand imaginative exercises and problems, this book stimulates curiosity about numbers and their properties. |
| elementary number theory underwood dudley: Number Theory George E. Andrews, 2012-04-30 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. |
| elementary number theory underwood dudley: Excursions in Number Theory Charles Stanley Ogilvy, John Timothy Anderson, 1988-01-01 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. |
| elementary number theory underwood dudley: A Course in Number Theory and Cryptography Neal Koblitz, 2012-09-05 . . . both Gauss and lesser mathematicians may be justified in rejoic ing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. - G. H. Hardy, A Mathematician's Apology, 1940 G. H. Hardy would have been surprised and probably displeased with the increasing interest in number theory for application to ordinary human activities such as information transmission (error-correcting codes) and cryptography (secret codes). Less than a half-century after Hardy wrote the words quoted above, it is no longer inconceivable (though it hasn't happened yet) that the N. S. A. (the agency for U. S. government work on cryptography) will demand prior review and clearance before publication of theoretical research papers on certain types of number theory. In part it is the dramatic increase in computer power and sophistica tion that has influenced some of the questions being studied by number theorists, giving rise to a new branch of the subject, called computational number theory. This book presumes almost no background in algebra or number the ory. Its purpose is to introduce the reader to arithmetic topics, both ancient and very modern, which have been at the center of interest in applications, especially in cryptography. For this reason we take an algorithmic approach, emphasizing estimates of the efficiency of the techniques that arise from the theory. |
| elementary number theory underwood dudley: 17 Lectures on Fermat Numbers Michal Krizek, Florian Luca, Lawrence Somer, 2013-03-14 French mathematician Pierre de Fermat became most well known for his pioneering work in the area of number theory. His work with numbers has been attracting the attention of amateur and professional mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth and is based on a series of lectures given by the authors. The purpose of this book is to provide readers with an overview of the many properties of Fermat numbers and to demonstrate their numerous appearances and applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers and will provide invaluable reading for the amateur and professional alike. |
| elementary number theory underwood dudley: Mathematical Cranks Underwood Dudley, 2019-07-11 A delightful collection of articles about people who claim they have achieved the mathematically impossible (squaring the circle, duplicating the cube); people who think they have done something they have not (proving Fermat's Last Theorem); people who pray in matrices; people who find the American Revolution ruled by the number 57; people who have in common eccentric mathematical views, some mild (thinking we should count by 12s instead of 10s), some bizarre (thinking that second-order differential equations will solve all problems of economics, politics and philosophy). This is a truly uniqu. |
| elementary number theory underwood dudley: Beginning Number Theory Neville Robbins, 2006 Thoroughly Revised And Updated, The New Second Edition Of Neville Robbins' Beginning Number Theory Includes All Of The Major Topics Covered In A Classic Number Theory Course And Blends In Numerous Applications And Specialized Treatments Of Number Theory, Including Cryptology, Fibonacci Numbers, And Computational Number Theory. The Text Strikes A Balance Between Traditional And Algorithmic Approaches To Elementary Number Theory And Is Supported With Numerous Exercises, Applications, And Case Studies Throughout. Computer Exercises For CAS Systems Are Also Included. |
| elementary number theory underwood dudley: Elementary Theory of Analytic Functions of One or Several Complex Variables Henri Cartan, 2013-04-22 Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition. |
| elementary number theory underwood dudley: Number Theory Kuldeep Singh, 2020 Number Theory: Step by Step is an undergraduate-level introduction to number theory that assumes no prior knowledge, but works to gradually increase the reader's confidence and ability to tackle more difficult number theory material. |
| elementary number theory underwood dudley: Discrete Mathematics and Its Applications Kenneth Rosen, 2006-07-26 Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields. |
| elementary number theory underwood dudley: A Friendly Introduction to Number Theory Joseph H. Silverman, 2013-10-03 For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results. |
| elementary number theory underwood dudley: Topics In Number Theory Minking Eie, 2008-12-22 This is a first-ever textbook written in English about the theory of modular forms and Jacobi forms of several variables. It contains the classical theory as well as a new theory on Jacobi forms over Cayley numbers developed by the author from 1990 to 2000. Applications to the classical Euler sums are of special interest to those who are eager to evaluate double Euler sums or more general multiple zeta values. The celebrated sum formula proved by Granville in 1997 is given in a more general form here. |
| elementary number theory underwood dudley: Student's Solutions Manual Elementary Number Theory David Burton, 2010-01-29 |
| elementary number theory underwood dudley: Problem Solving Through Recreational Mathematics Bonnie Averbach, Orin Chein, 2012-03-15 Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website. |
| elementary number theory underwood dudley: Elementary Number Theory Underwood Dudley, 2008-09-25 Minimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher's guide is available. 1978 edition. |
| elementary number theory underwood dudley: A Guide to Elementary Number Theory Underwood Dudley, 2009 A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through a traditional text, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for the qualifying exams. Though Plato did not quite say, He is unworthy of the name of man who does not know which integers are the sums of two squares. he came close. This guide can make everyone more worthy. |
| elementary number theory underwood dudley: Numerology, Or, What Pythagoras Wrought Underwood Dudley, 1997 Numerology is about numerology, which is the delusion that numbers have power over events. ... The message of the book is that numbers indeed have power, but the power is not over events, it is over the human minds. It is intended for anyone interested in human folly and requires no mathematical knowledge beyond arithmetic to understand.--Cover |
| elementary number theory underwood dudley: The Theory of Functions of Real Variables Lawrence M. Graves, 2013-09 |
| elementary number theory underwood dudley: An Illustrated Theory of Numbers Martin H. Weissman, 2017 Seeing arithmetic -- Foundations -- The Euclidean algorithm -- Prime factorization -- Rational and constructible numbers -- Gaussian and Eisenstein integers -- Modular arithmetic -- The modular worlds -- Modular dynamics -- Assembling the modular worlds -- Quadratic residues -- Quadratic forms -- The topograph -- Definite forms -- Indefinite forms |
| elementary number theory underwood dudley: Lure of the Integers Joe Roberts, 1992 This book describes many interesting and unusual properties of integers. |
| elementary number theory underwood dudley: Mathematics of Choice Ivan Niven, 1965 |
| elementary number theory underwood dudley: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition. |
| elementary number theory underwood dudley: The Trisectors Underwood Dudley, 2019-07-01 Underwood Dudley is well known for his collection of books on mathematical cranks. Here he offers yet another--angle trisectors. It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. According to Dudley: Hardly any mathematical training is necessary to read this book. There is a little trigonometry here and there, but it may be safely skipped. There are hardly any equations. There are no exercises and there will be no final examination. The worst victim o. |
| elementary number theory underwood dudley: Introduction to Graph Theory Richard J. Trudeau, 2013-04-15 Aimed at the mathematically traumatized, this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition. |
| elementary number theory underwood dudley: Elementary Number Theory and Its Applications Kenneth H. Rosen, 2005 Elementary Number Theory and Its Applications is noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years. |
| elementary number theory underwood dudley: Abstract Algebra Thomas W. Hungerford, 1997 |
| elementary number theory underwood dudley: Elementary Symbolic Logic William Gustason, Dolph E. Ulrich, 1989-01-01 This volume offers a serious study of the fundamentals of symbolic logic that will neither frustrate nor bore the reader. The emphasis is on developing the students grasp of standard techniques and concepts rather than on achieving a high degree of sophistication. Coverage embraces all of the standard topics in sentential and quantificational logic, including multiple quantification, relations, and identity. Semantic and deductive topics are carefully distinguished, and appendices include an optional discussion of metatheory for sentential logic and truth trees. |
| elementary number theory underwood dudley: Chaos Kathleen T. Alligood, Tim D. Sauer, James A. Yorke, 2006-04-06 Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise. |
| elementary number theory underwood dudley: Common Sense Mathematics: Second Edition Ethan D. Bolker, Maura B. Mast, 2021-01-21 Ten years from now, what do you want or expect your students to remember from your course? We realized that in ten years what matters will be how students approach a problem using the tools they carry with them—common sense and common knowledge—not the particular mathematics we chose for the curriculum. Using our text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans. We use search engines, calculators, and spreadsheet programs as tools to reduce drudgery, explore patterns, and get information. Technology is an integral part of today's world—this text helps students use it thoughtfully and wisely. This second edition contains revised chapters and additional sections, updated examples and exercises, and complete rewrites of critical material based on feedback from students and teachers who have used this text. Our focus remains the same: to help students to think carefully—and critically—about numerical information in everyday contexts. |
| elementary number theory underwood dudley: Elementary Introduction to Number Theory Calvin T. Long, 1965 |
| elementary number theory underwood dudley: A First Course In Theory Of Numbers K. C. Chowdhury, 2007-07-01 Contents: Number System; Congruencies And Its Basic Properties; Algebraic Congruences And Primitive Roots; Arithmetic Functions; Farey Sequence, Continued Fraction, Pell S Equations; Quadratic Residues, Levender S Symbols, Jacobi S Symbols; Homogeneous Quadratic Diophantine Equation; Some Number Theoretic Problems Related To Mathematics Olympiads; Answers; Etc. |
| elementary number theory underwood dudley: Elementary Number Theory James K. Strayer, 2001-12-04 In this student-friendly text, Strayer presents all of the topics necessary for a first course in number theory. Additionally, chapters on primitive roots, Diophantine equations, and continued fractions allow instructors the flexibility to tailor the material to meet their own classroom needs. Each chapter concludes with seven Student Projects, one of which always involves programming a calculator or computer. All of the projects not only engage students in solving number-theoretical problems but also help familiarize them with the relevant mathematical literature. |
| elementary number theory underwood dudley: Mathematical Time Capsules Dick Jardine, Amy Shell-Gellasch, 2011-06-16 Mathematical Time Capsules offers teachers historical modules for immediate use in the mathematics classroom. Relevant history-based activities for a wide range of undergraduate and secondary mathematics courses are included. Readers will find articles and activities from mathematics history that enhance the learning of topics typically associated with undergraduate or secondary mathematics curricula. Each capsule presents one topic, or perhaps a few related topics, or a historical thread that can be used throughout a course. The capsules were written by experienced practitioners to provide other teachers with the historical background, suggested classroom activities and further references and resources on the subject addressed. After reading a capsule, a teacher will have increased confidence in engaging students with at least one activity rich in the history of mathematics that will enhance student learning of the mathematical content of the course. |
| elementary number theory underwood dudley: Understanding Analysis Stephen Abbott, 2012-12-06 Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its Taylor series? In giving these topics center stage, the hard work of a rigorous study is justified by the fact that they are inaccessible without it. |
| elementary number theory underwood dudley: A Classical Introduction to Modern Number Theory Kenneth Ireland, Michael Rosen, 2013-04-17 This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves. |
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