Combinatorics Modeling Elementary Number Theory From Basic To Advanced

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Combinatorics, Modeling, Elementary Number Theory

Ivan Cherednik
Combinatorics Modeling Elementary Number Theory Book PDF

Author : Ivan Cherednik
Publisher : Unknown
Page : 0 pages
File Size : 43,7 Mb
Release : 2023
Category : Combinatorial analysis
ISBN : 9811265402

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Combinatorics, Modeling, Elementary Number Theory by Ivan Cherednik Pdf

"A unique textbook devoted to introductory combinatorics, modeling and elementary number theory It is relatively simple to use in the classroom: 1 Chapter is designed for 2 weeks, and the notes can be provided designed for remote teaching or to display in the classroom Some of the advanced topics are good for research projects; the most popular ones in the author's classes were dimers, modeling tree growth, Magic squares and Pisano periods via finite fields Elementary number theory is exposed systematically (with complete proofs and good ones) An impressive collection of about 135 problems and 270 exercises (mostly with hints and answers) It contains a lot of history of mathematics and the games of chance, and many topics traditional in recreational mathematics The book also serves motivated high-school students, teachers of mathematics, and specialists in neighboring fields interested in combinatorics and its applications"--

Combinatorics, Modeling, Elementary Number Theory

Ivan Cherednik
Combinatorics Modeling Elementary Number Theory Book PDF

Author : Ivan Cherednik
Publisher : World Scientific Publishing Company
Page : 0 pages
File Size : 41,6 Mb
Release : 2023
Category : Combinatorial analysis
ISBN : 9811265399

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Combinatorics, Modeling, Elementary Number Theory by Ivan Cherednik Pdf

"A unique textbook devoted to introductory combinatorics, modeling and elementary number theory It is relatively simple to use in the classroom: 1 Chapter is designed for 2 weeks, and the notes can be provided designed for remote teaching or to display in the classroom Some of the advanced topics are good for research projects; the most popular ones in the author's classes were dimers, modeling tree growth, Magic squares and Pisano periods via finite fields Elementary number theory is exposed systematically (with complete proofs and good ones) An impressive collection of about 135 problems and 270 exercises (mostly with hints and answers) It contains a lot of history of mathematics and the games of chance, and many topics traditional in recreational mathematics The book also serves motivated high-school students, teachers of mathematics, and specialists in neighboring fields interested in combinatorics and its applications"--

Combinatorics, Modeling, Elementary Number Theory: From Basic To Advanced

Ivan V Cherednik
Combinatorics Modeling Elementary Number Theory From Basic To Advanced Book PDF

Author : Ivan V Cherednik
Publisher : World Scientific
Page : 392 pages
File Size : 42,9 Mb
Release : 2023-05-03
Category : Mathematics
ISBN : 9789811265419

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Combinatorics, Modeling, Elementary Number Theory: From Basic To Advanced by Ivan V Cherednik Pdf

This book is mostly based on the author's 25 years of teaching combinatorics to two distinct sets of students: first-year students and seniors from all backgrounds, not just limited to only those majoring in mathematics and physics. The prerequisites are kept to a minimum; essentially, only high school algebra is required. The design is to go from zero knowledge to advanced themes and various applications during a semester of three or three and a half months with quite a few topics intended for research projects and additional reading.This unique book features the key themes of classical introductory combinatorics, modeling (mainly linear), and elementary number theory with a constant focus on applications in statistics, physics, biology, economics, and computer science. These applications include dimers, random walks, binomial and Poisson distributions, games of chance (lottery, dice, poker, roulette), pricing options, population growth, tree growth, modeling epidemic spread, invasion ecology, fission reactors, and networks.A lot of material is provided in the form of relatively self-contained problems, about 135, and exercises, about 270, which are almost always with hints and answers. A systematic introduction to number theory (with complete justifications) is a significant part of the book, including finite fields, Pell's equations, continued fractions, quadratic reciprocity, the Frobenius coin problem, Pisano periods, applications to magic and Latin squares and elements of cryptography. The recurrence relations and modeling play a very significant role, including the usage of Bessel functions for motivated readers. The book contains a lot of history of mathematics and recreational mathematics.

Elementary Number Theory

James S. Kraft,Lawrence C. Washington
Elementary Number Theory Book PDF

Author : James S. Kraft,Lawrence C. Washington
Publisher : CRC Press
Page : 407 pages
File Size : 52,6 Mb
Release : 2014-11-24
Category : Mathematics
ISBN : 9781498702690

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Elementary Number Theory by James S. Kraft,Lawrence C. Washington Pdf

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the tex

Elementary Number Theory with Programming

Marty Lewinter,Jeanine Meyer
Elementary Number Theory with Programming Book PDF

Author : Marty Lewinter,Jeanine Meyer
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 41,7 Mb
Release : 2015-06-02
Category : Mathematics
ISBN : 9781119062769

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Elementary Number Theory with Programming by Marty Lewinter,Jeanine Meyer Pdf

A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area. Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes: Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor’s Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.

A Guide to Elementary Number Theory

Underwood Dudley
A Guide to Elementary Number Theory Book PDF

Author : Underwood Dudley
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 45,9 Mb
Release : 2009-12-31
Category : Mathematics
ISBN : 9780883859186

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A Guide to Elementary Number Theory by Underwood Dudley Pdf

An introductory guide to elementary number theory for advanced undergraduates and graduates.

Combinatorial Number Theory and Additive Group Theory

Alfred Geroldinger,Imre Ruzsa
Combinatorial Number Theory and Additive Group Theory Book PDF

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 51,9 Mb
Release : 2009-04-15
Category : Mathematics
ISBN : 9783764389611

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Combinatorial Number Theory and Additive Group Theory by Alfred Geroldinger,Imre Ruzsa Pdf

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Number Theory

George E. Andrews
Number Theory Book PDF

Author : George E. Andrews
Publisher : Courier Corporation
Page : 292 pages
File Size : 48,7 Mb
Release : 1994-10-12
Category : Mathematics
ISBN : 9780486682525

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Number Theory by George E. Andrews Pdf

Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Advanced Number Theory

Harvey Cohn
Advanced Number Theory Book PDF

Author : Harvey Cohn
Publisher : Courier Corporation
Page : 292 pages
File Size : 52,8 Mb
Release : 1980-08-01
Category : Mathematics
ISBN : 048664023X

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Advanced Number Theory by Harvey Cohn Pdf

"A very stimulating book ... in a class by itself." — American Mathematical Monthly Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject. The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups. Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints. In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.

Elementary Number Theory

Gove Effinger,Gary L. Mullen
Elementary Number Theory Book PDF

Author : Gove Effinger,Gary L. Mullen
Publisher : CRC Press
Page : 254 pages
File Size : 48,9 Mb
Release : 2021-09-08
Category : Mathematics
ISBN : 9781000427110

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Elementary Number Theory by Gove Effinger,Gary L. Mullen Pdf

Elementary Number Theory, Gove Effinger, Gary L. Mullen This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject. Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter. The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular.

Elementary Number Theory

Charles Vanden Eynden
Elementary Number Theory Book PDF

Author : Charles Vanden Eynden
Publisher : Waveland Press
Page : 278 pages
File Size : 47,9 Mb
Release : 2006-02-15
Category : Electronic
ISBN : 9781478639152

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Elementary Number Theory by Charles Vanden Eynden Pdf

This practical and versatile text evolved from the author’s years of teaching experience and the input of his students. Vanden Eynden strives to alleviate the anxiety that many students experience when approaching any proof-oriented area of mathematics, including number theory. His informal yet straightforward writing style explains the ideas behind the process of proof construction, showing that mathematicians develop theorems and proofs from trial and error and evolutionary improvement, not spontaneous insight. Furthermore, the book includes more computational problems than most other number theory texts to build students’ familiarity and confidence with the theory behind the material. The author has devised the content, organization, and writing style so that information is accessible, students can gain self-confidence with respect to mathematics, and the book can be used in a wide range of courses—from those that emphasize history and type A problems to those that are proof oriented.

Fundamental Number Theory with Applications

Richard A. Mollin
Fundamental Number Theory with Applications Book PDF

Author : Richard A. Mollin
Publisher : CRC Press
Page : 382 pages
File Size : 53,6 Mb
Release : 2008-02-21
Category : Mathematics
ISBN : 9781420066616

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Fundamental Number Theory with Applications by Richard A. Mollin Pdf

An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.

Analytic and Elementary Number Theory

Krishnaswami Alladi,P.D.T.A. Elliott,Andrew Granville,G. Tenenbaum
Analytic and Elementary Number Theory Book PDF

Author : Krishnaswami Alladi,P.D.T.A. Elliott,Andrew Granville,G. Tenenbaum
Publisher : Springer
Page : 289 pages
File Size : 45,6 Mb
Release : 2013-12-21
Category : Mathematics
ISBN : 9781475745078

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Analytic and Elementary Number Theory by Krishnaswami Alladi,P.D.T.A. Elliott,Andrew Granville,G. Tenenbaum Pdf

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.

Elementary Number Theory

Gareth A. Jones,Josephine M. Jones
Elementary Number Theory Book PDF

Author : Gareth A. Jones,Josephine M. Jones
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 45,6 Mb
Release : 1998-07-31
Category : Mathematics
ISBN : 3540761977

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Elementary Number Theory by Gareth A. Jones,Josephine M. Jones Pdf

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 Book PDF

Author : Underwood Dudley
Publisher : Courier Corporation
Page : 274 pages
File Size : 50,7 Mb
Release : 2012-06-04
Category : Mathematics
ISBN : 9780486134871

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Elementary Number Theory by Underwood Dudley Pdf

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.