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Another Integer Algorithm To Solve Linear Equations Using Congruences
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Book Synopsis INTEGER ALGORITHMS TO SOLVE LINEAR EQUATIONS AND SYSTEMS by : Florentin Smarandache
Download or read book INTEGER ALGORITHMS TO SOLVE LINEAR EQUATIONS AND SYSTEMS written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two algorithms for solving Diophantine linear equations and five algorithms for solving Diophantine linear systems, together with many examples, are presented in this paper.
Book Synopsis Another Integer Algorithm To Solve Linear Equations (Using Congruences) by : FLORENTIN SMARANDACHE
Download or read book Another Integer Algorithm To Solve Linear Equations (Using Congruences) written by FLORENTIN SMARANDACHE and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this section is presented a new integer number algorithm for linear equation. This algorithm is more “rapid” than W. Sierpinski’s presented in [1] in the sense that it reaches the general solution after a smaller number of iterations. Its correctness will be thoroughly demonstrated.
Book Synopsis Discrete Mathematics by : Oscar Levin
Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2016-08-16 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.
Book Synopsis Elementary Number Theory: Primes, Congruences, and Secrets by : William Stein
Download or read book Elementary Number Theory: Primes, Congruences, and Secrets written by William Stein and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 predetermined secret; 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.
Book Synopsis Collected Papers. Volume I by : Florentin Smarandache
Download or read book Collected Papers. Volume I written by Florentin Smarandache and published by Infinite Study. This book was released on 2007-01-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles, notes, generalizations, paradoxes, miscellaneous in mathematics, linguistics, and education.
Book Synopsis Theory of Linear and Integer Programming by : Alexander Schrijver
Download or read book Theory of Linear and Integer Programming written by Alexander Schrijver and published by John Wiley & Sons. This book was released on 1998-06-11 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
Book Synopsis Methods of Solving Number Theory Problems by : Ellina Grigorieva
Download or read book Methods of Solving Number Theory Problems written by Ellina Grigorieva and published by Birkhäuser. This book was released on 2018-07-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the representations 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.
Book Synopsis Advanced Topics in Computational Number Theory by : Henri Cohen
Download or read book Advanced Topics in Computational Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2012-10-29 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Book Synopsis The Mathematics of Ciphers by : S.C. Coutinho
Download or read book The Mathematics of Ciphers written by S.C. Coutinho and published by CRC Press. This book was released on 1999-01-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes many interesting historical notes.
Book Synopsis Elementary Number Theory by : Charles Vanden Eynden
Download or read book Elementary Number Theory written by Charles Vanden Eynden and published by Waveland Press. This book was released on 2006-02-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book EPIA'91 written by Pedro Barahona and published by Springer Science & Business Media. This book was released on 1991-09-23 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Portuguese Association for Artificial Intelligence has been organizing Portuguese Conferences on Artificial Intelligence, now held every second year, since 1985. This volume contains selected papers from the Fifth Conference on Artificial Intelligence. The conference has an international status: 62 contributions from 13 countries were received, of which 26 were from Portugal. To guarantee a high scientific standard, all the contributions were reviewed by at least three researchers,and only 20 papers were accepted and included in these proceedings. The papers are organized into sections on constraints, search, knowledge representation, temporal reasoning, planning, diagnosis and repair, and learning.
Book Synopsis Integers, Fractions, and Arithmetic by : Judith D. Sally
Download or read book Integers, Fractions, and Arithmetic written by Judith D. Sally and published by American Mathematical Soc.. This book was released on 2012 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and the Mathematical Sciences Research Institute. This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K–8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals because of their importance in the classroom curriculum. The standard topics are covered in detail, but are arranged in an order that is slightly different from the usual one. Multiplication is treated first, and with that in hand, common denominators and equivalent fractions are more readily understood and are available for use when discussing addition. The book is intended for the professional development of teachers. It is appropriate for teacher education programs as well as for enrichment programs such as Mathematical Circles for Teachers. There are numerous activities in each seminar that teachers can bring into their classrooms. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.--Publisher website.
Book Synopsis An Elementary Transition to Abstract Mathematics by : Gove Effinger
Download or read book An Elementary Transition to Abstract Mathematics written by Gove Effinger and published by CRC Press. This book was released on 2019-11-05 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role. The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials. Features: The material is presented in many short chapters, so that one concept at a time can be absorbed by the student. Two "looking back" chapters at the outset (pre-calculus and calculus) are designed to start the student’s transition by working with familiar concepts. Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns. A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.
Book Synopsis Algorithms and Theory of Computation Handbook by : Mikhail J. Atallah
Download or read book Algorithms and Theory of Computation Handbook written by Mikhail J. Atallah and published by CRC Press. This book was released on 1998-11-23 with total page 1328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
Book Synopsis Quadratic Number Theory by : J. L. Lehman
Download or read book Quadratic Number Theory written by J. L. Lehman and published by American Mathematical Soc.. This book was released on 2019-02-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured—the author's notation makes these computations particularly illuminating. Quadratic Number Theory, with its exceptionally clear prose, hundreds of exercises, and historical motivation, would make an excellent textbook for a second undergraduate course in number theory. The clarity of the exposition would also make it a terrific choice for independent reading. It will be exceptionally useful as a fruitful launching pad for undergraduate research projects in algebraic number theory.
Book Synopsis Discrete Maths and Its Applications Global Edition 7e by : Kenneth Rosen
Download or read book Discrete Maths and Its Applications Global Edition 7e written by Kenneth Rosen and published by McGraw Hill. This book was released on 2012-09-16 with total page 972 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are pleased to present this Global Edition which has been developed specifically to meet the needs of international students of discrete mathematics. In addition to great depth in key areas and a broad range of real-world applications across multiple disciplines, we have added new material to make the content more relevant and improve learning outcomes for the international student.This Global Edition includes: An entire new chapter on Algebraic Structures and Coding Theory New and expanded sections within chapters covering Foundations, Basic Structures, and Advanced Counting Techniques Special online only chapters on Boolean Algebra and Modeling Computation New and revised problems for the international student integrating alternative methods and solutions.This Global Edition has been adapted to meet the needs of courses outside of the United States and does not align with the instructor and student resources available with the US edition.
Book Synopsis Algorithms and Computations by : Alok Aggarwal
Download or read book Algorithms and Computations written by Alok Aggarwal and published by Springer. This book was released on 2003-06-26 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Symposium on Algorithms and Computation, ISAAC'99, held in Chennai, India, in December 1999. The 40 revised full papers presented together with four invited contributions were carefully reviewed and selected from 71 submissions. Among the topics covered are data structures, parallel and distributed computing, approximation algorithms, computational intelligence, online algorithms, complexity theory, graph algorithms, computational geometry, and algorithms in practice.
