Methods Used to Solve discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of discretemathematics presents methods for solving counting problems and other types of pr...
ISBN:
(纸本)9781138435865
Methods Used to Solve discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of discretemathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascals triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuins sequence, and Rook and Queen paths and the equivalent Nim and Wythoffs Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannons theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discretemathematics.
A Students Guide to the Study, Practice, and Tools of Modern mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use vari...
ISBN:
(纸本)1439846065;9781439846063
A Students Guide to the Study, Practice, and Tools of Modern mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica and Maple to MATLAB and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities. The first section of the book covers issues pertaining to studying mathematics. The authors explain how to write mathematical proofs and papers, how to perform mathematical research, and how to give mathematical presentations. The second section focuses on the use of mathematical tools for mathematical typesetting, generating data, finding patterns, and much more. The text describes how to compose a LaTeX file, give a presentation using Beamer, create mathematical diagrams, use computer algebra systems, and display ideas on a web page. The authors cover both popular commercial software programs and free and open source software, such as Linux and R. Showing how to use technology to understand mathematics, this guide supports students on their way to becoming professional mathematicians. For beginning mathematics students, it helps them study for tests and write papers. As time progresses, the book aids them in performing advanced activities, such as computer programming, typesetting, and research.
This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discretemathematics, engineering and theoreti...
详细信息
ISBN:
(数字)9781482299816
ISBN:
(纸本)9781482299809;9781315371993
This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discretemathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.
Methods Used to Solve discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this area Pearls of discretemathematics presents methods for solving counting problems and other types of pro...
详细信息
ISBN:
(数字)9781439816172
ISBN:
(纸本)1439816166
Methods Used to Solve discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this area Pearls of discretemathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascals triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuins sequence, and Rook and Queen paths and the equivalent Nim and Wythoffs Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannons theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discretemathematics.
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Writte...
详细信息
ISBN:
(纸本)1420083287
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data. With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermats Last Theorem (FLT) and numerous consequences of the ABC conjecture, including ThueSiegelRoth theorem, Halls conjecture, the ErdsMollin-Walsh conjecture, and the GranvilleLangevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes, Selbergs, Linniks, and Bombieris sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring. By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.
暂无评论