pearls of discrete mathematics discrete mathematics and its applications

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Pearls Of Discrete Mathematics

Author : Martin Erickson
ISBN : 9781439816172
Genre : Computers
File Size : 23. 84 MB
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Methods Used to Solve Discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics 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 Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s 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 discrete mathematics.

Discrete Structures And Their Interactions

Author : Jason I. Brown
ISBN : 9781466579422
Genre : Computers
File Size : 30. 27 MB
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Discover the Connections between Different Structures and Fields Discrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics, such as linear and multilinear algebra, analysis, probability, logic, and topology. The text introduces a number of discrete structures, such as hypergraphs, finite topologies, preorders, simplicial complexes, and order ideals of monomials, that most graduate students in combinatorics, and even some researchers in the field, seldom experience. The author explains how these structures have important applications in many areas inside and outside of combinatorics. He also discusses how to recognize valuable research connections through the structures. Intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory, this book shows how discrete structures offer new insights into the classical fields of mathematics. It illustrates how to use discrete structures to represent the salient features and discover the underlying combinatorial principles of seemingly unrelated areas of mathematics.

Proceedings Of The Fifth Annual Acm Siam Symposium On Discrete Algorithms

Author :
ISBN : 0898713293
Genre : Science
File Size : 86. 37 MB
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The January 1994 Symposium was jointly sponsored by the ACM Special Interest Group for Automata and Computability Theory and the SIAM Activity Group on Discrete Mathematics. Among the topics in 79 (unrefereed) papers: comparing point sets under projection; on-line search in a simple polygon; low- degree tests; maximal empty ellipsoids; roots of a polynomial and its derivatives; dynamic algebraic algorithms; fast comparison of evolutionary trees; an efficient algorithm for dynamic text editing; and tight bounds for dynamic storage allocation. No index. Annotation copyright by Book News, Inc., Portland, OR

Probabilistic Methods For Algorithmic Discrete Mathematics

Author : Michel Habib
ISBN : 9783662127889
Genre : Mathematics
File Size : 46. 93 MB
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Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

A Student S Guide To The Study Practice And Tools Of Modern Mathematics

Author : Donald Bindner
ISBN : 9781439846070
Genre : Mathematics
File Size : 24. 75 MB
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A Student’s 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 MapleTM 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.

Boolesche Algebra Und Ihre Anwendungen

Author : John Eldon Whitesitt
ISBN : 9783322894403
Genre : Mathematics
File Size : 46. 35 MB
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Discrete Mathematics

Author : Richard Johnsonbaugh
ISBN : 9780131593183
Genre : Mathematics
File Size : 49. 60 MB
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Focused on helping readers understand and construct proofs – and, generally, expanding their mathematical maturity – this best-seller is an accessible introduction to discrete mathematics. Takes an algorithmic approach that emphasizes problem-solving techniques. Expands discussion on how to construct proofs and treatment of problem solving. Increases number of examples and exercises throughout.

Moderne Algebra

Author : Bartel Eckmann L. Van der van der Waerden
ISBN : 9783662364345
Genre : Mathematics
File Size : 89. 9 MB
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Library Recommendations For Undergraduate Mathematics

Author : Lynn Arthur Steen
ISBN : UOM:39015057374137
Genre : Mathematics
File Size : 89. 68 MB
Format : PDF
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Logik Ritter Und Andere Schurken

Author : Raymond M. Smullyan
ISBN : 3596103495
Genre :
File Size : 53. 52 MB
Format : PDF
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