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Algorithmic Mathematics

Author: Stefan Hougardy

Publisher: Springer

Published: 2016-10-14

Total Pages: 163

ISBN-13: 3319395580

Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

Mathematics for Algorithm and Systems Analysis

Author: Edward A. Bender

Publisher: Courier Corporation

Published: 2005-01-01

Total Pages: 258

ISBN-13: 0486442500

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Discrete mathematics is fundamental to computer science, and this up-to-date text assists undergraduates in mastering the ideas and mathematical language to address problems that arise in the field's many applications. It consists of 4 units of study: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory.

Discrete Algorithmic Mathematics, Third Edition

Author: Stephen B. Maurer

Publisher: CRC Press

Published: 2005-01-21

Total Pages: 805

ISBN-13: 1568811667

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Thoroughly revised for a one-semester course, this well-known and highly regarded book is an outstanding text for undergraduate discrete mathematics. It has been updated with new or extended discussions of order notation, generating functions, chaos, aspects of statistics, and computational biology. Written in a lively, clear style that talks to the reader, the book is unique for its emphasis on algorithmics and the inductive and recursive paradigms as central mathematical themes. It includes a broad variety of applications, not just to mathematics and computer science, but to natural and social science as well. A manual of selected solutions is available for sale to students; see sidebar. A complete solution manual is available free to instructors who have adopted the book as a required text.

Probabilistic Methods for Algorithmic Discrete Mathematics

Author: Michel Habib

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 342

ISBN-13: 3662127881

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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.

Algorithmic Principles of Mathematical Programming

Author: Ulrich Faigle

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 343

ISBN-13: 9401598967

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Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.

Algorithmic Information Theory

Author: Peter Seibt

Publisher: Springer Science & Business Media

Published: 2007-02-15

Total Pages: 446

ISBN-13: 3540332197

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Algorithmic Information Theory treats the mathematics of many important areas in digital information processing. It has been written as a read-and-learn book on concrete mathematics, for teachers, students and practitioners in electronic engineering, computer science and mathematics. The presentation is dense, and the examples and exercises are numerous. It is based on lectures on information technology (Data Compaction, Cryptography, Polynomial Coding) for engineers.

Discrete Algorithmic Mathematics, Second Edition

Author: Stephen B. Maurer

Publisher: A K Peters/CRC Press

Published: 1998

Total Pages: 926

ISBN-13:

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What is discrete algorithmic mathematics. Mathematical preliminaries. Algorithms. Mathematical induction. Graphs and trees. Fundamental counting methods. Difference equations. Probability. An introduction to mathematical logic. Algorithmic linear algebra. Infinite processes in discrete mathematics. Sorting things out with sorting.

Algorithmic Graph Theory and Perfect Graphs

Author: Martin Charles Golumbic

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 307

ISBN-13: 1483271978

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Algorithmic Graph Theory and Perfect Graphs provides an introduction to graph theory through practical problems. This book presents the mathematical and algorithmic properties of special classes of perfect graphs. Organized into 12 chapters, this book begins with an overview of the graph theoretic notions and the algorithmic design. This text then examines the complexity analysis of computer algorithm and explains the differences between computability and computational complexity. Other chapters consider the parameters and properties of a perfect graph and explore the class of perfect graphs known as comparability graph or transitively orientable graphs. This book discusses as well the two characterizations of triangulated graphs, one algorithmic and the other graph theoretic. The final chapter deals with the method of performing Gaussian elimination on a sparse matrix wherein an arbitrary choice of pivots may result in the filling of some zero positions with nonzeros. This book is a valuable resource for mathematicians and computer scientists.

Mathematical and Algorithmic Foundations of the Internet

Author: Fabrizio Luccio

Publisher: CRC Press

Published: 2011-07-06

Total Pages: 224

ISBN-13: 1439831386

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To truly understand how the Internet and Web are organized and function requires knowledge of mathematics and computation theory. Mathematical and Algorithmic Foundations of the Internet introduces the concepts and methods upon which computer networks rely and explores their applications to the Internet and Web. The book offers a unique approach to mathematical and algorithmic concepts, demonstrating their universality by presenting ideas and examples from various fields, including literature, history, and art. Progressing from fundamental concepts to more specific topics and applications, the text covers computational complexity and randomness, networks and graphs, parallel and distributed computing, and search engines. While the mathematical treatment is rigorous, it is presented at a level that can be grasped by readers with an elementary mathematical background. The authors also present a lighter side to this complex subject by illustrating how many of the mathematical concepts have counterparts in everyday life. The book provides in-depth coverage of the mathematical prerequisites and assembles a complete presentation of how computer networks function. It is a useful resource for anyone interested in the inner functioning, design, and organization of the Internet.

Discrete Algorithmic Mathematics

Author: Stephen B. Maurer

Publisher: CRC Press

Published: 2005-01-21

Total Pages: 793

ISBN-13: 143986375X

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Thoroughly revised for a one-semester course, this well-known and highly regarded book is an outstanding text for undergraduate discrete mathematics. It has been updated with new or extended discussions of order notation, generating functions, chaos, aspects of statistics, and computational biology. Written in a lively, clear style, the book is unique in its emphasis on algorithmics and the inductive and recursive paradigms as central mathematical themes. It includes a broad variety of applications, not just to mathematics and computer science, but to natural and social science as well.