Concrete Mathematics

A Foundation for Computer Science

Author: Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik

Publisher: Addison-Wesley Professional

ISBN: 9780201558029

Category: Computers

Page: 657

View: 9776

This book, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every discipline.

Concrete mathematics

a foundation for computer science

Author: Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik

Publisher: Addison Wesley Publishing Company


Category: Mathematics

Page: 625

View: 1654

Companion to Concrete Mathematics

Author: Z. A. Melzak

Publisher: Courier Corporation

ISBN: 0486457818

Category: Mathematics

Page: 683

View: 1643

A two-volume treatment in a single binding, this supplementary text stresses intuitive appeal and ingenuity. It employs physical analogies, encourages problem formulation, and supplies problem-solving methods. 1973 and 1976 editions.

A Concrete Approach to Classical Analysis

Author: Marian Muresan

Publisher: Springer Science & Business Media

ISBN: 0387789332

Category: Mathematics

Page: 433

View: 1259

Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.

Mathematics for the Analysis of Algorithms

Author: Daniel H. Greene,Donald E. Knuth

Publisher: Springer Science & Business Media

ISBN: 0817647295

Category: Computers

Page: 132

View: 4681

This monograph collects some fundamental mathematical techniques that are required for the analysis of algorithms. It builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions. The authors cover recurrence relations, operator methods, and asymptotic analysis in a format that is concise enough for easy reference yet detailed enough for those with little background with the material.

A Concrete Introduction to Higher Algebra

Author: Lindsay N. Childs

Publisher: Springer Science & Business Media

ISBN: 0387745270

Category: Mathematics

Page: 604

View: 5541

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.

Abstract and Concrete Categories

The Joy of Cats

Author: Jiri Adamek,Jiří Adámek (ing.),Horst Herrlich,George E. Strecker

Publisher: N.A

ISBN: 9780486469348

Category: Mathematics

Page: 517

View: 4887

This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases. A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

Statistical Mechanics of Lattice Systems

A Concrete Mathematical Introduction

Author: Sacha Friedli,Yvan Velenik

Publisher: Cambridge University Press

ISBN: 1107184827

Category: Mathematics

Page: 628

View: 6032

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

The Concrete Tetrahedron

Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates

Author: Manuel Kauers,Peter Paule

Publisher: Springer Science & Business Media

ISBN: 9783709104453

Category: Mathematics

Page: 203

View: 9934

The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates. Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.

Mathematical Writing

Author: Donald E. Knuth,Tracy Larrabee,Paul M. Roberts

Publisher: Cambridge University Press

ISBN: 9780883850633

Category: Mathematics

Page: 115

View: 1806

This book will help those wishing to teach a course in technical writing, or who wish to write themselves.

Introduction to Matrix Theory

With Applications to Business and Economics

Author: Ferenc Szidarovszky,S ndor Moln r

Publisher: World Scientific

ISBN: 9789810245139

Category: Business & Economics

Page: 501

View: 9180

In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.

Algorithmic Information Theory

Mathematics of Digital Information Processing

Author: Peter Seibt

Publisher: Springer Science & Business Media

ISBN: 3540332197

Category: Computers

Page: 443

View: 1481

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.

Conics and Cubics

A Concrete Introduction to Algebraic Curves

Author: Robert Bix

Publisher: Springer Science & Business Media

ISBN: 1475729758

Category: Mathematics

Page: 292

View: 8221

Algebraic curves are the graphs of polynomial equations in two vari 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.

A Concrete Approach to Abstract Algebra

Author: W. W. Sawyer

Publisher: Courier Dover Publications

ISBN: 0486833313

Category: Mathematics

Page: 240

View: 903

Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.

Discovering Mathematics with Magma

Reducing the Abstract to the Concrete

Author: Wieb Bosma,John Cannon

Publisher: Springer Science & Business Media

ISBN: 3540376348

Category: Computers

Page: 364

View: 1459

Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results.