Concrete Mathematics

Author : Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Publisher : Addison-Wesley Professional
Page : 811 pages
File Size : 48,5 Mb
Release : 1994-02-28
Category : Computers
ISBN : 9780134389981

Get Book

Concrete Mathematics by Ronald L. Graham,Donald E. Knuth,Oren Patashnik Pdf

This book 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 sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

Author : Ronald L. Graham
Publisher : Pearson Education India
Page : 648 pages
File Size : 47,7 Mb
Release : 1994
Category : Asymptotic expansions
ISBN : 8131708411

Get Book

Concrete Mathematics: A Foundation for Computer Science by Ronald L. Graham Pdf

Author : Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik
Publisher : Addison Wesley Publishing Company
Page : 650 pages
File Size : 48,6 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015013838613

Get Book

Concrete Mathematics by Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik Pdf

"This book 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 sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline."--from Amazon.com.

Author : Z. A. Melzak
Publisher : Wiley-Interscience
Page : 294 pages
File Size : 52,6 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015017286348

Get Book

Companion to Concrete Mathematics by Z. A. Melzak Pdf

Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 48,5 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243

Get Book

How to Prove It by Daniel J. Velleman Pdf

This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

Author : Marian Muresan
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 55,6 Mb
Release : 2015-09-16
Category : Mathematics
ISBN : 9780387789330

Get Book

A Concrete Approach to Classical Analysis by Marian Muresan Pdf

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.

Author : Jiri Adamek,Horst Herrlich,George E. Strecker
Publisher : Unknown
Page : 0 pages
File Size : 54,8 Mb
Release : 2009
Category : Categories (Mathematics)
ISBN : 0486469344

Get Book

Abstract and Concrete Categories by Jiri Adamek,Horst Herrlich,George E. Strecker Pdf

This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures, offering a unifying perspective on earlier work and summarizing recent developments. Numerous examples, ranging from general to specific, illuminate the text. 1990 edition, updated 2004.

Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 574 pages
File Size : 42,5 Mb
Release : 2012-02-25
Category : Applied mathematics
ISBN : 9781105559297

Get Book

Applied Discrete Structures by Ken Levasseur,Al Doerr Pdf

Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

Author : W. W. Sawyer
Publisher : Courier Dover Publications
Page : 241 pages
File Size : 53,8 Mb
Release : 2018-08-15
Category : Mathematics
ISBN : 9780486824611

Get Book

Concrete Approach to Abstract Algebra by W. W. Sawyer Pdf

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.

Author : Manuel Kauers,Peter Paule
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 53,7 Mb
Release : 2011-01-15
Category : Mathematics
ISBN : 9783709104453

Get Book

The Concrete Tetrahedron by Manuel Kauers,Peter Paule Pdf

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.

Author : Robert Bix
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 43,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475729757

Get Book

Conics and Cubics by Robert Bix Pdf

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.

Author : Lindsay N. Childs
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 44,8 Mb
Release : 2012-12-04
Category : Mathematics
ISBN : 9781441987020

Get Book

A Concrete Introduction to Higher Algebra by Lindsay N. Childs Pdf

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, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated 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, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.

Author : Sacha Friedli,Yvan Velenik
Publisher : Cambridge University Press
Page : 643 pages
File Size : 50,5 Mb
Release : 2017-11-23
Category : Mathematics
ISBN : 9781107184824

Get Book

Statistical Mechanics of Lattice Systems by Sacha Friedli,Yvan Velenik Pdf

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

Author : Rod Haggarty
Publisher : Addison Wesley Publishing Company
Page : 0 pages
File Size : 41,5 Mb
Release : 2002
Category : Computer science
ISBN : 0201730472

Get Book

Discrete Mathematics for Computing by Rod Haggarty Pdf

A concise introduction to key mathematical ideas for computing students which develops their understanding of discrete mathematics and its application in computing. The topics are presented in a logical order that build upon each other and are constantly reinforced by worked examples. Reliance on students' previous mathematical experience is kept to a minimum, though some basic algebraic manipulation is required.

Author : Lindsay Childs
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468400656

Get Book

A Concrete Introduction to Higher Algebra by Lindsay Childs Pdf

This book is written as an introduction to higher algebra for students with a background of a year of calculus. The book developed out of a set of notes for a sophomore-junior level course at the State University of New York at Albany entitled Classical Algebra. In the 1950s and before, it was customary for the first course in algebra to be a course in the theory of equations, consisting of a study of polynomials over the complex, real, and rational numbers, and, to a lesser extent, linear algebra from the point of view of systems of equations. Abstract algebra, that is, the study of groups, rings, and fields, usually followed such a course. In recent years the theory of equations course has disappeared. Without it, students entering abstract algebra courses tend to lack the experience in the algebraic theory of the basic classical examples of the integers and polynomials necessary for understanding, and more importantly, for ap preciating the formalism. To meet this problem, several texts have recently appeared introducing algebra through number theory.