Dover Books on Computer Science

Complete, rigorous expositions of economic models analyzed primarily according to their mathematical properties. Optimizing theory, static and dynamic models, mathematical reviews, more.

Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.

Operations research originated during World War II with the military's need for a scientific method of providing executives with a quantitative decision-making basis. This text explores strategical kinematics, tactical analysis, gunnery and bombardment problems, more.

Engineers and scientists who want to avoid insidious errors in their computer-assisted calculations will welcome this concise guide to trouble-shooting. Real Computing Made Real offers practical advice on detecting and removing bugs. It also outlines techniques for preserving significant figures, avoiding extraneous solutions, and finding efficient iterative processes for solving nonlinear equations. Those who compute with real numbers (for example, floating-point numbers stored with limited precision) tend to develop techniques that increase the frequency of useful answers. But although there might be ample guidance for those addressing linear problems, little help awaits those negotiating the nonlinear world. This book, geared toward upper-level undergraduates and graduate students, helps rectify that imbalance. Its examples and exercises (with answers) help readers develop problem-formulating skills and assist them in avoiding the common pitfalls that software packages seldom detect. Some experience with standard numerical methods is assumed, but beginners will find this volume a highly practical introduction, particularly in its treatment of often-overlooked topics.

This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems. Chapters 0–3 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material. Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization ― the minimal spanning tree problem and the shortest distance problem ― are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix.