This book describes highly applicable mathematics without using calculus or limits in general. The study agrees with the opinion that the traditional calculus/analysis is not necessarily the only proper grounding for academics who wish to apply mathematics. The choice of topics is based on a desire to present those facets of mathematics which will be useful to economists and social/behavioral scientists. The volume is divided into seven chapters. Chapter I presents a brief review of the solution of systems of linear equations by the use of matrices. Chapter III introduces the theory of probability. The rest of the book deals with new developments in mathematics such as linear and dynamic programming, the theory of networks and the theory of games. These developments are generally recognized as the most important field in the `new mathematics' and they also have specific applications in the management sciences.

This book describes highly applicable mathematics without using calculus or limits in general. The study agrees with the opinion that the traditional calculus/analysis is not necessarily the only proper grounding for academics who wish to apply mathematics. The choice of topics is based on a desire to present those facets of mathematics which will be useful to economists and social/behavioral scientists. The volume is divided into seven chapters. Chapter I presents a brief review of the solution of systems of linear equations by the use of matrices. Chapter III introduces the theory of probability. The rest of the book deals with new developments in mathematics such as linear and dynamic programming, the theory of networks and the theory of games. These developments are generally recognized as the most important field in the `new mathematics' and they also have specific applications in the management sciences.

Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the $3n+1$ conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P, NP and PSPACE. What Beck does is very different: he studies interesting concrete systems, which can give new insights into the mystery of complexity. The book is divided into three parts. Part A is mostly an essay on the big picture. Part B is partly new results and partly a survey of real game theory. Part C contains new results about graph games, supporting the main conjecture. To make it accessible to a wide audience, the book is mostly self-contained.

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.

“Introductory Discrete Mathematics” provides a thorough and understandable introduction to the basic ideas and methods of discrete mathematics. It is an invaluable resource for students, instructors, and professionals looking to establish a solid foundation in ideas critical to subjects such as computer science, engineering, cryptography, and operations research. The book is well-organized, beginning with an investigation of fundamental concepts like as sets, logic, and proving procedures. These early chapters establish the framework for comprehending more complex subjects like as combinatorics, graph theory, and discrete probability. Each idea is presented in a way that encourages understanding and retention, so readers can move through the material with confidence. “Introductory Discrete Mathematics” excels in concise explanations. Readers with different mathematical backgrounds may understand complex topics since they are simplified. Each topic has real-world examples to help readers understand its practicality. The book includes several exercises and challenges to reinforce and test knowledge. Readers may improve their grasp and confidence in using discrete mathematics to solve issues by doing these activities. In addition, “Introductory Discrete Mathematics” emphasises discrete mathematics’ practical applications in numerous domains. Using these principles to solve real-world problems, the book shows how discrete mathematics is relevant and important today.

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

This text offers a complete coverage in the Decision Mathematics module, also known as Discrete Mathematics, of the syllabuses of English A-level examination boards. it is a rewritten and modern version of Decision Mathematics (published by Ellis Horwood Ltd in 1986 for The Spode Group, so well known for its development of innovative mathematics teaching). It is also a suitable text for foundation and first year undergraduate courses in qualitative studies or operational research, or for access courses for students needing strengthening in mathematics, or for students who are moving into mathematics from another subject discipline.Compact and concise, it reflects the combined teaching skills and experience of its authors who know exactly what mathematics must be learnt at the readership level today. The text is built up in modular fashion, explaining concepts used in decision mathematics and related operational research, and electronics. It emphasises an understanding of techniques and algorithms, which it relates to real life situations and working problems that will apply throughout future working careers. - Clear explanations of algorithms and all concepts - Plentiful worked examples, clear diagrams - Many exercises (with answers for self-study)

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Discrete mathematics, also called finite mathematics or Decision Maths, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets, such as integers, finite graphs, and formal languages. Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasise concepts for computer science majors.

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