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Discrete mathematics : Elementary and beyond / László Lovász, J Pelikán, K Vsztergombi
New York : Springer, 2003
297 p. ; cm.
Ký hiệu phân loại (DDC): 511.6
Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book. Laszlo Lovasz is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Godel Prize for the top paper in Computer Science. Jozsef Pelikan is Professor of Mathematics in the Department of Algebra and Number Theory at Eotvos Lorand University, Hungary.; In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington
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Guide to Discrete Mathematics : An Accessible Introduction to the History, Theory, Logic and Applications / Gerard O’Regan
Switzerland : Springer, 2016
378 p. ; cm.
Ký hiệu phân loại (DDC): 004.0151
This stimulating textbook/reference presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. Topics and features: Provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions Describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations Presents the essentials of algebra, covering simultaneous and quadratic equations, and the laws of logarithms and indices, in addition to such structures in abstract algebra as monoids, groups, rings, integral domains, fields, and vector spaces Explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability Reviews the history of logic, discussing propositional and predicate logic, as well as such advanced topics as fuzzy logic, temporal logic, intuitionistic logic, undefined values, theorem provers, and the applications of logic to AI Examines the important field of software engineering, describing formal methods, including the Z specification language Investigates probability and statistics, covering discrete random variables, probability distributions, sample spaces, variance and standard deviation, and hypothesis testing This engaging and clearly written work offers an invaluable overview of discrete mathematics for undergraduate computer science students, and to students of mathematics interested in the rich applications of discrete mathematics to the field of computing.
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Mathematics : a discrete introduction / Edward R Scheinerman
Belmont, CA : Thomson Brooks/Cole, 2006
xxvii, 560 p. ; 28 cm.
Ký hiệu phân loại (DDC): 004.0151
Teaches students fundamental concepts in discrete mathematics (from counting to basic cryptography to graph theory), and proof-writing skills. This book teaches students not only how to write proofs, but how to think and present cases logically beyond this course. It is an introduction to mathematics.
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