離散數(shù)學(xué)及其應(yīng)用--第4版--英文

作者簡介

ABOUT THE AUTHOR
Kenneth H. Rosen is a Distinguished Member ofthe Technical Staffin the New
Concepts Area of AT&T Laboratories in Holmdel, New Jersey.
Dr. Rosen received his B.S. in Mathematics from the University ofMichi-
gan, Ann Arbor (1972), and his Ph.D. in Mathematics from M.I.T. (1976), where he
wrote his thesis in the area of number theory under the direction of Harold Stark. Be-
forejoining Bell Laboratories in 1982, he held positions at the University ofColorado,
Boulder; the Ohio State University, Columbus; and the University of Maine, Orono,
where he was an associate professor of mathematics. While working at AT&T Labs,
Ken has taught in the evening program in computer science at Monmouth University,
teaching courses in discrete mathematics, coding theory, and data security.
Dr. Rosen has published numerous articles in professional joumals in the areas of
number theory and mathematical modeling. He is the author ofthe textbooks Elemen-
tary Number Theory and Its Applications, currently in its third edition, published by
Addison-Wesley, and Discrete Mathematics and Its Applications, m its fourth edition,
published by McGraw-Hill. Both books have been used extensively at hundreds of uni-
versities. He is coauthor of UNIX System VRelease 4: An lntroduction, which has sold
more than 100,000 copies and has been translated into Spanish and German, and Best
UNIX Tips Ever, translated into Chinese, both published by Osbome McGraw-Hill.
Ken is also the editor of the Handbook ofDiscrete Mathematics, a new publication to
be published in 1999 by CRC Press, and he is the editor of the CRC series of books in
discrete mathematics. Ken is also interested in integrating mathematical software into
the educational and professional environments and is working on projects with Waterloo
MAPLE software in both these areas.
At Bell Laboratories and now AT&T Laboratories, Dr. Rosen has worked on a
wide range of projects, including operations research studies and product line planning
for computers and data communications equipment. He has helped plan AT&T's fu-
ture products and services in the area of multimedia, including video communications,
speech recognition, and image networking. He has evaluated new technology for use
by AT&T. He has also invented many new services and holds or has submitted many
patents. One of his more interesting projects involved helping evaluate technology for
the AT&T attraction at EPCOT Center.

書籍目錄

Preface ix
The companion web site xix
To the student xxi
PRAT 1	The foundations : logic , sets , and function
1.	Logic
2.	Propositional equivalences
3.	Predicates and quantifiers
4.	Sets 
5.	Set operations
6.	Functions
7.	Sequences and summations
8.	The growth of functions
PART 2	The fundamentals : algorithms , the integers , and matrices
1.	Algorithms
2.	Complexity of algorithms
3.	The integers and division
4.	Integers and algorithms
5.	Applications of number theory
6.	Matrices
PART 3	Mathematical reasoning
1.	Methods of proof
2.	Mathematical induction
3.	Recursive definitions
4.	Recursive algorithms
5.	Program correctness
PART 4	Counting
1.	The basics of counting
2.	The pigeonhole principle
3.	Permutations and combinations
4.	Discrete probability
5.	Probability theory
6.	Generalized permutations and combinations
7.	Generating permutations and combinations
PART 5	Advanced counting techniques
1.	Recurrence relations
2.	Solving recurrence relations
3.	Divide-and-conquer relations
4.	Generating functions
5.	Inclusion-Exclusion
6.	Applications of inclusion-exclusion
PART 6	Relations
1.	Relations and their properties
2.	n-ary relations and their applications
3.	Representing relations
4.	Closures of relations
5.	Equivalence relations
6.	Partial orderings
PART 7	Graphs
1.	Introduction to graphs
2.	Graph terminology
3.	Representing graphs and graph isomorphism
4.	Connectivity
5.	Euler and Hamilton paths
6.	Shortest path problems
7.	Planar graphs
8.	Graph coloring
PART 8	Trees
1.	Introduction to trees
2.	Applications of trees
3.	Tree traversal
4.	Trees and sorting
5.	Spanning trees
6.	Minimum spanning trees
PART 9	Boolean algebra
1.	Boolean functions
2.	Representing Boolean functions
3.	Logic gates
4.	Minimization of circuits
PART 10	Modeling computation
1.	Languages and grammars
2.	Finite-state machines with output
3.	Finite-state machines with no output
4.	Language recognition
5.	Turing machines
App

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