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Rosen 博士于1972年获密歇根大学数学学士学位，1976年获麻省理工学院数学博士学位，其博士论文研究的是数论，导师是Harold Stark 。曾就职于科罗拉多大学、俄亥俄州立大学、缅因大学，后加盟贝尔实验室，现为AT&T实验室特别成员。他目前还是蒙茅斯大学客座研究教授，主要从事快速反应数据库项目的安全和保密方面的工作，同时教授密码应用课程。此外，他还是CRC出版社离散数学丛书的编辑顾问。

Rosen博士在专业期刊上发表过许多关于数论及数学建模的文章。《初等数论及其应用》和《离散数学及其应用》这两本书均被国际上几百所大学广为采用。

《离散数学及其应用(英文版第7版)》
preface iv
about theauthor xiii
the companion website xiv
to the studentxvi
list of symbols xix
1 the foundations：logic and proofs
1．1 propositional logic
1．2 applications of propositional logic
1．3 propositional equivalences
1．4 predicates andquantifiers
1．5 nested quantifiers
1．6 rules of inference
1．7 introduction to proofs
1．8 proofmethods and strategy
end-of-chaptermaterial-
2 basic structures：sets，functions，sequences，sums，and matrices
2．1 sets
2．2 set operations
2．3 functions
.2．4 sequences and summations
2．5 cardinality of sets
2．6 matrices
end-of-chaptermaterial
3 algorithms
3．1 algorithms
3．2 the growth of functions
3．3 complexity of algofithms
end-of-chapter material
4 number theory and cryptography
4．1 divisibilitv andmodular arithmetic
4．2 integer representations andalgorithms
4．3 primesand greatest common divisors
4．4 solving congruences
4．5 applications of congruences
4．6 cryptography
end-of-chapter material
5 induction and recursion
5．1 mathematical induction
5．2 strong induction and well-ordering
5．3 recursive definitions and structural induction
5．4 recursive algorithms
5．5 program correctness
end-of-chapter material
6 counting
6．1 tlle basics of counting
6．2 the pigeonhole principle
6．3 permutations and combinations
6．4 binomial coefficients and identities
6．5 generalized permutations and combinations
6．6 generating permutations and combinations
end-of-chapter material
7 discrete probability
7．1 an introduction to discrete probability
7．2 probability theory
7．3 bayes’theorem
7．4 expected value and variance
end-of-chapter material
8 advanced counring technigues
8．1 applications of recurrence relations
8．2 solving linear recurrence relations
8．3 divide-and-conquer algorithms and recurrence relations
8．4 generating functions
8．5 inclusion-exclusion
8．6 applications of inclusion-exclusion
end—of-chapter material
9 relations
9．1 relations and their properties
9．2 n-ary relations and theirapplications
9．3 representing relations
9．4 closures of relations
9．5 equivalence relations
9．6 partial orderings
end-of-chapter material
10 graphs
10．1 graphs andgraphmodels
10．2 graph terminology and special types of graphs
10．3 representing graphs and graph isomorphism
10．4 connectivity
10．5 eulerandhamiltonpaths
10．6 shortest．pathproblems
10．7 planargraphs
10．8 graphcoloring
end-of-chapter material
11 trees
11．1 introduction to trees
11．2 applications of trees
11．3 tree travcrsal
11．4 spanning trees
11．5 minimum spanning trees
end-of-chapter material
12 boolean algebra
12．1 boolean functions
12．2 representing boolean functions
12．3 logic gates
12．4 minimization of circuits
end-of-chapter material
13 modeling cornputation
13．1 languagesand grammars
13．2 finite-state machines with output
13．3 finite-state machines with no output
13．4 languagerecognition
13．5 turing machines
end-of-chapter material
appendixes
1 axioms for the real numbers and the positive integers
2 exponential and logarithmic functions
3 pseudocode
suggestedreadings b-1
answers to odd-numbered exercises s-1
photo credits c-1
index ofbiographies i-1
index i-2
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