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离散数学及其应用 第3版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）苏杉娜（Susanna，S.E.）著 著
- 出版社： 北京：高等教育出版社
- ISBN：704016230X
- 出版时间：2005
- 标注页数：906页
- 文件大小：251MB
- 文件页数：927页
- 主题词：离散数学－高等学校－教材－英文
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图书目录
Chapter 1 The Logic of Compound Statements1
1.1 Logical Form and Logical Equivalence1
1.2 Conditional Statements17
1.3 Valid and Invalid Arguments29
1.4 Application:Digital Logic Circuits43
1.5 Application:Number Systems and Circuits for Addition57
Chapter 2 The Logic of Quantified Statements75
2.1 Introduction to Predicates and Quantified Statements Ⅰ75
2.2 Introduction to Predicates and Quantified Statements Ⅱ88
2.3 Statements Containing Multiple Quantifiers97
2.4 Arguments with Quantified Statements111
Chapter 3 Elementary Number Theory and Methods of Proof125
3.1 Direct Proof and Counterexample Ⅰ:Introduction126
3.2 Direct Proof and Counterexample Ⅱ:Rational Numbers141
3.3 Direct Proof and Counterexample Ⅲ:Divisibility148
3.4 Direct Proof and Counterexample Ⅳ:Division into Cases and the Quotient-Remainder Theorem156
3.5 Direct Proof and Counterexample Ⅴ:Floor and Ceiling164
3.6 Indirect Argument:Contradiction and Contraposition171
3.7 Two Classical Theorems179
3.8 Application:Algorithms186
Chapter 4 Sequences and Mathematical Induction199
4.1 Sequences199
4.2 Mathematical Induction Ⅰ215
4.3 Mathematical Induction Ⅱ227
4.4 Strong Mathematical Induction and the Well-Ordering Principle235
4.5 Application:Correctness of Algorithms244
Chapter 5 Set Theory255
5.1 Basic Definitions of Set Theory255
5.2 Properties of Sets269
5.3 Disproofs,Algebraic Proofs,and Boolean Algebras282
5.4 Russell's Paradox and the Halting Problem293
Chapter 6 Counting and Probability297
6.1 Introduction298
6.2 Possibility Trees and the Multiplication Rule306
6.3 Counting Elements of Disjoint Sets:The Addition Rule321
6.4 Counting Subsets of a Set:Combinations334
6.5 r-Combinations with Repetition Allowed349
6.6 The Algebra of Combinations356
6.7 The Binomial Theorem362
6.8 Probability Axioms and Expected Value370
6.9 Conditional Probability,Bayes'Formula,and Independent Events375
Chapter 7 F unctions389
7.1 Functions Defined on General Sets389
7.2 One-to-One and Onto,Inverse Functions402
7.3 Application:The Pigeonhole Principle420
7.4 Composition of Functions431
7.5 Cardinality with Applications to Computability443
Chapter 8 Recursion457
8.1 Recursively Defined Sequences457
8.2 Solving Recurrence Relations by lteration475
8.3 Second-Order Linear Homogenous Recurrence Relations with Constant Coefficients487
8.4 General Recursive Definitions499
Chapter 9 The Efficiency of Algorithms510
9.1 Real-Valued Functions of a Real Variable and Their Graphs510
9.2 O,Ω，and？Notations518
9.3 Application:Efficiency of Algorithms Ⅰ531
9.4 Exponential and Logarithmic Functions:Graphs and Orders543
9.5 Application:Efficiency of Algorithms Ⅱ557
Chapter 10 Relations571
10.1 Relations on Sets571
10.2 Reflexivity,Symmetry,and Transitivity584
10.3 Equivalence Relations594
10.4 Modular Arithmetic with Applications to Cryptography611
10.5 Partial Order Relations632
Chapter 11 Graphs and Trees649
11.1 Graphs:An Introduction649
11.2 Paths and Circuits665
11.3 Matrix Representations of Graphs683
11.4 Isomorphisms of Graphs697
11.5 Trees705
11.6 Spanning Trees723
Chapter 12 Regular Expressions and Finite-State Automata734
12.1 Formal Languages and Regular Expressions735
12.2 Finite-State Automata745
12.3 Simplifying Finite-State Automata763