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## Discrete and combinatorial mathematics : an applied introduction / Ralph P. Grimaldi.

Editor: Reading, Mass. : Addison-Wesley, c1989Edición: 2nd edDescripción: xvi, 722, [93] p. : il. ; 25 cmISBN: 0201119544Otra clasificación: 00A05 (03-01 05-01 94-01 68-01)
Contenidos:
```CHAPTER [1]
Fundamental Principles of Counting
1.1 The Rules of Sum and Product [1]
1.2 Permutations [4]
1.5 Combinations: The Binomial Theorem [14]
1.4 Combinations With Repetition: Distributions [23]
1.5 An Application in the Physical Sciences (Optional) [32]
1.6 Summary and Historical Review [32]
CHAPTER [2]
Fundamentals of Logic
2.1 Basic Connectives and Truth Tables [41]
2.2 Logical Equivalence: The Laws of Logic [49]
2.3 Logical Implication: Methods of Proof [60]
2.4 The Use of Quantifiers [77]
2.5 Summary and Historical Review [91]
CHAPTER [3]
Set Theory
3.1 Sets and Subsets [97]
3.2 Set Operations and the Laws of Set Theory [106]
3.3 Counting and Venn Diagrams [117]
3.4 A Word on Probability [120]
3.5 Summary and Historical Review [123]
CHAPTER [4]
Properties of the Integers: Mathematical Induction
4.1 The Well-Ordering Principle: Mathematical Induction [129]
4.2 The Division Algorithm: Prime Numbers [145]
4.3 The Greatest Common Divisor: The Euclidean Algorithm [153]
4.4 The Fundamental Theorem of Arithmetic [159]
4.5 Summary and Historical Review [161]
CHAPTER [5]
Relations and Functions
5.1 Cartesian Products and Relations [166]
5.2 Functions: Plain and One-to-One [170]
5.3 Onto Functions: Stirling Numbers of the Second Kind [175]
5.4 Special Functions [180]
5.5 The Pigeonhole Principle [186]
5.6 Function Composition and Inverse Functions [190]
Computational Complexity [199]
Analysis of Algorithms [204]
Summary and Historical Review [212]
CHAPTER [6]
Languages: Finite State Machines
6.1 Language: The Set Theory of Strings [220]
6.2 Finite State Machines: A First Encounter [228]
6.3 Finite State Machines: A Second Encounter [236]
6.4 Summary and Historical Review [243]
CHAPTER [7]
Relations: The Second Time Around
7.1 Relations Revisited: Properties of Relations [249]
7.2 Computer Recognition: Zero-One Matrices and Directed Graphs [255]
7.3 Partial Orders: Hasse Diagrams [266]
7.4 Equivalence Relations and Partitions [276]
7.5 Finite State Machines: The Minimization Process [281]
7.6 Summary and Historical Review [287]
CHAPTER [8]
The Principle of Inclusion and Exclusion
8.1 The Principle of Inclusion and Exclusion [295]
8.2 Generalizations of the Principle [305]
8.3 Derangements: Nothing Is in Its Right Place [309]
8.4 Rook Polynomials [311]
8.5 Arrangements with Forbidden Positions [315]
8.6 Summary and Historical Review [319]
CHAPTER [9]
Generating Functions
9.1 Introductory Examples [323]
9.2 Definition and Examples: Calculational Techniques [327]
9.3 Partitions of Integers [336]
9.4 The Exponential Generating Function [339]
9.5 The Summation Operator [344]
9.6 Summary and Historical Review [345]
CHAPTER [10]
Recurrence Relations
10.1 The First-Order Linear Recurrence Relation [351]
10.2 The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients [361]
10.3 The Nonhomogeneous Recurrence Relation [371]
10.4 The Method of Generating Functions [377]
10.5 A Special Kind of Nonlinear Recurrence Relation (Optional) [382]
10.6 Divide-and-Conquer Algorithms (Optional) [388]
10.7 Summary and Historical Review [399]
CHAPTER [11]
An Introduction to Graph Theory
11.1 Definitions and Examples [405]
11.2 Subgraphs, Complements, and Graph Isomorphism [413]
11.3 Vertex Degree: Euler Trails and Circuits [424]
11.4 Planar Graphs [433]
11.5 Hamilton Paths and Cycles [448]
11.6 Graph Coloring and Chromatic Polynomials [457]
11.7 Summary and Historical Review [466]
CHAPTER [12]
Trees
12.1 Definitions, Properties and Examples [475]
12.2 Rooted Trees [482]
12.3 Trees and Sorting Algorithms [501]
12.4 Weighted Trees and Prefix Codes [506]
12.5 Biconnected Components and Articulation Points [511]
12.6 Summary and Historical Review [517]
CHAPTER [13]
Optimization and Matching
13.1 Dijkstra’s Shortest-Path Algorithm [523]
13.2 Minimal Spanning Trees: The Algorithms of Kruskal and Prim [531]
13.3 Transport Networks: The Max-Flow Min-Cut Theorem [538]
13.4 Matching Theory [549]
13.5 Summary and Historical Review [558]
CHAPTER [14]
Rings and Modular Arithmetic
14.1 The Ring Structure: Definition and Examples [563]
14.2 Ring Properties and Substructures [568]
14.3 The Integers Modulo n [575]
14.4 Ring Homomorphisms and Isomorphisms [580]
14.5 Summary and Historical Review [587]
CHAPTER [15]
Boolean Algebra and Switching Functions
15.1 Switching Functions: Disjunctive and Conjunctive Normal Forms [591]
15.2 Gating Networks: Minimal Sums of Products: Karnaugh Maps [600]
15.3 Further Applications: Don’t-Care Conditions [609]
15.4 The Structure of a Boolean Algebra (Optional) [615]
15.5 Summary and Historical Review [624]
CHAPTER [16]
Groups, Coding Theory, and Polya’s Method of Enumeration
16.1 Definition, Examples, and Elementary Properties [629]
16.2 Homomorphisms, Isomorphisms, and Cyclic Groups [635]
16.3 Cosets and Lagrange’s Theorem [639]
16.4 Elements of Coding Theory [642]
16.5 The Hamming Metric [647]
16.6 The Parity-Check and Generator Matrices [649]
16.7 Group Codes: Decoding with Coset Leaders [654]
16.8 Hamming Matrices [658]
16.9 Counting and Equivalence: Burnside’s Theorem [661]
16.10 The Cycle Index [669]
16.11 The Pattern Inventory: Polya’s Method of Enumeration [673]
16.12 Summary and Historical Review [679]
CHAPTER [17]
Finite Fields and Combinatorial Designs
17.1 Polynomial Rings [685]
17.2 Irreducible Polynomials: Finite Fields [693]
17.3 Latin Squares [700]
17.4 Finite Geometries and Affine Planes [707]
17.5 Block Designs and Projective Planes [713]
17.6 Summary and Historical Review [718]
Answers A-1
Index I-1```
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Incluye referencias bibliográficas e índice.

CHAPTER [1] --
Fundamental Principles of Counting --
1.1 The Rules of Sum and Product [1] --
1.2 Permutations [4] --
1.5 Combinations: The Binomial Theorem [14] --
1.4 Combinations With Repetition: Distributions [23] --
1.5 An Application in the Physical Sciences (Optional) [32] --
1.6 Summary and Historical Review [32] --
CHAPTER [2] --
Fundamentals of Logic --
2.1 Basic Connectives and Truth Tables [41] --
2.2 Logical Equivalence: The Laws of Logic [49] --
2.3 Logical Implication: Methods of Proof [60] --
2.4 The Use of Quantifiers [77] --
2.5 Summary and Historical Review [91] --
CHAPTER [3] --
Set Theory --
3.1 Sets and Subsets [97] --
3.2 Set Operations and the Laws of Set Theory [106] --
3.3 Counting and Venn Diagrams [117] --
3.4 A Word on Probability [120] --
3.5 Summary and Historical Review [123] --
CHAPTER [4] --
Properties of the Integers: Mathematical Induction --
4.1 The Well-Ordering Principle: Mathematical Induction [129] --
4.2 The Division Algorithm: Prime Numbers [145] --
4.3 The Greatest Common Divisor: The Euclidean Algorithm [153] --
4.4 The Fundamental Theorem of Arithmetic [159] --
4.5 Summary and Historical Review [161] --
CHAPTER [5] --
Relations and Functions --
5.1 Cartesian Products and Relations [166] --
5.2 Functions: Plain and One-to-One [170] --
5.3 Onto Functions: Stirling Numbers of the Second Kind [175] --
5.4 Special Functions [180] --
5.5 The Pigeonhole Principle [186] --
5.6 Function Composition and Inverse Functions [190] --
Computational Complexity [199] --
Analysis of Algorithms [204] --
Summary and Historical Review [212] --
CHAPTER [6] --
Languages: Finite State Machines --
6.1 Language: The Set Theory of Strings [220] --
6.2 Finite State Machines: A First Encounter [228] --
6.3 Finite State Machines: A Second Encounter [236] --
6.4 Summary and Historical Review [243] --
CHAPTER [7] --
Relations: The Second Time Around --
7.1 Relations Revisited: Properties of Relations [249] --
7.2 Computer Recognition: Zero-One Matrices and Directed Graphs [255] --
7.3 Partial Orders: Hasse Diagrams [266] --
7.4 Equivalence Relations and Partitions [276] --
7.5 Finite State Machines: The Minimization Process [281] --
7.6 Summary and Historical Review [287] --
CHAPTER [8] --
The Principle of Inclusion and Exclusion --
8.1 The Principle of Inclusion and Exclusion [295] --
8.2 Generalizations of the Principle [305] --
8.3 Derangements: Nothing Is in Its Right Place [309] --
8.4 Rook Polynomials [311] --
8.5 Arrangements with Forbidden Positions [315] --
8.6 Summary and Historical Review [319] --
CHAPTER [9] --
Generating Functions --
9.1 Introductory Examples [323] --
9.2 Definition and Examples: Calculational Techniques [327] --
9.3 Partitions of Integers [336] --
9.4 The Exponential Generating Function [339] --
9.5 The Summation Operator [344] --
9.6 Summary and Historical Review [345] --
CHAPTER [10] --
Recurrence Relations --
10.1 The First-Order Linear Recurrence Relation [351] --
10.2 The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients [361] --
10.3 The Nonhomogeneous Recurrence Relation [371] --
10.4 The Method of Generating Functions [377] --
10.5 A Special Kind of Nonlinear Recurrence Relation (Optional) [382] --
10.6 Divide-and-Conquer Algorithms (Optional) [388] --
10.7 Summary and Historical Review [399] --
CHAPTER [11] --
An Introduction to Graph Theory --
11.1 Definitions and Examples [405] --
11.2 Subgraphs, Complements, and Graph Isomorphism [413] --
11.3 Vertex Degree: Euler Trails and Circuits [424] --
11.4 Planar Graphs [433] --
11.5 Hamilton Paths and Cycles [448] --
11.6 Graph Coloring and Chromatic Polynomials [457] --
11.7 Summary and Historical Review [466] --
CHAPTER [12] --
Trees --
12.1 Definitions, Properties and Examples [475] --
12.2 Rooted Trees [482] --
12.3 Trees and Sorting Algorithms [501] --
12.4 Weighted Trees and Prefix Codes [506] --
12.5 Biconnected Components and Articulation Points [511] --
12.6 Summary and Historical Review [517] --
CHAPTER [13] --
Optimization and Matching --
13.1 Dijkstra’s Shortest-Path Algorithm [523] --
13.2 Minimal Spanning Trees: The Algorithms of Kruskal and Prim [531] --
13.3 Transport Networks: The Max-Flow Min-Cut Theorem [538] --
13.4 Matching Theory [549] --
13.5 Summary and Historical Review [558] --
CHAPTER [14] --
Rings and Modular Arithmetic --
14.1 The Ring Structure: Definition and Examples [563] --
14.2 Ring Properties and Substructures [568] --
14.3 The Integers Modulo n [575] --
14.4 Ring Homomorphisms and Isomorphisms [580] --
14.5 Summary and Historical Review [587] --
CHAPTER [15] --
Boolean Algebra and Switching Functions --
15.1 Switching Functions: Disjunctive and Conjunctive Normal Forms [591] --
15.2 Gating Networks: Minimal Sums of Products: Karnaugh Maps [600] --
15.3 Further Applications: Don’t-Care Conditions [609] --
15.4 The Structure of a Boolean Algebra (Optional) [615] --
15.5 Summary and Historical Review [624] --
CHAPTER [16] --
Groups, Coding Theory, and Polya’s Method of Enumeration --
16.1 Definition, Examples, and Elementary Properties [629] --
16.2 Homomorphisms, Isomorphisms, and Cyclic Groups [635] --
16.3 Cosets and Lagrange’s Theorem [639] --
16.4 Elements of Coding Theory [642] --
16.5 The Hamming Metric [647] --
16.6 The Parity-Check and Generator Matrices [649] --
16.7 Group Codes: Decoding with Coset Leaders [654] --
16.8 Hamming Matrices [658] --
16.9 Counting and Equivalence: Burnside’s Theorem [661] --
16.10 The Cycle Index [669] --
16.11 The Pattern Inventory: Polya’s Method of Enumeration [673] --
16.12 Summary and Historical Review [679] --
CHAPTER [17] --
Finite Fields and Combinatorial Designs --
17.1 Polynomial Rings [685] --
17.2 Irreducible Polynomials: Finite Fields [693] --
17.3 Latin Squares [700] --
17.4 Finite Geometries and Affine Planes [707] --
17.5 Block Designs and Projective Planes [713] --
17.6 Summary and Historical Review [718] --
Answers A-1 --
Index I-1 --

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