Discrete and Combinatorial Mathematics: An Applied Introduction, 4/e (精裝)
- 出版商: Addison Wesley Publishing Company
- 售價: $1,100
- 貴賓價: 9.5 折 $1,045
- 語言: 英文
- 頁數: 896
- 裝訂: Hardcover
- ISBN: 0201199122
- ISBN-13: 9780201199123
This fourth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses: discrete mathematics, graph theory, modern algebra, and/or combinatorics. More elementary problems were added, creating a greater variety of level in problem sets, which allows students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.
- This text has an enhanced mathematical approach, with carefully thought out examples, including many examples with computer sciences applications.
- Historical reviews and biographies bring a human element to their assignments.
- Chapter summaries allow students to review what they have learned.
I. FUNDAMENTALS OF DISCRETE MATHEMATICS.
Combinations: The Binomial Theorem.
Combinations with Repetition.
An Application in the Physical Sciences (Optional).
The Catalan Numbers (Optional).
2. Fundamentals of Logic.
Logical Equivalence: The Laws of Logic.
Logical Implication: Rules of Inference.
The Use of Quantifiers.
Quantifiers, Definitions, and the Proofs of Theorems.
3. Set Theory.
Set Operations and the Laws of Set Theory.
Counting and Venn Diagrams.
A Word on Probability.
4. Properties of the Integers: Mathematical Induction.
The Division Algorithm: Prime Numbers.
The Greatest Common Divisor: The Euclidean Algorithm.
The Fundamental Theorem of Arithmetic.
5. Relations and Functions.
Functions: Plain and One-to-One.
Onto Functions: Stirling Numbers of the Second Kind.
The Pigeonhole Principle.
Function Composition and Inverse Functions.
Analysis of Algorithms.
6. Languages: Finite State Machines.
Finite State Machines: A First Encounter.
Finite State Machines: A Second Encounter.
7. Relations: The Second Time Around.
Computer Recognition: Zero-One Matrices and Directed Graphs.
Partial Orders: Hasse Diagrams.
Equivalence Relations and Partitions.
Finite State Machines: The Minimization Process.
II. FURTHER TOPICS IN ENUMERATION.
Generalizations of the Principle (Optional).
Derangements: Nothing Is in Its Right Place.
Arrangements with Forbidden Positions.
9. Generating Functions.
Definition and Examples: Calculational Techniques.
Partitions of Integers.
The Exponential Generating Functions.
The Summation Operator.
10. Recurrence Relations.
The Second-Order Linear Recurrence Relation with Constant Coefficients.
The Nonhomogeneous Recurrence Relation.
The Method of Generating Functions.
A Special Kind of Nonlinear Recurrence Relation (Optional).
Divide and Conquer Algorithms (Optional).
III. GRAPH THEORY AND APPLICATIONS.
Subgraphs, Complements, and Graph Isomorphism.
Vertex Degree: Euler Trails and Circuits.
Hamilton Paths and Cycles.
Graph Coloring and Chromatic Polynomials.
Trees and Sorting.
Weighted Trees and Prefix Codes.
Biconnected Components and Articulation Points.
13. Optimization and Matching.
Minimal Spanning Trees: The Algorithms of Kruskal and Prim.
Transport Networks: The Max-Flow Min-Cut Theorem.
IV. MODERN APPLIED ALGEBRA.
Ring Properties and Substructures.
The Integers Modulo n.
Ring Homomorphisms and Isomorphisms.
15. Boolean Algebra and Switching Functions.
Gating Networks: Minimal Sums of Products: Karnaugh Maps.
Further Applications: Don't Care Conditions.
The Structure of a Boolean Algebra (Optional).
16. Groups, Coding Theory, and Polya's Method of Enumeration.
Homomorphisms, Isomorphisms, and Cyclic Groups.
Cosets and Lagrange's Theorem.
Elements of Coding Theory.
The Hamming Metric.
The Parity-Check and Generator trices.
Group Codes: Decoding with Coset Leaders.
Counting and Equivalence: Burnside's Theorem.
The Cycle Index.
The Pattern Inventory: Polya's Method of Enumeration.
17. Finite Fields and Combinatorial Designs.
Irreducible Polynomials: Finite Fields.
Finite Geometries and Affine Planes.
Block Designs and Projective Planes.
Matrices, Matrix Operations, and Determinants.
Countable and Uncountable Sets.
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- Instructor's Solutions Manual / 0-201-43448-2