Discrete and combinatorial mathematics : an applied introduction
著者
書誌事項
Discrete and combinatorial mathematics : an applied introduction
Addison-Wesley Longman, c1999
4th ed
大学図書館所蔵 全9件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes index
内容説明・目次
内容説明
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.
目次
1. Fundamentals of Discrete Mathematics. Fundamental Principles of Counting. The Rules of Sum and Product. Permutations. Combinations:. The Binomial Theorem. Combinations with Repetition: Distributions. An Application in the Physical Sciences (Optional). 2. Fundamentals of Logic. Basic Connectives and Truth Tables. 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. Sets and Subsets. Set Operations and the Laws of Set Theory. Counting and Venn Diagrams. A Word on Probability. 4. Properties of the Integers: Mathematical Induction. The Well-Ordering Principle: Mathematical Induction. Recursive Definitions. The Division Algorithm: Prime Numbers. The Greatest Common Divisor: The Euclidean Algorithm. The Fundamental Theorem of Arithmetic. 5. Relations and Functions. Cartesian Products and Relations. Functions: Plain and One-to-One. Onto Functions: Stirling Numbers of the Second Kind. Special Functions. The Pigeonhole Principle. Function Composition and Inverse Functions. Computational Complexity. Analysis of Algorithms. 6. Languages: Finite State Machines. Language: The Set Theory of Strings. Finite State Machines: A First Encounter. Finite State Machines: A Second Encounter. Relations: The Second Time Around. Relations Revisited: Properties of Relations. Computer Recognition: Zero-One Matrices and Directed Graphs. Partial Orders: Hasse Diagrams. Equivalence Relations and Partitions. Finite State Machines: The Minimization Process. 7. Further Topics in Enumeration. The Principle of Inclusion and Exclusion. Generalizations of the Principle (Optional). Derangements: Nothing Is in Its Right Place. Rook Polynomials. Arrangements with Forbidden Positions. 8. Generating Functions. Introductory Examples. Definition and Examples: Calculational Techniques. Partitions of Integers. Exponential Generating Functions. The Summation Operator. 9. Recurrence Relations. The First-Order Linear Recurrence Relation. 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). 10. Graph Theory and Applications. An Introduction to Graph Theory. Definitions and Examples. Subgraphs, Complements, and Graph Isomorphism. Vertex Degree: Euler Trails and Circuits. Planar Graphs. Hamilton Paths and Cycles. Graph Coloring and Chromatic Polynomials. 11. Trees. Definitions, Properties, and Examples. Rooted Trees. Trees and Sorting Algorithms. Weighted Trees and Prefix Codes. Biconnected Components and Articulation Points. 12. Optimization and Matching. Dijkstras Shortest Path Algorithm. Minimal Spanning Trees. Transport Networks: The Max-Flow Min-Cut Theorem. Matching Theory. 13. Modern Applied Algebra. Rings and Modular Arithmetic. The Ring Structure: Definition and Examples. Ring Properties and Substructures. The Integers Modulo n. Ring Homomorphisms and Isomorphisms. 14. Boolean Algebra and Switching Functions. Switching Functions: Disjunctive and Conjunctive Normal Forms. Gating Networks: Minimal Sums of Products: Karnaugh Maps. Further Applications: Dont Care Conditions. The Structure of a Boolean Algebra (Optional). 15. Groups, Coding Theory, and Polyas Method of Enumeration. Definition, Examples, and Elementary Properties. Homomorphisms, Isomorphisms, and Cyclic Groups. Cosets and Lagranges Theorem. Elements of Coding Theory. The Hamming Metric. The Parity-Check and Generator trices. Group Codes: Decoding with Coset Leaders. Hamming Matrices. Counting and Equivalence: Burnsides Theorem. The Cycle Index. The Pattern Inventory: Polyas Method of Enumeration. 16. Finite Fields and Combinatorial Designs. Polynomial Rings. Irreducible Polynomials: Finite Fields. Latin Squares. Finite Geometries and Affine Planes. Block Designs and Projective Planes. Appendices. Exponential and Logarithmic Functions. Matrices, Matrix Operations, and Determinants. Countable and Uncountable Sets. Solutions. Index.
「Nielsen BookData」 より