計算機數學

Computer Mathematics

學期

109-2

學分

3 學分

當期課號

2910

永久課號

SET1309

開課單位

系統工程與科技學士學位學程

授課教師

系統工程與科技學程

類別

選修

上課時間表

節	週一
6 14:20–15:10	計算機數學 3 節連堂
7 15:30–16:20
8 16:30–17:20

* 根據陽明交大上課時間表所列

概述

創新與運用資訊科技及數學知識的能力。執行資訊科技實務所需技術、技巧及使用工具的能力。發掘、分析及處理問題的能力。

先修科目

離散數學

評分方式

小考、期中考、期末考、作業

週次計畫

週次

主題

第 1 週

1. Ch6. Languages: Finite State Machines • Languages: The Set Theory of Strings • Finite State Machine: A First Encounter • Finite State Machine: A Second Encounter 2. Ch7. Relation: 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 3. Ch8. The Principle of Inclusion and Exclusion • The Principle of Inclusion and Exclusion • Generalizations of the Principle • Derangements: Nothing Is in Its Right Place • Rook Polynomials • Arrangements with Forbidden Positions 4. Ch9. Generating Functions • Introductory Examples • Definition and Examples: Calculational Techniques • Partitions of Integers • The Exponential Generating Function • The Summation Operator 5. Ch10. PRecurrence Relations • The First-Order Linear Recurrence Relation • The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients • The Nonhomogeneous Recurrence Relation • The Method of Generating Functions • A Special Kind of Nonlinear Recurrence Relation • Divide-and-Conquer Algorithms 6. Ch13. Optimization and Matching • Dijkstra’s Shortest-Path Algorithm • Minimal Spanning Trees: The Algorithms of Kruskal and Prim • Transport Networks: The Max-Flow Min-Cut Theorem • Matching Theory 7. Ch14. Rings and Modular Arithmetic • The Ring Structure: Definition and Examples • Ring Properties and Substructures • The Integers Modulo n • Ring Homomorphisms and Isomorphisms 8. Ch16. Groups, Coding Theory, and Polya’s Method of Enumeration • Definition, Examples, and Elementary Properties • Homomorphisms, Isomorphisms, and Cyclic Groups • Cosets and Lagrange’s Theorem • The RSA Cryptosystem • Elements of Coding Theory • The Hamming Metric • The Parity-Check and Generator Matrices • Group Codes: Decoding with Coset Leaders • Hamming Matrices • Counting and Equivalence: Burnside’s Theorem • The Cycle Index • The Pattern Inventory: Polya’s Method of Enumeration•

教科書

Discrete and Combinatorial Mathematics, 5ed