介紹離散數學的數學理論及其應用

Introduction to the mathematical theory and its application of dispersed mathematics

本課程為大學部三年級之必修課程，本課程除了教授學生們已知的數學外還教導學生們如何利用數理邏輯方法進行分析，建立出適當的模式，再發展出一個有效率的演算法來解決相關的問題。
本課程共有四個主要教學主題，分別為(一)教學推論(含基本運算和證明建構方法)、(二)組合學分析、(三)離散結構(含圖論)、(四)演算法
本課程教授上述四個主題之外，也強調相關的應用，例如使用基本整數論和知識，發展出和模算數相關演算法(如超大整數的四則運算)，在進行RSA譯碼學分析。
學生們順利修讀本課程後，除了可以學習到一些數學的知識外，更重要的是建立符合邏輯的數理分析與推論態度與方法，碰到實務問題時，可以順利解析問題的重點，再運用或發展合宜的模式與演算法解決問題。

This course is a three-year compulsory course in the university department. In addition to teaching students known mathematics, this course also teaches students how to use mathematical logic methods to analyze, establish an appropriate model, and develop an efficient algorithm to solve related problems.
There are four main teaching topics in this course, namely (1) teaching recommendations (including basic calculation and certification construction methods), (2) combined analysis, (3) dispersion structure (including diagrams), and (4) algorithms
In addition to teaching the above four topics, this course also emphasizes related applications, such as using basic integers and knowledge, developing algorithms related to modular algorithms (such as four calculations of super-large integers) to conduct RSA translation analysis.
After students successfully read this course, in addition to learning some mathematical knowledge, it is more important to establish logically numerical analysis and recommendation attitudes and methods. When encountering practical problems, they can successfully analyze the key points of the problem, and then use or develop appropriate models and algorithms to solve the problem.

參考書籍
1. Kenneth H. Rosen, Discrete Mathematics and Its Applications
2. Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction

Reference Books
1. Kenneth H. Rosen, Discrete Mathematics and Its Applications
2. Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction