Discrete Mathematics ( 離散數學 ) Ming-Jer Tsai

Outline What is Discrete Mathematics? Why learn Discrete Mathematics? What will be taught in the class? How to grade?

What is Discrete Mathematics? Discrete Math. VS Continuous Math.  The objects studied in Continuous Math. – such as real numbers – vary smoothly. Topics includes calculus, etc.  The objects studied in Discrete Math. – such as integers, graphs, and statements in logic – do not vary smoothly. Topics includes probability, set theory, etc.

Why Learn Discrete Mathematics? Research in discrete mathematics increased due to the development of digital computers which operate in discrete steps and store data in discrete bits. [From Wikipedia] Concepts from discrete mathematics are useful in studying problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. [From Wikipedia]

What will be taught in the class? Selected topics in the following chapters:  Chap. 2 Fundamentals of Logic  Chap. 5 Relations and Functions  Chap. 7 Relations: The Second Time  Chap. 9 Generating Functions  Chap. 10 Recurrence Relations  Chap. 11 Introduction to Graph Theory  Chap. 12 Trees  Chap. 13 Optimization and Matching  Chap. 16 Groups

Grades Attendance and Discussion (10%) 12 Quizzes (3/4, 3/11, 3/18, 3/25, 4/1, 4/29, 5/6, 5/13, 5/20, 5/27, 6/3, 6/10) (30%) Mid term (4/15) (30%) Final Exam (6/17) (30%)

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