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Discrete Mathematics and Its Applications Lecture 0: Course introduction MING GAO DASE @ ECNU (for course related communications) mgao@dase.ecnu.edu.cn Mar. 3, 2020 Outline Textbooks and References 1 Requirements and Assessment 2 Office

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Discrete Mathematics and Its Applications

Lecture 0: Course introduction MING GAO

DASE @ ECNU (for course related communications) mgao@dase.ecnu.edu.cn

Mar. 3, 2020

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Outline

1

Textbooks and References

2

Requirements and Assessment

3

Office Hour and Contact Information

4

Overview of This Course Course Schedule

5

Take-aways

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Textbooks and References

Important Dates for COVID-19 outbreak

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Textbooks and References

Required sources

Required sources Kenneth H. Rosen et al.: Discrete Mathematics and Its

Applications. (Seventh Edition

in Chinese) References

Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete Mathematics: a Foundation for Computer Science, 2nd ed., 1994. Chung Laung Liu, Elements of Discrete Mathematics, McGraw-Hill, 1985. Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, 5th ed., 2004.

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Requirements and Assessment

Requirements

1 Slides will be posted 1-2 days before lecture, but 2 Students are expected to

prepare lessons before class, including lecture content previewing, laptop, cell phone, and notebook, etc. take notes during lecture (no lecture note will be provided) read the assigned readings before and after the lecture address homework assignments individually think through the answers of tutorial (a set of questions) after every lecture

3 Examinations: monthly quiz, midterm, and final term (honestly

and independently) Course homepage: http://dase.ecnu.edu.cn/mgao/teaching/ DM_2020_Spring/DM.html Chaoxing Platform: http://ecnu.fanya.chaoxing.com/portal

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Requirements and Assessment

Grading policy

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Office Hour and Contact Information

Contact information

Lecturer: GAO Ming—- Office: Rm. East 115, Math. Building Phone: 6223 2061 Mobile: 189 1694 3299 Email: mgao@dase.ecnu.edu.cn Research focus:

Computional education Knowledge graph and knowledge engineering Data mining and machine learning

Teaching assistant: Shu Zheng—- Office: Rm. East 110, Math. Building Email: shzheng@stu.ecnu.edu.cn

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Overview of This Course

It’s like learning a new language

E0 = M0C 2. Do you remember the time when you start learning English? There are a few things you have to learn and get used to. They might not make so much sense in the beginning, but over time, you will get comfortable with how the language is used. As your knowledge of the language gets better, everything becomes more natural. Learning a new language sometimes expands your view of the world. I hope it is also true with this course.

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Overview of This Course

The goals of this course

There are three goals: To learn how to make mathematical arguments. To learn various fundamental mathematical concepts that are very useful in computer science. To learn how to model a real problem in mathematical manner.

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Overview of This Course Course Schedule

Why care about discrete mathematics?

Digital computers are based on discrete atoms (bits) Therefore, both a computer’s

structure (circuits)

perations (execution of algorithms)

can be described by discrete mathematics.

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Overview of This Course Course Schedule

Discrete mathematics

Discrete mathematics Study of mathematics structures and objects that are fundamentally discrete rather than continuous. Examples of objects with discrete values are integers, graphs,

r statements in logic

Discrete mathematics and computer science Concepts from discrete mathematics are useful for describing objects and problems in computer algorithms and programming languages. It can be applied to many applications, such as cryptography, au- tomated theorem proving, and software development, etc.

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Overview of This Course Course Schedule

Examples

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Overview of This Course Course Schedule

Examples Cont’d

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Overview of This Course Course Schedule

Course syllabus

Tentative topics

1 Logic and proofs 2 Sets 3 Functions 4 Sequences 5 Counting 6 Probability 7 Relations 8 Graphs MING GAO (DaSE@ecnu) Discrete Mathematics and Its Applications

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Take-aways

Advices to learning DM Not a reading course. More than a mathematics course, it is therefore workload-heavy. Course homepage Course homepage: http://dase.ecnu.edu.cn/mgao/ teaching/DM_2020_Spring/DM.html

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