Discrete Structures Summer 2016 This Class Textbook Kenneth H. - - PowerPoint PPT Presentation

Discrete Structures

Summer 2016

This Class

Textbook

Kenneth H. Rosen Discrete Mathematics and Its Applications, 7th edition, McGraw-Hill Also available as PDF (without DRM) Not necessary, but helpful

3 / 19

Course Requirements

Homework 25 % First Exam 25 % June 30, during class Second Exam 25 % July 21, during class Final Exam 25 % Aug 4, during class

4 / 19

Course Requirements

Homework

◮ includes extra credit problems (EC) ◮ one %-value for each homework ◮ at the end: average of %-values

Exams

◮ closed book examination ◮ one handwritten sheet (one side) allowed

5 / 19

Attendance

Attendance is not required, but I highly recommend it.

If you are in class...

◮ Participating in class: Awesome ◮ Just listening or doing nothing: Ok ◮ Disrupting the class: Not ok

6 / 19

Office Hours

By arrangement. Room 352, Math and CS Building

◮ Send me an email. ◮ Please tell me directly when you have time to meet.

7 / 19

Website and Contact

Website

◮ www.cs.kent.edu/∼aleitert/summer15/ ◮ Important information ◮ Slides ◮ Homework

Email

◮ aleitert@cs.kent.edu

8 / 19

Tips

Homework

◮ Do it! ◮ Do it by your self.

If you do it in groups...

◮ Do it in small groups. ◮ First try it alone, then discus your approaches. ◮ Talk about the approach, not the solution.

10 / 19

Homework

Write something for every subquestion!

11 / 19

Homework

Write something for every subquestion! Question: Which of the following is true? a) Ture b) False c) False d) True

11 / 19

Homework

Write something for every subquestion! Question: Which of the following is true? a) Ture b) False c) False d) True Partial credit answer: a, d My comment: What is with b) and c)?

11 / 19

Homework

Write something for every subquestion! Question: Which of the following is true? a) Ture b) False c) False d) True Partial credit answer: a, d My comment: What is with b) and c)? Full credit answers:

◮ a, d but not b, c ◮ Only a, b ◮ a, b, the others are false

11 / 19

General Tips

◮ Know the basics

◮ Types of numbers: N, Z, Q, R ◮ Prime numbers ◮ Variables ◮ Basic functions ◮ ...

◮ Come to class (and participate). ◮ Do odd number problems. ◮ Ask questions.

◮ Good question: What is a right approach for this problem? ◮ Better question: Where is the mistake in my approach? ◮ Feel free to interrupt me in class if you have a question. 12 / 19

Discrete Mathematics

What is Discrete Mathematics?

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. Wikipedia

14 / 19

What is Discrete Mathematics?

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. Wikipedia Difference between discreet and continuous?

14 / 19

What is Discrete Mathematics?

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. Wikipedia

Continuous

◮ Between two different

• bjects is always a third.

Examples:

◮ real numbers R ◮

Discrete

◮ There are two different

• bjects without a third in

between. Examples:

◮ natural numbers N ◮

14 / 19

Topics in discrete mathematics

Logic: artificial intelligence (AI), circuit design, puzzles Combinatorics: probability, analysis of algorithm Graph theory: networks, data structures, path finding Number theory: cryptography

15 / 19

Logic

Artificial intelligence Circuit design Puzzles

16 / 19

Combinatorics

How many combination/permutations exist? How many steps are needed to sort n numbers?

17 / 19

Graph theory

What is the best path? What is the best drawing? (circuit design) Which nodes are important in a (social) network?

18 / 19

Number theory

Cryptography

19 / 19