Discrete Structures

Spring 2015

This Class

Textbook

Kenneth H. RosenDiscrete Mathematics and ItsApplications,7th edition, McGraw-Hill

Also available as PDF(without DRM)

Not necessary, but helpful

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Course Requirements

Option 1

Homework 25 %First Exam 25 % February 4, during classSecond Exam 25 % February 25, during classThird Exam 25 % March 18, during classFinal Exam 25 % Friday, May 8, 10:15 a. m. – 12:30 p. m.I will ignore the worst of them.

Option 2

First Exam 20 % February 4, during classSecond Exam 20 % February 25, during classThird Exam 20 % March 18, during classForth Exam 20 % April 22, during classFinal Exam 40 % Friday, May 8, 10:15 a. m. – 12:30 p. m.I will ignore the worst of them. (Final counts as two 20 % exams.)

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Course Requirements

HomeworkI includes extra credit problems (EC)

I one %-value for each homework

I at the end: average of %-values

ExamsI closed book examination

I one handwritten sheet (one side) allowed

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Attendance

Attendance is not required, but I highly recommend it.

If you are in class...I Participating in class: Awesome

I Just listening or doing nothing: Ok

I Disrupting the class: Not ok

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Office Hours

Tuesday and Thursday, 2.00 – 3.00 p. m.Room 352, Math and CS Building

“I have class during office hours”I Send me an email. We will find some time.

I Please tell me directly when you have time to meet.

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Website and Contact

WebsiteI www.cs.kent.edu/∼aleitert/spring15/

I Important information

I Slides

I Homework

EmailI aleitert@cs.kent.edu

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Tips

Homework

I Do it!

I Do it by your self.

If you do it in groups...I Do it in small groups.

I First try it alone, then discus your approaches.

I Talk about the approach, not the solution.

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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, dMy comment: What is with b) and c)?

Full credit answers:

I a, d but not b, c

I Only a, b

I a, b, the others are false

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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, dMy comment: What is with b) and c)?

Full credit answers:

I a, d but not b, c

I Only a, b

I a, b, the others are false

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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, dMy comment: What is with b) and c)?

Full credit answers:

I a, d but not b, c

I Only a, b

I a, b, the others are false

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, dMy comment: What is with b) and c)?

Full credit answers:

I a, d but not b, c

I Only a, b

I a, b, the others are false

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General Tips

I Know the basicsI Types of numbers: N, Z, Q, RI Prime numbersI VariablesI Basic functionsI ...

I Come to class (and participate).

I Do odd number problems.I Ask questions.

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

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Discrete Mathematics

What is Discrete Mathematics?

Discrete mathematics is the study of mathematical structures thatare fundamentally discrete rather than continuous.

Wikipedia

ContinuousI Between two different

objects is always a third.

Examples:

I real numbers RI

DiscreteI There are two different

objects without a third inbetween.

Examples:

I natural numbers NI

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What is Discrete Mathematics?

Discrete mathematics is the study of mathematical structures thatare fundamentally discrete rather than continuous.

Wikipedia

Difference between discreet and continuous?

ContinuousI Between two different

objects is always a third.

Examples:

I real numbers RI

DiscreteI There are two different

objects without a third inbetween.

Examples:

I natural numbers NI

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What is Discrete Mathematics?

Discrete mathematics is the study of mathematical structures thatare fundamentally discrete rather than continuous.

Wikipedia

ContinuousI Between two different

objects is always a third.

Examples:

I real numbers RI

DiscreteI There are two different

objects without a third inbetween.

Examples:

I natural numbers NI

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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

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Logic

Artificial intelligence Circuit design Puzzles

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Combinatorics

How many combination/permutations exist?

How many steps are needed to sort n numbers?

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Graph theory

What is the best path?

What is the best drawing? (circuit design)

Which nodes are important in a (social) network?

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Number theory

Cryptography

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