discrete structures - kent state universityaleitert/fall14/slides/dsintro.pdftextbook kenneth h....
TRANSCRIPT
![Page 1: Discrete Structures - Kent State Universityaleitert/fall14/slides/dsIntro.pdfTextbook Kenneth H. Rosen Discrete Mathematics and Its Applications, 7th edition, McGraw-Hill Also available](https://reader030.vdocuments.us/reader030/viewer/2022040211/5e66cb09ebcbd84c95364c07/html5/thumbnails/1.jpg)
Discrete Structures
Fall 2014
![Page 2: Discrete Structures - Kent State Universityaleitert/fall14/slides/dsIntro.pdfTextbook Kenneth H. Rosen Discrete Mathematics and Its Applications, 7th edition, McGraw-Hill Also available](https://reader030.vdocuments.us/reader030/viewer/2022040211/5e66cb09ebcbd84c95364c07/html5/thumbnails/2.jpg)
This Class
![Page 3: Discrete Structures - Kent State Universityaleitert/fall14/slides/dsIntro.pdfTextbook Kenneth H. Rosen Discrete Mathematics and Its Applications, 7th edition, McGraw-Hill Also available](https://reader030.vdocuments.us/reader030/viewer/2022040211/5e66cb09ebcbd84c95364c07/html5/thumbnails/3.jpg)
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
Homework 30 %First Exam 20 % September 18, during classSecond Exam 20 % October 9, during classThird Exam 15 % October 30, during classFinal Exam 15 % Friday, December 12, 7:45 – 10:00 a. m.
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/fall2014/
I Important information
I Slides
I Homework
EmailI [email protected]
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Tips
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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
10 / 18
![Page 13: Discrete Structures - Kent State Universityaleitert/fall14/slides/dsIntro.pdfTextbook Kenneth H. Rosen Discrete Mathematics and Its Applications, 7th edition, McGraw-Hill Also available](https://reader030.vdocuments.us/reader030/viewer/2022040211/5e66cb09ebcbd84c95364c07/html5/thumbnails/13.jpg)
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
10 / 18
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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?
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Discrete Mathematics
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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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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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