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 c) False b) False d) True 11 / 19
Homework Write something for every subquestion! Question: Which of the following is true? a) Ture c) False b) 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 c) False b) 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 Discrete ◮ Between two different ◮ There are two different objects is always a third. objects without a third in between. Examples: Examples: ◮ real numbers R ◮ 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
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