, 1

Discreet Mathematics Outline and Motivation

Lecture Notes on Discrete Mathematics (Comp233).Birzeit University, Palestine, 2015

mjarrar©2015

Mustafa Jarrar

Computer Science

Birzeit University, Palestine

mjarrar@birzeit.edu

http://www.jarrar.info

, 2

Watch this lecture and download the slides

Acknowledgement: This lecture is based on (but not limited to) to chapter 5 in “Discrete Mathematics with Applications by Susanna S. Epp (3rd Edition)”.

More Online Courses at: http://www.jarrar.infoCourse Page: http://www.jarrar.info/courses/DMath/

, 3

Video: Math is Fun

https://www.youtube.com/watch?v=_OHHrk0larQ

, 4

Video: History of Mathematics

https://www.youtube.com/watch?v=cy-8lPVKLIo

, 5

Video: We Use Math

https://www.youtube.com/watch?v=aYIv4jggQJc

, 6

Video: Real Life Math

https://www.youtube.com/watch?v=ahXIMUkSXX0

, 7

Welcome to

Most important mathematics for computing.

Essential to college-level mathematics and beyond

very much "real world" mathematics

Problem Solving skills

Logical Thinking skills

Analytical skills

Playing Games and Puzzles

Discrete math is fun

Discreet Mathematics at Birzeit University

, 8

What is Discrete Math

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

Such as: Logic and reasoning, number theory, sequences, set theory, functions, relations, graphs, and counting

, 9

Text Book

Discrete Mathematics with

Applications (4rd Edition), by

Susanna S. Epp. Brooks/Cole

Additional References:Discrete Mathematics with applications by Barnier & ChanDiscrete Mathematics and its Applications by Kenneth H. Rosen.Foundations of Computer Science by Aho and Ulman .

, 10

Outline

Chapter Sections Time

Outline and Motivation to Discrete

Mathematics

1

Ch.2 The Logic of Compound Statements

(Propositonal Logic)

2.1, 2.2, 2.3 4

Ch.3 The logic of quantified statements

(First Order Logic)

3.1, 3.2, 3.3 5

Ch.4 Number Theory & Proof Methods 4.1, 4.2, 4.3, 4.4 6

Ch.5 Sequences & Mathematical Induction 5.1, 5.2, 5.3 5

Midterm Exam

Ch.6 Set Theory 6.1, 6.2, 6.3 (+6.4 Agebra) 5

Ch.7 Functions 7.1, 7.2 3

Ch.8 Relations 8.1, 8.2, 8.3 5

Ch.9 Counting Theory 9.1, 9.2, 9.3, 9.5, 9.6 7

Ch.10 Graphs and Trees 10.1, 10.2 3

Final Exam

, 11

Course Objectives

To apply logically valid forms of argument and avoid logical

errors.

To employ both direct and indirect arguments to derive new

results from those already known to be true.

To work with symbolic representations as if they were concrete

objects.

To recursively think about problems and validate them using

mathematical induction.

To count random and chance events and compute the likelihood

of obtaining certain events in a sample space.

, 12

Evaluation

• Midterm exam 30%• Short Exams and Assignments 25%• Participation* 5%• Final Exam 40%

*Participation includes class attendance, contributions during lectures, and answering questions.

, 13

Student Responsibilities

Class participation and independent work. Students are expected to actively

participate in all classes and perform independent work.

Attendance. Attendance is mandatory. University regulations regarding this matter

will be strictly enforced.

Academic Honesty. Individual work must be each student’s own work. Plagiarism or

cheating will result in official University disciplinary review.

Missed Exams. There are no makeup exams.

Class Etiquette. Please keep all cell phones and other electronic devices turned off

during class. If your activities during class are deemed disruptive, you will be asked to

leave. Use of a personal computer during class is prohibited except for note taking with

Instructor permission.

Ritaj and Facebook: official communication through Ritaj. Students are assumed to

check Ritaj several times a day. A Facebook Group is created for (informal)

communication https://www.facebook.com/groups/115677325805515/