Discrete and Combinatorial Mathematics, An Applied Introduction ...

IZMIR UNIVERSITY OF ECONOMICS FACULTY OF COMPUTER SCIENCE DEPARTMENT OF COMPUTER & SOFTWARE ENGINEERING COURSE SEMESTER INSTRUCTOR E-MAIL CLASS SCHEDULE OFFICE AND PHONE OFFICE HOURS

Math 100 Discrete Mathematics Spring 2005-2006 Assis. Prof. Dr. Halil Oruç http://web.deu.edu.tr/halil.oruc/ [email protected] Wednesday 12:30-15:20 M505 Section 1-3. M431 Wednesday 8:30-11:20

COURSE OBJECTIVES This course is designed to study and investigate sets, relations, partially ordered sets, logic, algorithms, principles of counting, Boolean Algebra and Graph Theory. By the end of this course students are expected to • Gain enough mathematical thinking maturity to understand logic, discrete and algebraic structures • Appreciate how counting finite structures can be challenging • Be acquainted with the structure of graphs and apply the ideas to several subjects. TEXTBOOK Discrete Mathematics and its Applications, 5th edition, Kenneth H. Rosen, McGraw-Hill, ISBN: 0-07-289905-0 . FURTHER REFERENCES: Discrete and Combinatorial Mathematics, An Applied Introduction, 5th edition, R. P. Grimaldi, Addison-Wesley (1999), ISBN: 0-201-30424-4 Discrete Mathematics for Computer Scientists, 2nd edition J.K. Truss, Addison Wesley, (1999). ISBN: 0-201-36061-6. Introduction to Graph Theory, 4th edition, R. J. Wilson, Addison-Wesley Longman Ltd (1996). ISBN 0-582-24993-7 Concrete Mathematics, A Foundation For Computer Science, 2nd edition R. Graham, D. Knuth and O. Patashnik, Addison-Wesley (1995). ISBN 0-20-155802-5 Introductory Combinatorics 4th edition, R. Brualdi, Prentic Hall New Jersey, (2004). ISBN: 0-13-100119-1 Discrete Mathematics, N.L. Biggs, Clarendon Press (2002) ISBN 0198507178. I recommend you have the textbook and choose one more book in the references.

COURSE GRADING Course grades will be based on a weighted composite of performance evaluations in several areas: Midterm Exam Quizzes + HW + Class Final Exam

PERCENT 90-100 85-89 80-84 75-79 70-74 65-69 60-64 50-59 49 and below

40% 10% 50%

GRADE 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

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COURSE OUTLINE DATE 22.2 01.3

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TOPIC Logic and proofs, sets and functions Logic and proofs, sets and functions, method of proofs Growth of functions, algorithms and complexity, matrices Sequences, summations and induction Counting, permutations, combinations and binomial and multinomial coefficients Solving recurrence relations, divide and conquer algorithms Solving recurrence relations, divide and conquer algorithms Inclusion-Exclusion MIDTERM EXAM (may change) Relations, n-ary relations, recurrence relations Graphs, connectivity, Euler and Hamiltonian paths, shortest paths Planar graphs, graph coloring Trees, spanning trees, Application of Trees Trees, spanning trees, Application of Trees Boolean Functions

QUZZES -ASSIGMENTS There may be 2-3 brief quizzes, of one or two questions will happen about the topics covered. Each quiz takes about 15 minutes. The lowest grade of the quizzes (among them missed quizzes) will not be taken into account in the computation of the final course grade. No makeup quiz will be given in any circumstances.

Each section of text book has plenty of exercises. Some will be solved in the class and those that are not solved in the class will be given as assignments. You are strongly encouraged to solve by yourselves. “Mathematics is learnt by only doing and created by ideas”. RULES FOR ATTENDANCE: Attendance is an essential requirement of this course and is the responsibility of the student. Class begins promptly and you are expected to be present at the beginning and at the end of each class session. HOMEWORK POLICY: Homework problems are the best preparation for exams. You should try to work the homework problems without constant reference to the text or passively receiving help from others. I encourage to discuss problems with others, but you should try to do the actual problems yourself. If you have gotten the idea about how to solve a problem from another person or by looking things up in the text, try to do a related problem without outside aid. • • • •

The content of this syllabus can be changed by the instructor at any time by informing the related department’s head The student is supposed to be aware of the facts and notices written in this syllabus. The content of this syllabus can be changed by the instructor at any time by informing the related department’s head The student is supposed to be aware of the facts and notices written in this syllabus.