COURSE UNIT TITLE

: DISCRETE MATHEMATICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 1036 DISCRETE MATHEMATICS COMPULSORY 4 0 0 6

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course introduces students to the field of discrete and combinatorial mathematics. It aims to develop mathematical reasoning and problem solving skills through counting discrete structures and it also gives an opportunity to think algorithmically and to solve real world problems.

Learning Outcomes of the Course Unit

1   be able to use basic counting techniques
2   be able to formulate the principle of inclusion and exclusion and apply to the problems of counting
3   be able to identify recursive structures and solve their recurrence relations
4   be able to identify generating functions and apply to enumeration
5   be able to determine time complexity of basic searching and sorting algorithms

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 What is Discrete and Combinatorial Mathematics Examples of problems, The rules of sum and product Permutations and combinations, Pascal s identity, Binomial Theorem Sec. 1.1, 1.2, 5.5, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed.
2 Pascal s triangle identities, Vandermonde s identity, Permutations and with repetition, Multinomial Theorem, Combination with repetition, Pigeonhole principle Sec. 1.3, 1.4, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Sec. 4.3, 4.4 Discrete mathematics and its applications, K. Rosen 6th ed. Problem Set 1,
3 Principle of inclusion and exclusion, derangements and properties Sec. 8.1, 8.3, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed.
4 Principle of inclusion and exclusion counting onto functions and Stirling numbers, Euler phi function, counting primes Sec. 8.1, 8.3, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Sec. 7.5, 7.6 Discrete mathematics and its applications, K. Rosen 6th ed. Problem Set 2
5 Solutions of problem set 1 and set 2
6 Recursive definitions and solving linear recurrences, Fibonacci numbers Sec. 10.1,10.2, 10.3, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Sec. 7.2 Discrete mathematics and its applications, K. Rosen 6th ed. Problem Set 3
7 Solving nonhomogeneous linear recurrences, solutions of problem set 3. Sec. 10.1,10.2, 10.3, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed.
8 Special type of recurrences, Stirling numbers (first and second kind), Bell numbers Sec.10.5,10.6, 1.5, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Sec. 7.3 Discrete mathematics and its applications, K. Rosen 6th ed.
9 Mid-term Exam
10 Catalan numbers and applications, difference sequences, sum of powers of positive integers Sec.10.5,10.6, 1.5, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Sec. 7.3 Discrete mathematics and its applications, K. Rosen 6th ed.
11 Divide and conquer algorithms, Generating functions, exponential generating functions, convolution sequences Sec.10.6, 9.1, 9.2 Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Problem Set 4
12 Solving recurrence relations by the method of generating functions, integer partitions, solutions of problem set 4 Sec. 9.3,9.4, 10.4, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed.
13 Growth of functions, big O and big notation, time complexity, Sec. 5.7,5.8, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Sec. 3.1, 3.2 Discrete mathematics and its applications, K. Rosen 6th ed.
14 Binary search, bubble sort, insertion sort, merge sort and their time complexity. Sec. 5.7,5.8, Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. Sec. 3.1, 3.2 Discrete mathematics and its applications, K. Rosen 6th ed. Problem Set 5

Recomended or Required Reading

Textbook(s):

Ralph P. Grimaldi, Discrete and Combinatorial Mathematics. 5th edition, Pearson, 2004.

Supplementary Book(s):

Kenneth Rosen, Discrete Mathematics and Its Applications. Eighth edition, McGraw-Hill Education, 2019.

Polya, G. How to Solve It. A new aspect of mathematical method. Expanded version of the 1988 edition, with a new foreword by John H. Conway. Princeton University Press, 2004.

References:
Materials: Lecture notes and problems will be given in the class

Planned Learning Activities and Teaching Methods

Face to face and presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.30 + ASG * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

celalcem.sarioglu@deu.edu.tr
Tel: (232) 30 18585

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparations before/after weekly lectures 13 2 26
Preparation for midterm exam 1 25 25
Preparation for final exam 1 28 28
Preparing assignments 3 5 15
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 150

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.15544
LO.25534
LO.345544
LO.444444
LO.5445444

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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