COURSE UNIT TITLE

: DISCRETE MATHEMATICS AND ITS APPLICATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
FPE 0059 DISCRETE MATHEMATICS AND ITS APPLICATIONS ELECTIVE 3 0 0 5

Offered By

Faculty Of Science

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Chemistry
Biology
Computer Science
Statistics
Faculty Of Science
Physics
Mathematics

Course Objective

This course 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 applied mathematics problems.

Learning Outcomes of the Course Unit

1   be able to use basic counting techniques
2   be able to apply the principle of inclusion and exclusion
3   be able to solve recursive structures
4   be able to understand Euclid s algorithm and Fermat s Little Theorem
5   be able to use basic codes (RSA)

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 How to solve it
2 Permutations, combinations, Pascal identity, Binomial Theorem
3 Vandermonde s identity, Permutations and with repetition, Multinomial Theorem, Combination with repetition, Pigeonhole principle
4 Principle of inclusion and exclusion Applications
5 Solving linear recurrences
6 Solving nonhomogeneous linear recurrences
7 Fibonacci, Stirling, Catalan numbers
8 Mid-term Exam
9 Phythegorean triples geometric point of view
10 Divisibility, Euclid s algorithm
11 Prime numbers, Mersenne primes, perfect numbers
12 Congruences, Powers, and Fermat s Little Theorem
13 Euler's Phi Function and the Chinese Remainder Theorem
14 Unbreakable Codes (RSA)

Recomended or Required Reading

1. Discrete mathematics and its applications, K. Rosen 6th ed. ISBN 9780073229720.
2. Discrete and Combinatorial Mathematics, R. Grimaldi 5th ed. ISBN 9780201726343.
3. Joseph Silverman, A Friendly Introduction to Number Theory, Fourth Edition - ISBN: 978-0-321-81619-1 2012 Pearson Education

Planned Learning Activities and Teaching Methods

presentation, problem solving, questions-answers

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 QUZ QUIZ
3 FIN FINAL EXAM
4 FCGR FINAL COURSE GRADE (RESIT) 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)

Asst.Prof.Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Tel: (+90 232) 30 18585

Office Hours

To be announced

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 12 2 24
Preparation for midterm exam 1 20 20
Preparation for final exam 1 20 20
Preparation for quiz etc. 3 5 15
Midterm 1 2 2
Quiz etc. 3 1 3
Final 1 2 2
TOTAL WORKLOAD (hours) 125

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.111311212111111
LO.211311212111111
LO.311311212111111
LO.411411212111111
LO.511311313111111

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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