COURSE UNIT TITLE

: ENUMERATIVE COMBINATORICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5025 ENUMERATIVE COMBINATORICS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to give a broad introduction to combinatorial enumeration and to analyse combinatorial configurations .

Learning Outcomes of the Course Unit

1   1. Will be able to use basic counting techniques
2   2. Will be able to apply Inclusion-Exclusion
3   3. Will be able to use generating functions.
4   4. Will be able to enumerate finite structures.
5   5. Will be able to use symmetric functions.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Review of basic counting techniques
2 Inclusion Exlusion
3 Cylcles and inversion
4 Decents
5 Partition identites
6 Partition and q-binomail coefficients
7 Twelvefold way
8 Problems and discussion
9 Möbius invertion
10 Involution principle
11 Generating functions
12 Hypergeometric summation
13 Symmetric functions
14 Schur polynomials

Recomended or Required Reading

R. Stanley, Enumerative Combinatorics Vol I, Cambridge Stuies in Advanced Studies 49, 2nd ed. Cambridge University press, Cambridge 2012.
References:
M. Aigner, A course in Enumeration Graduate Text in Mathematics 238, Springer Verlag Berlin 2007.
M. Bona, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory (Fourth Edition), World Scientific, New Jersey 2017.

Planned Learning Activities and Teaching Methods

Lecture notes
Presentation
Problem solving

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 * 0.25 + ASG *0.25 +FIN *0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 + ASG *0.25 +RST *0.50


Further Notes About Assessment Methods

None

Assessment Criteria

Midterm, Assignement problems, Final exam

Language of Instruction

English

Course Policies and Rules

70 % attandence

Contact Details for the Lecturer(s)

e-mail: halil.oruc@deu.edu.tr
Office: (232) 301 85 77, B205
DEÜ Fen Fakültesi Matematik Bölümü Tınaztepe

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 13 4 52
Preparation for midterm exam 1 25 25
Preparation for final exam 1 30 30
Preparing assignments 1 20 20
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.14422233
LO.2443332433
LO.34533333433
LO.4443332433
LO.543224233

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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