Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH409ADVANCED TOPICS İN COMBINATORICS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The goal of this course is to further the knowledge of mathematics students in Combinatorics and give them the necessary knowledge for independent research. Moreover, it aims to further improve and develope the skill of Computer Engineering, Bioinformatic and Electronics students to apply Combinatorial tools in their own reseach problems.
Course Content Advanced Topics Combinatorics
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. BERKANT USTAOĞLU
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 1 % 20
Quizzes 0 % 0
Homeworks 6 % 60
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 20
Total
8
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 3 14 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 14 6 84
Exams and Exam Preparations 6 10 60
Total Work Load   Number of ECTS Credits 6 186

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 The ability to understand and apply mathematical techniques for solving problems.
2 To model and solve practical problems with the assistance of mathematical tools.
3 To identify some hard problems in computer science and discrete mathematics.
4 To be able to prove basic discrete mathematics theorems


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Bijections, decompositions, weights R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
2 Generating functions R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
3 Composition and differentiation lemmas R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
4 Algebra of formal power series R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
5 Strings on finite alphabets, unique factorization of strings R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
6 Integer partitions R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
7 Ferrehs graph, Durfee square R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
8 Partitions with distinct parts, self conjugate partitions R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
9 Inversion in permutations R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
10 Exponential generating functions, sum and product rules R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
11 Lagrange implicit function theorem R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
12 Topics in combinatorics of sequences R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
13 Topics in combinatorics of exponential generating functions R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
14 Topics in lattices and posets R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
15 Final 1st week R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press
16 Final 2nd week R. Stanley “Enumerative Combinatorics” volume I and II, Cambridge University Press


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 1 4 3 2 1 4 4 1 2 4 2
C2 4 4 2 4 1 3 2 4 4 4 2
C3 4 4 4 2 3 3 4 2 1 4 4 2
C4 4 1 2 1 4 4 4 4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163207&lang=en