Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
8MATH440INTRODUCTION TO KNOT THEORY AND ITS APPLICATIONS3+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 To introduce fundamental notions of knot theory in undergraduate level.
Course Content Knots, knot invariants, topological spaces.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Dr.Öğr.Üyesi Neslihan GUGUMCU
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources On Knots, Louis Kauffman, Knot Theory, Collin Adams
knots
5 odev
2 ara sinav, 1 final

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 3 % 80
Quizzes 0 % 0
Homeworks 5 % 10
Other activities 0 % 0
Laboratory works 0 % 0
Projects 1 % 10
Final examination 0 % 0
Total
9
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 42 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 5 12 60
Exams and Exam Preparations 3 27 81
Total Work Load   Number of ECTS Credits 6 183

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To have knowledge about the fundemantal topics of knot theory
2 To have knowledge about the applications of knot theory in biology and chemistry.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Review of surfaces, manifolds The Knot Book, Colin Adams
2 Definition of a smooth knot The Knot Book, Colin Adams
3 Basic knot invariants The Knot Book, Colin Adams
4 Coloring knots The Knot Book, Colin Adams
5 Determinant of a knot The Knot Book, Colin Adams
6 Orientation on knots, linking number, writhe The Knot Book, Colin Adams
7 Kauffman bracket polynomial The Knot Book, Colin Adams
8 Chirality in knots and chemical molecules, reversion, mutation, Tait Conjectures The Knot Book, Colin Adams
9 Tangles The Knot Book, Colin Adams
10 Rational tangles and DNA The Knot Book, Colin Adams
11 Braids, Alexander and Markov Theorems The Knot Book, Colin Adams
12 Seifert surface and genus of a knot The Knot Book, Colin Adams
13 Alexander polynomial via the Seifert matrix The Knot Book, Colin Adams
14 Types of knots The Knot Book, Colin Adams


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
All 4 4 4 4 4 4 4 4 4 4 4 4
C1 4 4 4 4 4 4 4 3 3 4 4 4 4
C2 4 4 4 4 4 4 4 4 3 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=163341&lang=en