Course Name Code Semester T+U Hours Credit ECTS
Knot Theory I MAT 593 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. İSMET ALTINTAŞ
Course Lecturers
Course Assistants
Course Category
Course Objective

Knot Theory I course aims to comprehend basic topics which are the bases for the studies of Master and PhD students working in topology algebraic topology, knot theory and related fields.
In this course, classical mathematical concepts are given with a modern approach.

Course Content

Fundamental concepts of knot theory, simple knot movements, rings, knot diagrams, regular diagrams and alternate knots, knot graphs, basic problems of knot theory, global problems, local problems, classical knot invariants, Reidemeister movements, minimum intersection number, torsion number , number of bridges, number of unknots, number of rings, number of colors, knot groups.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She learns the simple moves of knot diagrams Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Self Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Basic concepts of knot theory
2 Simpleknot movements, knot equations, Rings
3 Knot tables, Regular diagrams and alternate diagrams
4 Knot graphs
5 Simple problems of knot theory, Global problems,
6 Local problems
7 Classical knot invariants, Reidemeister movements, minimum number of intersections
8 Number of bridges, Number of non-knotting, Number of ringing, Number of torsion
9 Colors
10 Knot groups, tunnel neighborhood
11 Dehn representation, Wirtinger representation
12 Meridians and paralels
13 Surgical manifolds
14 Homotopy and homology groups of surgical manifolds
Resources
Course Notes <p>1.D. Rolfsen, Knots and Links, Math. Lecture series 7, Publ. Of Perish, 1976.<br /> 2.G. Burde and H. Ziezchang, Knots; de Grudyer, Berlin, 1986.<br /> 3.L.Kauffman, On knots, Princeton University Pres, Princeton,New Jersay, 1987</p>
Course Resources

1.L.Kauffman, Knots and physics, World Scientific Pub., 1991.
2.K. Murasugi, (translen by B. Kurpita), Knot theory and ıts applications, Birkhauser, Boston,Basel,Berlin, 1996.
3.A. Kawauchi, A survey of Knot Theory, Birkhauser, Boston, 1996.
4.C.C.Adams,The knot book, W.H. Freeman and Company , New York, 1999

Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Ödev 30
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 14 14
Assignment 1 14 14
Final examination 1 14 14
Total Workload 138
Total Workload / 25 (Hours) 5.52
dersAKTSKredisi 6