Course Name Code Semester T+U Hours Credit ECTS
Knot Theory and Its Applications MAT 629 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Doç.Dr. İSMET ALTINTAŞ
Course Lecturers
Course Assistants
Course Category
Course Objective

The aim of this course is to provide the students with a high level knowledge base on the work of the graduate and PhD students working in the field of topology, especially Geometrical topology and Algebraic topology, and to give the applications of mechanics, quantum physics, chemistry and biology ofknot theory.

Course Content

Jones polynomials, Jones polynomials, bracket polynomials, Kauffman polynomials, Homfly polynomials, polynomials of alternate knots, classical knots invariants and skein polynomials, theorems, and knot groups, knots and braids, knit indexes, , Statistical mechanics and nodes, 6-corner model, Partial function for braids, Graphs and graphs, Graph polynomials, Singular knots, Vassiliev invariants, Cord diagrams, knot structure of DNA , Virtual Knots.

 

# Course Learning Outcomes Teaching Methods Assessment Methods
Week Course Topics Preliminary Preparation
1 Tangles, rational tangles
2 2-bridged knots, rational knots
3 Braid Theory, Braid Groups
4 Knots and braids
5 Jones polynomials
6 bracket polynomials
7 Kauffman polynomials
8 Homfly polynomials
9 polynomials of alternate knots
10 classical knots invariants and skein polynomials
11 Statistical mechanics and nodes, 6-corner model
12 Partial function for braids
13 graph polynomials, singular nodes, Vassiliev invariants
14 Cord diagrams, knot structure of DNA, High-grade knot
Resources
Course Notes <p>1. D. Rolfsen, Knots and Links, Math. Lecture series 7, Publ. Of Perish, 1976.<br /> 2. L.Kauffman, Knots and physics, World Scientific Pub., 1991.<br /> 3. K. Murasugi, (translen by B. Kurpita), Knot theory and ıts applications, Birkhauser, Boston,Basel,Berlin, 1996.</p>
Course Resources

1. G. Burde and H. Ziezchang, Knots; de Grudyer, Berlin, 1986.
2 .L.Kauffman, On knots, Princeton University Pres, Princeton,New Jersay, 1987
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
iversity Pres, Princeton,New Jersay, 1987

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. 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