Course Name Code Semester T+U Hours Credit ECTS
Knot Theory II MAT 594 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 Teoris II course aims to make students comprehend the topics that provide a basis for the studies of graduate and PhD students working in algebraic and geometric topology in the field of topology.

Course Content

The basic concepts of Knot theory, Surfaces and Knots, the nature of a knot and Euler character, Seifert matrix, S-tuple of Sefart matrices, Invariants from Seifert matrix, Alexander polynomial, Convay polynomial, One knot sign, Tor knots, Classification of Tor knots, Satellite knots, knots, manifolds formed from knots,, cover spaces, revolving cover space of a knot, Alexander theorem.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 Define the basic concepts ofknot theory Lecture, Testing,
2 Knows the properties of knotted surfaces Lecture, Testing,
3 Returns the polynomial invariants of the knot5 Lecture, Testing,
4 Learn knots invariates from knots manifolds Lecture, Testing,
Week Course Topics Preliminary Preparation
1 The basic concepts of knot theory
2 Surfaces and knots
3 The genus and the Euler character of a knot
4 Seifert Matrix, S-equation of Sefart matrices
5 Alexander polynomial
6 Convay polynomial
7 Sign of a knot
8 Torus knots
9 Classification of Torus knots
10 Satellite knots, hyperbolic knots
11 Manifolds created from knots
12 Cover spaces
13 revolving cover space of a knot
14 Alexander theorem
Course Notes <p>1. G. Burde and H. Ziezchang, Knots; de Grudyer, Berlin, 1986.<br /> 2. L.Kauffman, On knots, Princeton University Pres, Princeton,New Jersay, 1987<br /> 3. K. Murasugi, (translen by B. Kurpita), Knot theory and ıts applications, Birkhauser, Boston,Basel,Berlin, 1996.<br /> 4. A. Kawauchi, A survey of Knot Theory, Birkhauser, Boston, 1996.</p>
Course Resources

1. C.C.Adams,The knot book, W.H. Freeman and Company , New York, 1999.
2. D. Rolfsen, Knots and Links, Math. Lecture series 7, Publ. Of Perish, 1976.
3. L.Kauffman, Knots and physics, World Scientific Pub., 1991.

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.
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