Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
KNOT THEORY AND ITS APPLICATIONS MAT 629 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. İSMET ALTINTAŞ Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı 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. Dersin İçeriği 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.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - 1 - 2 - 3 - 4 - 8 - 14 - 15 - A - C - 2 - 1 - 2 - 3 - 4 - 8 - 14 - 15 - A - C - 3 - 1 - 2 - 3 - 4 - 8 - 14 - 15 - A - C - 4 - 1 - 2 - 3 - 4 - 8 - 14 - 15 - A - C - 5 - 1 - 2 - 3 - 4 - 8 - 14 - 15 - A - C - 6 - 1 - 2 - 3 - 4 - 14 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 8:Group Study 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
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

#### Kaynaklar

Ders Notu

1. D. Rolfsen, Knots and Links, Math. Lecture series 7, Publ. Of Perish, 1976.
2. L.Kauffman, Knots and physics, World Scientific Pub., 1991.
3. K. Murasugi, (translen by B. Kurpita), Knot theory and ıts applications, Birkhauser, Boston,Basel,Berlin, 1996.

Ders Kaynakları

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

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
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

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
Odev 1 30
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
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
Toplam İş Yükü 138
Toplam İş Yükü /25(s) 5.52
Dersin AKTS Kredisi 5.52
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