▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Advanced topics in Geometry F
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Nosaka Takefumi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6(H104)
- Group
- -
- Course number
- MTH.B502
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 2Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
I give a lecture as an introduction to quandle theory.
In this course, we study basics of quandle, coloring, quandle homology, and applications to low-dimensional topology. This course follows from the reference below.
Student learning outcomes
・Study examples of quandles, and some relations to homogenous set.
・Study the relations to knot theory
・Study the construction of knot-invariants from quandles.
・Give some easy computation of the invariant we studied
Keywords
Quandle, knot, homology, coloring, homology
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Definitions and examples of quandles | Details will be provided during each class session |
| Class 2 | Associated group and basic properties of quandles | Details will be provided during each class session |
| Class 3 | Coloring I; Definitions and example | Details will be provided during each class session |
| Class 4 | Coloring II; examples | Details will be provided during each class session |
| Class 5 | Quandle cocycle invariant | Details will be provided during each class session |
| Class 6 | Quandle homology | Details will be provided during each class session |
| Class 7 | Applications of Quandle cocycle invariant | Details will be provided during each class session |
Textbook(s)
T. Nosaka, Quandles and Topological Pairs; Symmetry, Knots, and cohomology, Springer briefs
Reference books, course materials, etc.
T. Nosaka, Quandles and Topological Pairs; Symmetry, Knots, and cohomology, Springer briefs
Assessment criteria and methods
By reporting assignments
Related courses
- MTH.B341 ： Topology
- MTH.B505 ： Advanced topics in Geometry E1
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Although this course is independent of MTH.B505 ： Advanced topics in Geometry E1, it is better to attend the course E1.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
nosaka[at]math.titech.ac.jp
Office hours
N/A.
Contact by E-mails, or at the classroom.
Other
Not in particular
