WSA71001 Special Lectures in Mathematics

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program

Lecture Code WSA71001 Subject Classification Specialized Education

Subject Name 数学特別講義（カンドルと結び目不変量）

Subject Name
（Katakana）スウガクトクベツコウギ

Subject Name in
English Special Lectures in Mathematics

Instructor To be announced.,MURAO TOMO

Instructor
(Katakana) タントウキョウインミテイ,ムラオ　トモ

Campus Higashi-Hiroshima Semester/Term 1st-Year, First Semester, First Semester

Days, Periods, and Classrooms (1st) Inte：SCI E209

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Credits 1.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 5 : Graduate Basic

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Quandle, Knot, Knot invariant

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)

Class Objectives
/Class Outline Algebraic structures known as quandles, which are well suited to knot theory, have been actively studied in recent years. In this course, we explain the fundamental aspects of quandle theory, with particular emphasis on its relationship to knot theory. Specifically, the course has the following three objectives:
(1) to understand that the axioms of a quandle provide an algebraic formulation of the Reidemeister moves of knot diagrams;
(2) to understand that knot invariants derived from quandle theory arise as natural extensions of the classical notion of 3-colorability of knots; and
(3) to learn how to compute invariants for concrete knots using simple quandles and their
cocycles.

Class Schedule lesson1 Review of knot theory
lesson2 3-colorings for knots
lesson3 Quandles and quandle colorings
lesson4 Quandle homology thoery
lesson5 Quandle cocycle invariants
lesson6
lesson7
lesson8
lesson9
lesson10
lesson11
lesson12
lesson13
lesson14
lesson15

Text/Reference
Books,etc. Quandles: An Introduction to the Algebra of Knots, Mohamed Elhamdadi/Sam Nelson (著), American Mathematical Society.
Surfaces in 4-Space, J. Scott Carter/Seiichi Kamada/Masahico Saito (著), Springer.

PC or AV used in
Class,etc.

(More Details)

Learning techniques to be incorporated

Suggestions on
Preparation and
Review You need to review the contents after each lecture.

Requirements

Grading Method Evaluation will be based on homework assignments.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2026Year	School/Graduate School	Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program
Lecture Code	WSA71001	Subject Classification	Specialized Education
Subject Name	数学特別講義（カンドルと結び目不変量）
Subject Name （Katakana）	スウガクトクベツコウギ
Subject Name in English	Special Lectures in Mathematics
Instructor	To be announced.,MURAO TOMO
Instructor (Katakana)	タントウキョウインミテイ,ムラオ　トモ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, First Semester
Days, Periods, and Classrooms	(1st) Inte：SCI E209
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face

Credits	1.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	5 : Graduate Basic
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Quandle, Knot, Knot invariant
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)
Class Objectives /Class Outline	Algebraic structures known as quandles, which are well suited to knot theory, have been actively studied in recent years. In this course, we explain the fundamental aspects of quandle theory, with particular emphasis on its relationship to knot theory. Specifically, the course has the following three objectives: (1) to understand that the axioms of a quandle provide an algebraic formulation of the Reidemeister moves of knot diagrams; (2) to understand that knot invariants derived from quandle theory arise as natural extensions of the classical notion of 3-colorability of knots; and (3) to learn how to compute invariants for concrete knots using simple quandles and their cocycles.
Class Schedule	lesson1 Review of knot theory lesson2 3-colorings for knots lesson3 Quandles and quandle colorings lesson4 Quandle homology thoery lesson5 Quandle cocycle invariants lesson6 lesson7 lesson8 lesson9 lesson10 lesson11 lesson12 lesson13 lesson14 lesson15
Text/Reference Books,etc.	Quandles: An Introduction to the Algebra of Knots, Mohamed Elhamdadi/Sam Nelson (著), American Mathematical Society. Surfaces in 4-Space, J. Scott Carter/Seiichi Kamada/Masahico Saito (著), Springer.
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	You need to review the contents after each lecture.
Requirements
Grading Method	Evaluation will be based on homework assignments.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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