Topics in Mathematics and its Engineering Applications (II)

MIYAHARA, Keizo (Center for International Education and Exchange)

Course Objective
   This course would focus on the topics from group theory, which is one of the active mathematics subfields.
   Students will be exposed to abstract world in order to develop ones' logical thinking skills.

Learning Goals
   By the end of this course, successful students should be able to:
   demonstrate ones' understanding of the importance of mathematics in engineering field;
   explain the key concepts of the topics introduced in the class;
   continue further self-study of the topics with own interest.

Requirement / Prerequisite
   No prerequisite subjects in university-level courses.
   Basic knowledge of proving methods (ex. induction, contradiction) is required.
   Basic knowledge of the following fields is preferable, but not required:
   discrete math (ex. set theory, mapping, binary operator);
   linear algebra (ex. matrix multiplication).

Special Note
   This course is one of the "international exchange subjects" those are aiming at social exchange interactions among local/international students as a preferable secondary effect.
   All who are interested in student exchange activities are encouraged to join the course.

Class Plan
   This course is undergraduate-level, and begins with introductory concepts.
   This course covers the topics listed below:
     Introduction: Fundamental concepts for studying group theory;
     Definition and principle characteristics;
   Classes of group;
   Advanced topics: ex. Isomorphism;
     Examples of group found in engineering applications (to be researched as team activities).

	Theme	Content
Week 1	Introduction	Motivational problems
Week 2	Basics 1	Fundamental concepts
Week 3	Basics 2	Definitions
Week 4	Basics 3	Characteristics
Week 5	Classes 1	Classes of group 1
Week 6	Classes 2	Classes of group 2
Week 7	Classes 3	Classes of group 3
Week 8	Advanced 1	Advanced topics 1
Week 9	Advanced 2	Advanced topics 2
Week 10	Advanced 3	Advanced topics 3
Week 11	Mid-term	In-class assignment
Week 12	Team activities 1	Research and Presentation preparation 1
Week 13	Team activities 2	Research and Presentation preparation 2
Week 14	Team activities 3	In-class presentation
Week 15	Review	Review

Type of Class
   Lecture with Team activities

Independent Study Outside of Class
   Individual assignments and Presentation preparations

Textbooks
   Course materials will be distributed in the class and/or via CLE.
   No specific books are required for this course.

Reference
   For self-study of group theory, the following books are recommended, although these are not required for this course:
   "Group theory I" and ""Group theory II,"" Michio Suzuki, Springer-Verlag.
   For engineering mathematics basics the following books are recommended, although these are not required for this course:
   "Introductory Mathematics for Engineering Applications," Kuldip S. Rattan, Nathan W. Klingbeil, John Wiley & Sons, Inc. New York;
   "Advanced Engineering Mathematics," Erwin Kreyszig, John Wiley & Sons, Inc. New York.

Grading Policy
   Individual assignments 50%
   Team activities 30%
   Class participation 20%