Topics in Mathematics and its Engineering Applications (I)

MIYAHARA, Keizo (Center for International Education and Exchange)

Cource Objective
   This course would focus on the topics from graph 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 linear algebra (ex. matrix multiplication) is preferable, but not required.

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;
   Walks, Trails, Paths: Sequence of footprints;
   Bipartite graphs; A story of Black and White;
   Coloring: Much colorful story on maps, but upper boundary exists;
     Examples of graphs found in engineering applications (to be researched as team activities).

	Theme	Content
Week 1	Introduction	Motivational problems
Week 2	Fundamental concepts	Fundamental concepts 1, Team activity preparation 1
Week 3	Fundamental concepts	Fundamental concepts 2, Team activity preparation 2
Week 4	Fundamental concepts	Fundamental concepts 2, Team activity preparation 3
Week 5	Team activity	Research and Presentation preparation 1
Week 6	Team activity	Research and Presentation preparation 2
Week 7	Advanced topics	Advanced topics 1, In-class presentation 1
Week 8	Advanced topics	Advanced topics 2, In-class presentation 2
Week 9	Advanced topics	Advanced topics 3, In-class presentation 3
Week 10	Mid-term	In-class assignment
Week 11	Advanced topics	Advanced topics 4, In-class presentation 4
Week 12	Advanced topics	Advanced topics 5, In-class presentation 5
Week 13	Advanced topics	Advanced topics 6, In-class presentation 6
Week 14	Final	In-class assignment
Week 15	Review	Review

Type of Class
   Lectures 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 graph theory, the following books are recommended, although these are not required for this course:
   "Introduction to Graph Theory 2nd edition," Douglas B. West, Prentice Hall;
   "Introduction to Graph Theory," Vitaly Ivanovich Voloshin, Nova Sci. Pub;
   "Introduction to Graph Theory," Robin J. Wilson, Harlow/Longman.
   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%