Topics in Mathematics and its Engineering Applications (I)

Keizo MIYAHARA (Center for International Education and Exchange)

Course Objective
   By the end of this introdutory undergraduate-level 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 classes.
   Basic knowledge of the following fields is required:
     proving methos (ex. induction, contradiction);
     linear algebra (ex. matrix multiplication).
   Basic knowledge of discrete math is prefarrable, but not required.

Course Content
   This course would focus on the topics from graph theory which is one of the active mathematics subfields.

Class Plan
   This course covers the topics listed below:
     Introduction: Fundamental concepts;
     Matchings: Bipartite graphs;
     Connectivity: Walks, Trails, Paths;
     Coloring: Parinting on maps;
     Planar graphs: Gas Water and Electricity.

Textbooks
   Handouts will be distributed.
  
   For self-study of graph theory, the following books are recommended: "Introduction to Graph Theory 2nd edition (2001)," 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 assignment 50%
• Class participation 20%
• Group work 30% (15+15)