OSAKA UNIVERSITY SHORT-TERM STUDENT EXCHANGE PROGRAM _

02f-05
SELECTED TOPICS IN MATHEMATICS

Makoto NAMBA, et al. (Graduate School of Science)

Objective
In modern mathematics, there are 3 big branches: algebra, geometry and analysis. Algebra includes arithmetic. In this course, we choose some interesting topics mainly from old and modern arithmetic and geometry and give lectures on these. In the study or research of mathematics, calculation and logic are important. But the most important thing is the conception of idea. In this course, we introduce wonderful ideas by past mathematicians.

Reference Books
No particular textbook is used.

Lecture Outline
Topics are:
1. How to measure area
2. The legend of queen Cathandra - Isoperimetric problem
3. Symmetry of pictures - Concept of groups
4. Patterns and tiling
5. Pictures of points and edges - Graphs
6. Euler's theorem on polyhedrons
7. Minimal network
8. Riddle of numbers
9. Prime numbers
10. Puzzles and games

Grading
Grading is based on participation and reports. Every last 20 or 30 minutes of the lecture, we ask students to solve exercises, which relate the lecture. Students must submit the answers as a report.