Set Theory 1 : Introduction to Set Calculation

Set Theory 2 : Mapping and Image

Set Theory 3 : Inverse Image and Inverse Mapping

Set Theory 4 : Direct Product Set

Set Theory 5 : Relation(N.B. This chapter is not a must for the students who are going to take this course through the Internet)

Set Theory 6 : Cardinality(N.B. This chapter is not a must for the students who are going to take this course through the Internet)

In this course we will learn the basic mathematics of Information Engineering. to understand this course you have to have the knowledge of the course ‘Logic’. http://markun.cs.shinshu-u.ac.jp/learn/logic/index-j.html

Set theory is the fundamental of all kinds of mathematics and at the same time you will find this theory useful to arrange complex events and analyze those events statically.

Algebra is the fundamental mathematics of Cryptogram theory and Encoding theory. In the beginning algebra was developed as pure mathematics to solve algebraic equation but these years of Internet era algebra is one of the mostly used applied mathematics.

Graph theory is the mathematics that is used to express circuit and network. By using Graph theory you can also express the condition of software that are running in parallel. Among other theories, Optimization theory also is very essential concept.

In this course, we will discuss different theories in brief. Those who have interest on these theories may find many reference books searching the Internet.

Enrolled students of this course have to complete one chapter per week and do the CAI as the following order. You need not come to the class. You do everything at your home. If you have any question, please contact Prof. Nakamura by e-mail.(ynakamur@cs.shinshu-u.ac.jp)

1. Set Theory 1

2. Set Theory 2

3. Set Theory 3

4. Set Theory 4

(Set Theory 5 and Set Theory 6 are not compulsory)

5. Algebra 1 http://markun.cs.shinshu-u.ac.jp/learn/dirck/index-j.html

6. Algebra 2

7. Algebra 3

8. Algebra 4

9. Graph Theory 1 http://markun.cs.shinshu-u.ac.jp/learn/graph/GraphTheory-j.html

10. Graph Theory 2

11. Graph Theory 3

12. Graph Theory 4

13. Graph Theory 5

(Graph Theory 6 and Graph Theory 7 are not compulsory)

The test at the end of every chapter will be evaluated as the Final test. (There is no Final test). “Drill” and “Lecture” have individual credits. The deadline of this course is February 6, 2005. Everybody cheer up!

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