유한체이론 및 응용                                       2005년 1학기

 

본 과목은 영어로 강의가 진행됩니다.

담당교수: 송홍엽 hy.song@coding.yonsei.ac.kr   2123-4861   http://coding.yonsei.ac.kr/~hysong   B612-613

담당조교: 진석용 (부호및정보이론 연구실 박사과정 4학기)  B612-613

수업시간: 주당 1.5시간씩 2회 강의수업 = 총 3시간/주 (화목 5-6교시,   1시10분-2시50분,     100분수업  2회)

대상:   

과목소개:

교재:  Norman L. Biggs, Discrete Mathematics, revised edition, Oxford Science Publications, 1998.

 

 Objective

        ▶ Elementary Number Theory

        ▶ Important Concepts in Modern Algebra/Linear Algebra/Counting

        ▶ Finite Fields

        ▶ BCH and RS Codes, RSA/ElGamal Cryptography

Text

    ▶ Discrete Mathematics by Biggs

    ▶ Finite Fields for Computer Scientists and Engineers by McEleice

    ▶ Some Lecture Notes

Week

Summary

Remark

Homework

1

Integers and Congruence

 

HW#1

2

Groups and Permutations

 

HW#2

3

Simultaneous Equations and Vector Spaces

 

HW#3

4

Matrix/Determinants/Linear Transformations

 

HW#4

5

Some Concepts in Modern Algebra - Homomorphisms

 

HW#5

6

Burnside and Polya Theory of Counting I

 

HW#6

7

Burnside and Polya Theory of Counting II

 

 

8

Midterm Exam

 

 

9

Construction of Finite Fields using Irreducible Polynomials

 

HW#7

10

Abstract Properties of Finite Fields - Additive Structure

 

HW#8

11

Abstract Properties of Finte Fields - Multiplicative Structure

 

HW#9

12

BCH Codes - Encoding/Decoding

 

HW#10

13

Finite Field Fourier Transform

 

HW#11

14

Reed-Solomon Codes - Encoding/Decoding Algorithms

 

HW#12

15

RSA/ElGamal Encryption/Authentication Algorithms

 

 

16

Final Exam

 

 

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