유한체이론 및 응용 [이산수학과 유한체이론] 

 

 2006년 1학기        

본 과목은 영어로 강의가 진행됩니다.

담당교수:

담당조교: TBA

수업시간: 주당 1.5시간씩 2회 강의수업 = 총 3시간/주

대상:

과목소개:

교재:  TBA

평가방법:

기타사항:

 

Weekly Plan: (updated after midterm exam)

 

 Objective

        ▶ Elementary Number Theory

        ▶ Important Concepts in Modern Algebra

        ▶ Finite Fields

        ▶ BCH and RS Codes, RSA/ElGamal Cryptography

Week

Summary

Remark

Homework

1

Integers and Congruence

 

HW#1

2

 (응용) RSA/ElGamal Encryption Algorithms

 

Project #1

3

Groups and Permutations

 

HW#2

4

Theory of Counting - Burnside Lemma

 

HW#3

5

Simultaneous Equations and Vector Spaces

 

HW#4

6

Matrix/Determinants/Linear Transformations

 

HW#5

7

Review of the first half semester

 

 

8

Midterm Exam

 

 

9

Some Concepts in Modern Algebra

 

HW#6

10

Irreducible Polynomials over Fp

 

HW#7

11

Multiplicative Structure of Finite Fields

 

HW#8

12

Additive Structure of Finte Fields

 

HW#9

13

(응용) Hamming/BCH Codes - Encoding/Decoding

 

Project #2

14

(응용) Reed-Solomon Codes - Encoding/Decoding

 

HW#10

15

Review of the second half semester

 

 

16

Final Exam (12주-15주 수업내용)

 

 

 

 

 

 

Weekly Plan:

 

 Objective

        ▶ Elementary Number Theory

        ▶ Important Concepts in Modern Algebra

        ▶ Finite Fields

        ▶ BCH and RS Codes, RSA/ElGamal Cryptography

Week

Summary

Remark

Homework

1

Integers and Congruence

 

HW#1

2

 (응용) RSA/ElGamal Encryption Algorithms

 

Project #1

3

Groups and Permutations

 

HW#2

4

(응용) Burnside and Polya Theory of Counting

 

HW#3

5

Simultaneous Equations and Vector Spaces

 

HW#4

6

Matrix/Determinants/Linear Transformations

 

HW#5

7

Some Concepts in Modern Algebra

 

 

8

Midterm Exam (5,6,7주 수업내용)

 

 

9

Irreducible Polynomials over Fp

 

HW#6

10

Multiplicative Structure of Finite Fields

 

HW#7

11

Additive Structure of Finte Fields

 

HW#8

12

(응용) Linear Feedback Shift Register Sequences

 

HW#9

13

(응용) Hamming/BCH Codes - Encoding/Decoding

 

Project #2

14

(응용) Reed-Solomon Codes - Encoding/Decoding

 

HW#10

15

(응용) Latin Squares and Finite Projective Planes

 

 

16

Final Exam (12주-15주 수업내용)

 

 

 

 

Details

1주 Integers and Congruence

HW#1

 

2주  (응용) RSA/ElGamal Encryption Algorithms

Project #1: Implementation of ElGamal signature algorithm

 

3주 Groups and Permutations

HW#2

 

4주 (응용) Burnside and Polya Theory of Counting

HW#3

 

5주 Simultaneous Equations and Vector Spaces

HW#4

 

6주 Matrix/Determinants/Linear Transformations

HW#5

 

7주 Some Concepts in Modern Algebra

 

8주 Midterm Exam

 

9주 Irreducible Polynomials over GF(p)

HW#6

 

10주 Multiplicative Structure of Finte Fields

HW#7

 

11주 Additive Structure of Finite Fields

HW#8

 

12주 (응용) Linear Feedback Shift Register Sequences

HW#9

 

13주 (응용) Hamming/BCH Codes - Encoding/Decoding

Project #2: Implementation of BCH Encoder/Decoder

 

14주 (응용) Reed-Solomon Codes - Encoding/Decoding

HW#10

 

15주 (응용) Latin Squares and Finite Projective Planes

 

16주 Final Exam