Algebra2
Course Information
Course Information
Textbook: 현대대수학 (JB Fraleigh 지음, Addison Wesley)
Classes: 자5 109호 (월, 목 10:30~11:45)
Grades: 중간고사 (30%), 기말고사 (30%), 과제 및 퀴즈 (30%), 출석 및 기타 (10%)
Instructor's Office Hours: sy2kang@kangwon.ac.kr; 수요일 15~16 (자5 222호)
Announcement
Announcement
- 기말고사 (12/15 목요일) 범위: 29~33절, 45~47절, 48~51절
- 중간고사 (10/27 목요일) 범위: 18~23절, 26~27절, 29~30절 (해답)
Topics covered in class
Topics covered in class
- 9/1 Rings
- 9/5 Basic properties of rings, Division rings, Fields, Subrings(subfields)
- 9/8 Integral domains
- 9/12 Characteristic of rings and integral domains, Ring Homomorphisms
- 9/19 Properties of ring homomorphisms
- 9/22 Polynomial rings
- 9/26 Factorization of polynomials
- 9/29 Field of quotients of an integral domain
- 10/6 Ideals, Factor rings
- 10/10 Properties of ideals, Principal ideals, Principal Ideal Domains
- 10/13 Maximal and Prime ideals
- 10/17 Prime fields, Ideals in F[x]
- 10/22 Extension fields, Algebraic numbers, Monic polynomials
- 10/24 Simple extensions of a field, Simple extension as a vector space
- 10/31 Algebraic extension and finite extension of a field
- 11/3 Algebraic closure of a field
- 11/7 Algebraically closed field
- 11/10 Geometric construction
- 11/14 Finite fields 1
- 11/17 Finite fields 2
- 11/21 Finite fields 3
- 11/28 Introduction to Galois Theory 1
- 12/1 Introduction to Galois Theory 2
- 12/5 Introduction to Galois Theory 3
- 12/8 Unique Factorization domains, Euclidean domains
- 12/12 Gaussian integers and multiplicative norms
Homework Assignments
Homework Assignments
- Set 1 (Due 10/6) Homework Set #1 (9번 문제 수정: 기약인 2차 다항식의 개수 구하기)
- Set 2 (Due 11/17) Homework Set #2 (8번 추가. 정 7각형은 작도불능임을 증명하여라.) (해답 #1,2, #3,4,5, #6, #7, #8)
- Set 3 (Due 12/21) Homework Set #3 (21일 5시까지 연구실 또는 학과사무실에 제출)