Textbook: 현대대수학 (JB Fraleigh 지음, Addison Wesley)
Classes: 자5 109호 (월, 목 10:30~12)
Grades: 중간고사 (30%), 기말고사 (30%), 과제 및 퀴즈 (30%), 출석 및 기타 (10%)
Instructor's Office Hours: sy2kang@kangwon.ac.kr; 수요일 13~14 (자5 222호)
- 중간고사해답
- 중간고사 (10/26, 월요일) 범위: 4(18,19,22,23절), 5(26,27절), 9(45,46,47절) 장
- 기말고사 Q&A (12/7, 월요일) 10:30~11:45 am
- 기말고사 (12/10, 목요일) 범위: 4(21절), 6장
- 8/31 Introduction
- 9/3 Rings
- 9/7 Polynomial rings
- 9/10 Integral domains, Division rings, Fields
- 9/14 Characteristic of rings, Ring homomorphisms, Evaluation ring homomorphism
- 9/17 Ring isomorphism theorems, Factor rings, Ideals
- 9/21 Ideals, Factor rings, Principal ideals, 1st Isomorphism Theorems for rings
- 9/24 Prime ideals, Maximal Ideals
- 10/1 Maximal Ideals, Prime fields
- 10/5 Euclidean Domain, Principal Ideal Domain, ED is PID
- 10/8 Primality and irreducibility in an integral domain
- 10/12 Ascending Chain Condition, Unique Factorization Domain, PID is UFD
- 10/15 Ring of quadratic integers
- 10/19 Factorization in polynomial rings, Gauss lemma
- 10/22 If D is UFD, then D[x] is UFD, Eisenstein criterion
- 10/26 중간고사
- 10/29 Field of quotients of an integral domain, proof of [if D is UFD, then D[x] is UFD].
- 11/2 Extension fields, algebraic and transcendental numbers
- 11/5 Minimal polynomial (irreducible polynomial) of an algebraic number, simple extension
- 11/9 Algebraic extensions and finite extensions of a field 1
- 11/16 Algebraic extensions and finite extensions of a field 2
- 11/23 Algebraic closures and algebraically closed fields
- 11/26 Impossible constructions
- 11/30 Finite fields
- 12/3 Galois field of order pn
- Set 1 (Due 10/5) 18절 #42,47(46참고); 19절 #23,25; 22절 #24,25; 26절 #18,22; 27절 #24,28,30
- Set 2 (Due 10/19)
- 0. Prove that Z[squareroot{10}] is not a UFD.
- 1. Prove that if p is a element of PID, p is a prime if and only if p is irreducible.
- 2. Prove that every associate of an irreducible element in a commutative ring is irreducible.
- 3. Prove that every associate of a prime element in a commutative ring is prime.
- (Suggested problems) 23절 #10,17,19,25,34,35,37 45절 #10,21,29,31 46절 #12,13,18 47절 #8,14,15
- Set 3 (Due 11/16) 29절 #12,13,18; 30절 #6,10; 31절 #11,23,24
- Set 4 (Due 11/30) 32절 #5~9