Course Name	Modern Algebra I
Credits	3
Professor(s)	Name	Kwon Young In
	Affiliation	Department of Mathematics Education

COURSE DESCRIPTION

Course Objectives

It is to give the following topics:

(1) The Isomorphism and Homomorphism of Rings

(2) The structure of polynomial rings F[x]

(3) Ideals and quotients rings

(4) Congruence and Lagrange's Theorems

(5) Quotients groups

MAIN TEXTBOOK and FURTHER READINGS

Abstract Algebra an introduction, 2nd edition

A first course in abstract algebra, 7th edition, Fohn B. Fraleigh

현대대수학, 경문사, 박승안, 김응태

ASSIGNMENTS AND GRADING

Assignments: Solutions of exercises of each section

Grading Scheme: Attendance(10%), Mid-term exam(30%), Final exam(40%), Assignments(20%)

COURSE SCHEDULE

Course Outline

Week 1 : Congruence and congruence classes in Z

Week 2 : The structure of [eqn: Z_p] when p is prime.

Week 3 : Definitions and examples of ring.

Week 4 : Basic properties of rings

Week 5 : Isomorphisms and Homorphisms

Week 6 : Divisibility in F[x]

Week 7 : Irreducible and unique factorization

Week 8 : Polynomial functions, roots, and reducibility

Week 9 : Irreducibility in Q[x], R[x] and C[x]

Week 10 : Congruence and congruence classes in F[x]

Week 11 : Ideals and congruences

Week 12 : Quotient rings and homomorphism

Week 13 : The structure of R/I when I is a maximal ideal

Week 14 : Groups and subgroups

Week 15 : Mid-term Exam and Final Exam

CONTACT DETAILS

Tel: +82 55 772 2251         e-mail: yikwon@gnu.kr