ABSTRACT ALGEBRA I (Math 425)

Instructor: Dr.Bülent KÖKLÜCE
Office: A-323

Tel:+90 212 889 08 10 (Ext:2006)

Email: bkokluce@fatih.edu.tr

Office Hours: Friday:13 -15

Lectures Program: Monday 11-12, Tuesday 09-11

Course Description as Presented in Catalog: Groups. Isomorphism theorems, direct products. Groups acting on sets, Class equation. Statements of Sylow theorems and the F.T on finite abelian groups. Rings, isomorphism theorems. Prime and maximal ideals. Integral domains, field of fractions. Euclidean domains, PIDs, UFDs. Polynomials, polynomials in several variables. Field extensions. Impossibility of certain geometric constructions. Finite fields.

•  COURSE CONTENTS

1.Week Binary Operations

2.Week Groups

3.Week Subgroups

4.Week Cyclic Groups and Generators

5.Week Groups of Permutations

6.Week Orbits, Cycles, and the Alternating Groups

7.Week Cosets and the Theprem of Lagrange

8.Week Direct Product and Finetly Generated Abelian Groups

9.Week Homomorphism Isomorphism,

10.Week Factor Groups

11.Week Rings and Fields

12.Week Integral Domain, Rings of Polynomials

13.Week Factorization of Polynomials

14.Week Homomorphism and Factor Rings

Texts:

1- A First Course in Abstract Algebra John B. Fraleigh

Grading:Exam 1 (30%), Exam 2 (30%), Final Exam (40%)

The Dates of Exams

First Midterm:1.Midterm(PDF), 1.Midterm(DVI),1.Midterm(PS), Midterm Results

Second Midterm:

Final exam:

Download Texts (You can see this documents if you have Acrobat Reader):

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Notes on about Group Theory

Notes1,Notes2,Notes3,Notes4,Notes5,Notes6,Notes7,Notes8,Notes9,Notes10

Exercise1,Answers1,Exercise2,Answers2,Exercise3,Answers3,Exercise4,Answers4,

Exercise5,Answers5,Exercise6,Answers6,Exercise7,Answers7,Exercise8,Answers8,

Exercise10,Answers10,Exercise11,Answers11,

Online Resources: