TYPE OF COURSE UNIT	Elective Course
LEVEL OF COURSE UNIT	Doctorate Of Science
YEAR OF STUDY	-
SEMESTER	-
NUMBER OF ECTS CREDITS ALLOCATED	10
NAME OF LECTURER(S)	-
LEARNING OUTCOMES OF THE COURSE UNIT	At the end of this course, the students; 1) develop abstraction and fast thinking skills. 2) demonstrate inverse examples in some algebraic structures easily. 3) ask himself/herself mathematical questions.
MODE OF DELIVERY	Face to face
PRE-REQUISITES OF THE COURSE	No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT	None.
COURSE DEFINITION	Cartesian product and relation, Binary operation, Divisibility of integers, Lcm, Gcd, Euclid's Algorithm, Congruences, Groups, Subgroups, Normal subgroups, Symmetric Groups, Groups homomorphisms, Groups isomorphism, Cyclic Groups, Iternal direct sum, External direct sum, Rings, Subring, Ideals, Rings homomorphisms.
COURSE CONTENTS	WEEK TOPICS 1st Week Cartesian product and relation, Binary operations 2nd Week Divisibility of integers, Lcm, Gcd, Euclid's Algorithm 3rd Week Congruences 4th Week Groups 5th Week Subgroups 6th Week Normal subgroups 7th Week Symmetric Groups 8th Week Mid-Term Exam 9th Week Groups homomorphisms, Groups homomorphisms 10th Week Cyclic Groups 11th Week Iternal direct sum, External direct sum 12th Week Rings 13th Week Subring, Ideals 14th Week Rings homomorphisms 15th Week
RECOMENDED OR REQUIRED READING	Taşcı Dursun, ?Soyut Cebir?, Ankara (2010) Herstein I.N, (1975), Topics In Algebra, John Wiley nad Sons
PLANNED LEARNING ACTIVITIES AND TEACHING METHODS	Lecture,Questions/Answers,Practice
ASSESSMENT METHODS AND CRITERIA	Quantity Percentage(%) Mid-term 1 40 Total(%) 40 Contribution of In-term Studies to Overall Grade(%) 40 Contribution of Final Examination to Overall Grade(%) 60 Total(%) 100
ECTS WORKLOAD	Activities Number Hours Workload Midterm exam Preparation for Quiz Individual or group work 14 12 168 Preparation for Final exam 1 60 60 Course hours 14 3 42 Preparation for Midterm exam Laboratory (including preparation) Final exam 1 1,5 1,5 Homework 1 20 20 Project Weekly Articles and Resource Research Total Workload 291,5 Total Workload / 30 9,71 ECTS Credits of the Course 10
LANGUAGE OF INSTRUCTION	Turkish
WORK PLACEMENT(S)	No