Yozgat Bozok University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT514	ELEMENTS OF GROUP THEORY AND SEMI GROUP THEORY OF OPERATORS II	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

To give detailed information on groups.

Name of Lecturer(s)

Dr.Öğr.Üyesi Funda TAŞDEMİR

Learning Outcomes

1	The learners have information about Free groups, free products, generators, free abelian groups, finitely generated abelian groups.
2	The learners have information about Krull-Schmidt Theorem, Group actions, Sylow Theorems.
3	The learners have information about Classification of finite groups, nilpotent and solvable groups.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Strong, continuous semi-groups, properties of semi-groups, infinitesimal generator of semi-groups, Hille-Yosida theorem and its applications, dual semi-groups and their properties, solutions of differential equations in Banach spaces, analytic semi-groups, applications of semi-groups in partalvation theory solutions

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Free groups, fre products
2	Free groups, fre products
3	Free groups, fre products
4	generators, free abelian groups
5	generators, free abelian groups
6	finitely generated abelian groups, Krull-Schmidt Theorem
7	finitely generated abelian groups, Krull-Schmidt Theorem
8	MID TERM EXAM
9	Group actions, Sylow Theorems
10	Group actions, Sylow Theorems
11	Group actions, Sylow Theorems
12	Classification of finite groups
13	Classification of finite groups
14	Classification of finite groups
15	nilpotent and solvable groups.
16	FINAL EXAM

Recommended or Required Reading

1. Hersteın I.N, (1975), Topics In Algebra, Jahn Wiley nad Sons Inc. 2. Hungerford Tomas, (1974), Algebra Springer Verlag New York. 3. Fraleigh John, (1973), A First Course In Abstract Algebra, Addison-Wesley Publishing Company London.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Attending Lectures	14	3	42
Self Study	14	3	42
Individual Study for Mid term Examination	7	6	42
Individual Study for Final Examination	7	6	42
TOTAL WORKLOAD (hours)			172

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High