Ordu 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
MAT20720121310	TOPOLOGY –I	Compulsory	2	3	5

Level of Course Unit

First Cycle

Objectives of the Course

The aim of the course is • to ıntroduce the basic concepts and to provide methods of proof in general topology.

Name of Lecturer(s)

Yrd. Doç. Dr. Serkan KARATAŞ

Learning Outcomes

1	Students who successfully complete this course : They will develop the right thinking and the ability to interpret and will gain basic knowledge about mathematics.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

Recommended Optional Programme Components

Week 1 Metric spaces Week 2 topological spaces, topology and open the lower sentences. Week 3 Neighbourhood and axioms of neighborhoods. Week 4 Internal point of a sentence in topological space Week 5 interior, closure, baundary, and accumulation points of a sentence in topological space Week 6 Hausdorff space Week 7 grazing value and limit of the series in Hausdorf space. Week 8 Topological subspaces Week 9 Midterm exam Week 10 the reduced topology and open the bottom of the lower sentence in topological subspace Week 11 İnterior points of a sentence in topological subspace. Week 12 Closure points of a sentence in topological subspace. Week 13 interior of a sentence in topological subspace. Week 14 Boundary of a sentence in topological subspace Week 15 Accumulation points of a sentence in topological subspace. Week 16 Final exam

Course Contents

• Metric spaces, • Topological spaces, • Topology and open the lower sentences. • Comparison of topologies. • Neighbourhood and axioms of neighborhoods. • Internal point, interior, closure, baundary, and accumulation points of a sentence in topological space. • Hausdorff space, • Grazing value and limit of the series in Hausdorf space. • Topological subspaces, • The reduced topology and open the bottom of the lower sentence in topological subspace. • Closure, interior, boundary and accumulation points of a sentence in topological subspace.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Metric spaces
2	Topological spaces, topology and open subsets
3	Neighbourhood.
4	Interior of a set in topological space.
5	Interior, closur, bound and limit point of of a set
6	Hausdorff space
7	Limit of a sequence in Hausdorf space
8	Topological sub spaces
9	Mid-Term Exam
10	Reduced topology and open sets in sub space
11	Open sets in sub space
12	Closure of a set in sub space
13	Interior of a set in sub space
14	Bound of a set in sub space
15	Limit points of a set in topological sub space.
16	Final Exam

Recommended or Required Reading

S. Lipschutz, General Topology, Schaum’s Outline Series, McGraw-Hill Pub. Com

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	12	5	60
Problem Solving	10	2	20
Self Study	8	5	40
Individual Study for Mid term Examination	8	2	16
Individual Study for Final Examination	6	2	12
TOTAL WORKLOAD (hours)			154

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	3	4	3	3	3	3	4

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