COURSE UNIT TITLE

: TOPOLOGY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6021 TOPOLOGY ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to provide an introduction to parts of the topology.

Learning Outcomes of the Course Unit

1   will be able to use the definitions of a topological space and its fundamental concepts.
2   Will be able to understand new topological spaces from given ones.
3   Will be able to use the inadequacy of sequences.
4   Will able to understand Nets and Filters.
5   Will be able to understand separation and countability axioms.
6   Will be able to understand the properties of metrizable spaces.
7   Will be able to use the connectedness and compactness concepts.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Topological spaces
2 Basic topological concepts
3 Compactness and connectedness
4 Compactness and connectedness
5 Separation and countability
6 An Embedding Theorem
7 Midterm
8 Compactness
9 Local compactness and compactifications
10 Paracompactness
11 Metrization
12 Manifolds
13 Manifolds
14 Relations between topological spaces

Recomended or Required Reading

Texbook(s):
1. Willard, S., General Topology, Dover, 2004, ISBN 978-0486434797
2. Munkres, J. R., Topology, 2nd ed., Prentice Hall, 2000, ISBN 978-0131816299
Supplementary Books:
3. Patty, C. W., Foundations of Topology, 2nd ed., Jones & Bartlett Publishers, 2008, ISBN 978-0763742348
4. Gemignani, M. C., Elementary Topology, 2nd ed., Dover, 1990, ISBN 978-0486665221
5. Steen, L.A. & Seebach, J. A., Counter Examples in Topology, Dover, 1995, ISBN 978-0486687353
6. Karaçay, T., Genel Topoloji, Seckin Yayıncılık, 2009, ISBN 978-1111354701, http://www.acikders.org.tr/course/view.php id=21

Materials:
Özçelik, Ahmet Z., Topoloji Ders Notları

Planned Learning Activities and Teaching Methods

Lecture notes
Presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

ahmet.ozcelik@deu.edu.tr
Office: 0232 3018585

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparation for midterm exam 1 15 15
Preparation for final exam 1 25 25
Preparing Individual Assignments 10 5 50
Preparations before/after weekly lectures 13 5 65
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 200

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.13424332333
LO.23424332333
LO.33424332333
LO.43424332333
LO.53424332333
LO.63424332333
LO.73424332333

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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