COURSE UNIT TITLE

: INTRODUCTION TO TOPOLOGY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3049 INTRODUCTION TO TOPOLOGY COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR ASLI GÜÇLÜKAN ILHAN

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course aims to teach the fundamentals of point set topology and constitute an awareness of need for the topology in Mathematics. It expresses how can be recoup the distance concept of Analysis.

Learning Outcomes of the Course Unit

1   Will be able to write the definitions of a metric space, a topological space, and their fundamental concepts
2   Will be able to describe the open and closed sets of a given topological space
3   Will be able to derive new topological spaces from given ones
4   Will be able to discuss homeomorphisms between topological spaces and some of the topological invariants
5   Will be able to discuss the continuity of a function between topological spaces
6   Will be able to discuss the connectedness and compactness

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Topology, Open Sets (1.1 & 1.2)
2 Finite-Closed Topology, Euclidean Topology (1.3 & 2.1)
3 Basis for a Topology, Basis for a Given Topogy (2.2 & 2.3)
4 Limit Points and Closue (3.1)
5 Neighbourhoods, Connectedness (3.2 & 3.3)
6 Subspaces, Homeomorphism (4.1 & 4.2)
7 Non-homeomorphic Spaces (4.3)
8 Continuous Mappings (5.1) Midterm
9 Intermediate Value Theorem-Connectedness & Path Connedtedness (5.2)
10 Metric Spaces (6.1)
11 Convergence of Sequences, Completeness (6.2 & 6.3)
12 Compact Spaces, Heine-Borel Theorem ( 7.1 & 7.2)
13 Product Topology, Projections (8.1 & 8.2)
14 Tychonoff's Theorem for Finite Products, Products and Connectedness (8.3 & 8.4)

Recomended or Required Reading

Textbooks: Morris, S. A., Topology Without Tears

Supplementary Books:
1. Gemignani, M. C., Elementary Topology, 2nd ed., Dover, 1990, ISBN 978-0486665221
2. Munkres, J. R., Topology, 2nd ed., Prentice Hall, 2000, ISBN 978-0131816299
3. Willard, S., General Topology, Dover, 2004, ISBN 978-0486434797
4. Karaçay, T., Genel Topoloji, Seckin Yayıncılık, 2009, ISBN 978-1111354701, http://www.acikders.org.tr/course/view.php id=21

Planned Learning Activities and Teaching Methods

Lectures, Lecture notes and problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE 1 MIDTERM EXAM 1
2 MTE 2 MIDTERM EXAM 2
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE1 * 0.30 + MTE2 * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE1 * 0.30 + MTE2 * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

E-mail: asli.ilhan@deu.edu.tr
Phone : 0 232 3018593

Office Hours

Thursday: 13:55- 15:30

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 2,5 42
Preparation for midterm exam 1 25 25
Preparation for final exam 1 30 30
Preparation for quiz etc. 4 5 20
Final 1 2,5 3
Midterm 1 2,5 3
Quiz etc. 4 1 4
TOTAL WORKLOAD (hours) 183

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.15433
LO.25433
LO.354333
LO.4543333
LO.55535433
LO.654353333

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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