COURSE UNIT TITLE

: GENERAL TOPOLOGY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4031 GENERAL TOPOLOGY ELECTIVE 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

The aim of this course is to introduce the geometric ideas and the basics of algebraic topology to undergraduate students.

Learning Outcomes of the Course Unit

1   will learn the concept of topological equivalences and invariants
2   will be able to compute the Alexander polynomial of a knot
3   will be able to compute the Jones polynomial of a knot
4   will see basic examples of surfaces and their three dimensional analogs
5   will discuss the basics of the algebraic techniques
6   will learn topological and metric spaces motivated by geometric examples
7   will be able to discuss 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 Preliminaries: Equivalence, Continuous Functions
2 Topological Equivalence, Topological Invariants, Isotopy
3 Knot, Links and Reidemeister Moves
4 Colorings, The Alexander Polynomial
5 Skein Relations and The Jones Polynomials
6 Surfaces, The Euler Characteristic
7 Classification of Surfaces
8 Classification of Surfaces
9 Three-dimensional Manifolds, Euler Characteristic
10 Fundamental Group: Definition, Algebraic Properties
11 Invariance of the Fundamental Group
12 Examples: The Fundamental Group of Circle and Sphere
13 Topological Spaces and Metric Spaces
14 Connectedness, Compactness

Recomended or Required Reading

Textbook:
1. R. Messer and P. Straffin, Topology Now, The MAthematical Association of America, 2006

Supplementary Books:
2. H.G. Flegg, From Geometry to Topology, Dover, 2001
3. V.V. Prasolov, Intuitive Topology, AMS, 1995
4. S. Goodman, Beginning Topology, Brooks/Cole, 2005
5. P. Cromwell, Knots and Links, Cambridge University Press, 2004
6. R. Crowell and R. Fox, Introduction to Knot Theory, Springer-Verlag, 1963
7. N.D. Gilbert and T. Porter, Knots and Surface, Oxford University Press, 1994
8. L.C. Kinsey, Topology of Surfaces, Springer-Verlag, 1993
9. W. Massey, Algebraic Topology: Am Introduction, Springer-Verlag, 1989
10. M.A. Armstrong, Basic Topology, Spinger-Verlag, 1997
11. J. Munkres, Topology, Prentice Hall, 2000

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

Office Hours

Wednesday: 14:50-15:50

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 3 42
Preparation for midterm exam 2 20 40
Preparation for final exam 1 30 30
Final 1 2 2
Midterm 2 2 4
TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1544333
LO.25444333
LO.35544433
LO.4543333
LO.55433333
LO.654333333
LO.7553443333

CONTACT INFORMATION
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