COURSE UNIT TITLE

: ELEMENTARY ALGEBRAIC TOPOLOGY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4049 ELEMENTARY ALGEBRAIC TOPOLOGY ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics (Evening)
Mathematics

Course Objective

The main goal of this course is to introduce students to algebraic topology and standart topological invariants.

Learning Outcomes of the Course Unit

1   will be able to give the definitions of some fundamental concepts such as homotopy, fundamental group, covering space, etc.
2   will be able to know how to compute the fundamental group of a space
3   will be able to calculate the fundamental group of a circle, torus, cylinder, a compact Riemann surface of genus g, wedge of circles etc.
4   will be able to compute homology group of a surface
5   will be able to use the fundamental group and homology group to classify surfaces

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Review of point set topology: Topological spaces
2 Review of point set topology: Connected and compact spaces
3 Review of point set topology: Continuous functions, Product spaces, the thychonoff theorem
4 Homotopy, Fundamental group
5 Fundamental group
6 Covering spaces
7 Fundamental group of the circle, Retractions and fixed points, Deformation retracts and homotopy type
8 Midterm
9 Fundamental groups of an n-dimensional sphere and fundamental groups of some surfaces
10 Direct sums of abelian groups, Free products of groups, The Seifert-van Kampen theorem
11 The fundamental group of a wedge of circles, adjoining a two cell, Fundamental groups of some surfaces (Torus, genus g surface)
12 Homology of surfaces, cutting and pasting, Classification theorem of surfaces, constracting compact surfaces
13 Classification of covering spaces
14 Universal covering space, Covering transformations

Recomended or Required Reading

Textbooks:
1. Singer, I. M., Thorpe, J.A., Lecture Notes on Elementary Topology and Geometry, Springer, 1976, ISBN 978-0387902029
2. Munkres, J. R., Topology, 2nd ed., Prentice Hall, 2000, ISBN 978-0131816299
Supplementary Books:
3. Hatcher, A., Algebraic Topology, Cambridge University Press, 2001, ISBN 978-0521795401
References:
4. Bredon, G. E., Topology and Geometry, corrected ed., Springer, 1993, ISBN 978-0387979267
5. May, J.P., A Concise Course in Algebraic Topology, University of Chicago Press, 1999, ISBN 978-0226511832

Planned Learning Activities and Teaching Methods

Lectures, Lecture notes and problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FINS FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.30 + ASG * 0.20 + FIN * 0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.20 + RST * 0.50


*** 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: bedia.akyar@deu.edu.tr
Office : 0 232 3018590

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparations before/after weekly lectures 12 2 24
Preparation for midterm exam 1 30 30
Preparation for final exam 1 35 35
Preparation for quiz etc. 2 3 6
Preparing assignments 4 3 12
Final 1 2,5 3
Midterm 1 2,5 3
Quiz etc. 2 0,5 1
TOTAL WORKLOAD (hours) 166

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1543433
LO.255434433
LO.3554344353
LO.45443433
LO.554434333

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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