COURSE UNIT TITLE

: DIFFERENTIABLE MANIFOLDS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5030 DIFFERENTIABLE MANIFOLDS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ILHAN KARAKILIÇ

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

This course aims to give an introduction to the basic concepts of Differential Geometry, Differential Topology and Lie Theory

Learning Outcomes of the Course Unit

1   will be able to deal with various examples of differentiable manifolds and smooth maps
2   will be able to have familiarity with tangent vectors, tensors and differential forms
3   will be able to work practically with vector fields and differential forms
4   will be able to appreciate the basic ideas of de Rham cohomology and its examples
5   will be able to apply the ideas of differentiable manifolds to other areas
6   will be able to apply the basic techniques, results and concepts of the course to concrete examples
7   will be able to combine concepts from algebra, analysis and geometry

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Smooth manifolds and Smooth maps
2 The tangent bundle
3 The cotangent bundle
4 Submanifolds, Embedding and Approximation theorems
5 Lie group actions
6 Tensors
7 Differential forms
8 Problem solving Midterm
9 Integration on manifolds
10 De Rham cohomology
11 Integral curves and flows
12 Lie derivatives
13 Integral manifolds and foliations
14 Lie algebras and Lie groups

Recomended or Required Reading

Textbook:
1. John M. Lee, Introduction to Smooth Manifolds, Springer, 2002, ISBN-13: 978-0387954486
Supplementary Book(s):
2. W. M.Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed., Academic press, 2002, ISBN-13: 978-012116051767
3. Shigeyuki Morita, Geometry of Differential Forms, AMS, 2001, ISBN-13: 978-0821810453
4. Loring W. Tu, An Introduction to Manifolds, Springer, 2007, ISBN 978-0387480985

Planned Learning Activities and Teaching Methods

Lecture notes, Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 PRS PRESENTATION
3 FCG FINAL COURSE GRADE ASG * 0.50 + PRS * 0.50


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)

E-mail: ilhan.karakilic@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 14 4 56
Preparation for midterm exam 1 20 20
Preparation for final exam 1 30 30
Preparing assignments 3 8 24
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.1434433343
LO.2434434343
LO.3434433343
LO.4434434343
LO.5434534353
LO.6434433343
LO.7433454353

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

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