Information Of Programmes

INSTITUTE OF SCIENCE / MAT504 - MATHEMATICS

Code: MAT504

Course Title: CATEGORY THEORY II

Theoretical+Practice: 3+0

ECTS: 6

Year/Semester of Study

1 / Spring Semester

Level of Course

2nd Cycle Degree Programme

Type of Course

Optional

Department

MATHEMATICS

Pre-requisities and Co-requisites

None

Mode of Delivery

Face to Face

Teaching Period

14 Weeks

Name of Lecturer

SAMED ÖZKAN (ozkans@nevsehir.edu.tr)

Name of Lecturer(s)

Language of Instruction

Turkish

Work Placement(s)

None

Objectives of the Course

The aim of the course is to teach some concepts in Category Theory in detail, to create the ability of Mathematical idea and commend, to help to gain the categorical knowledge and ability for their graduate educations.

Learning Outcomes		PO	MME
The students who succeeded in this course:
LO-1	Can define the concepts of functor, adjoint functor, natural transformation and natural isomorphism, can give examples.	PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas.	Examination
LO-2	Learn the equivalence of categories. Know the concepts of groupoid and fundamental groupoid.	PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. PO-5 Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.	Examination
LO-3	Can define the concept of topological category. Learn the important topological categories.	PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas.	Examination
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
Functors and Some Properties, Examples, Adjoint Functors, Natural Transformations, Natural Isomorphisms, Examples, The Equivalence of Categories, Groupoids, Examples, Fundamental Groupoids, Topological Category, Some Important Topological Categories, Examples, General Exercises
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Functors and Some Properties	Lecturing
2	Examples	Lecturing
3	Adjoint Functors	Lecturing
4	Natural Transformations	Lecturing
5	Natural Isomorphisms	Lecturing
6	Examples	Lecturing
7	The Equivalence of Categories	Lecturing
8	mid-term exam
9	Groupoids	Lecturing
10	Examples	Lecturing
11	Fundamental Groupoids	Lecturing
12	Topological Category	Lecturing
13	Some Important Topological Categories	Lecturing
14	Examples	Lecturing
15	General Exercises	Lecturing
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010.
2	İ. Karaca, Kategori Teorisi, Yüksek Lisans Ders Notları, 2010.
3	J. Adamek, H. Herrlich, G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990.
Required Course instruments and materials

Assessment Methods
Type of Assessment	Week	Hours	Weight(%)
mid-term exam	8	2	40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam	16	2	60

Student Work Load
Type of Work	Weekly Hours	Number of Weeks	Work Load
Weekly Course Hours (Theoretical+Practice)	3	14	42
Outside Class
a) Reading	5	14	70
b) Search in internet/Library	2	14	28
c) Performance Project			0
d) Prepare a workshop/Presentation/Report			0
e) Term paper/Project			0
Oral Examination			0
Quiz			0
Laboratory exam			0
Own study for mid-term exam	4	4	16
mid-term exam	2	1	2
Own study for final exam	5	4	20
final exam	2	1	2
			0
			0
Total work load;			180