COURSE UNIT TITLE

: CATEGORIES

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5049 CATEGORIES 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 ENGIN MERMUT

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to introduce categories together with its applications to some constructions with rings and modules.

Learning Outcomes of the Course Unit

1   Will be able to master the basic concepts and methods of categories.
2   Will be able to understand how category theory can be used to structure mathematical ideas, with the concepts of functoriality, naturality and universality.
3   Will be able to understand how reasoning with objects and arrows can replace reasoning with sets and elements.
4   Will be able to learn the basic ideas of using commutative diagrams and unique existence properties.
5   Will be able to understand the connections between categories and logic.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Fundamental properties of categories.
2 Functors, Natural transformations.
3 Adjoint functors.
4 Universal object.
5 Product, Coproduct
6 Pullback, Pushout.
7 Additive categories.
8 Abelian categories.
9 Exact categories.
10 Direct limits.
11 Inverse limits.
12 The Morita theory: Projective generators, Morita equivalence.
13 Tensor products.
14 Localization, local-global methods.

Recomended or Required Reading

Main Textbook:
1. Saunders Mac Lane, Categories for the Working Mathematician, 2nd ed., Springer, 1998.
Supplementary Book(s):
2. A. J. Berrick and M. E. Keating, Categories and Modules with K-theory in view, Cambridge University Press, 2000.
3. Peter Hilton, Yel-Chang Wu, A course in Modern Algebra, Wiley-Interscience, 1989.

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

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


Further Notes About Assessment Methods

Homework
1 Midterm Exam
Final Exam

Assessment Criteria

%30 (Homework) + %30 (Midterm examination) +%40 (Final examination)

Language of Instruction

English

Course Policies and Rules

You can be successful in this course by studying from your textbooks and lecture notes on the topics to be covered every week, coming to class by solving the given problems, establishing the concepts by discussing the parts you do not understand with your questions, learning the methods, and actively participating in the course.

Contact Details for the Lecturer(s)

Engin Mermut
e-mail: engin.mermut@deu.edu.tr
Phone: (232) 301 85 82

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 3 42
Preparation for midterm exam 1 15 15
Preparation for final exam 1 20 20
Preparing assignments 10 5 50
Final 1 3 3
Midterm 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.13434434343
LO.24434434343
LO.33334444443
LO.43334433343
LO.53333433443

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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