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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, Pullback, Pushout. 6 Additive categories. 7 Abelian categories. 8 Midterm 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

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

Planned Learning Activities and Teaching Methods

Lecture Notes, Presentation, Problem Solving

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 *** 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

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

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

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 13 3 39 Preparation for midterm exam 1 15 15 Preparation for final exam 1 25 25 Preparing assignments 10 5 50 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 3 4 3 4 4 3 4 3 4 3 LO.2 4 4 3 4 4 3 4 3 4 3 LO.3 3 3 3 4 4 4 4 4 4 3 LO.4 3 3 3 4 4 3 3 3 4 3 LO.5 3 3 3 3 4 3 3 4 4 3