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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6037 HOMOLOGICAL METHODS IN ABELIAN GROUPS ELECTIVE 3 0 0 8

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 Mathematics

Course Objective

This aim of this course is to introduce the main homological algebra techniques in abelian group theory.

Learning Outcomes of the Course Unit

1   Will be able to understand the group structure on the set Ext(C,A) of extensions of an abelian group A by an abelian group C. 2   Will be able to understand how the inexactness of the functor Hom is measured by the functor Ext. 3   Will be able to understand how the inexactness of the tensor product functor is measured by the functor Tor. 4   Will be able to understand the structure of cotorsion groups. 5   Will be able to understand the homological use of the proper class of pure-exact sequences of abelian groups and its generalizations.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Groups of Homomorphisms of Abelian Groups. Exact Sequences for Hom. 2 Group Extensions. Extensions as Short Exact Sequences. 3 Group Structure on Ext(C,A). 4 Exact Sequences for Ext. 5 Elementary Properties of Ext. 6 Pure-exact sequences. The Functor Pext. 7 Proper classes of short exact sequences of abelian groups. 8 Midterm. 9 Cotorsion Groups. Injective Properties of Cotorsion Groups. 10 Tensor Product. 11 Exact Sequences for Tensor Products. The Structure of Tensor Products. 12 The Torsion Product. 13 Exact sequences for Tor. 14 The Structure of Torsion Products.

Recomended or Required Reading

[1] Laszlo F. Infinite abelian groups. Vol. I. Academic Press, New York, 1970. [2] Maclane, S. Homology. Springer, 1963.

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 5 65 Preparation for midterm exam 1 15 15 Preparation for final exam 1 25 25 Preparing assignments 10 5 50 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 200

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 4 3 2 2 4 3 3 LO.2 4 3 2 2 4 3 3 LO.3 4 3 2 2 4 3 3 LO.4 4 3 2 2 4 3 3 LO.5 4 3 2 2 4 3 3