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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4010 MODULES AND RINGS ELECTIVE 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ENGIN MERMUT

Offered to

Mathematics (Evening) Mathematics (English)

Course Objective

This course is an introductory course of modules.

Learning Outcomes of the Course Unit

1   Modules and some basic examples of modules should be known. 2   Free modules should be known. 3   Direct product and sum of modules should be known. 4   Injective-projective modules should be known. 5   Tensor products should be known.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Definition of Modules, examples, module homomorphisms. 2 Direct product and direct sum of modules. 3 Generators in modules, torsion and torsion free modules. 4 Free Modules. 5 Exact Sequences. 6 Exact Sequences II. 7 Hom as a functor. 8 Hom as a functor II. 9 Projective Modules. 10 Hom and Projective Modules. 11 Injective Modules. 12 Hom and Injective Modules. 13 Tensor product of modules. 14 Tensor product of modules II.

Recomended or Required Reading

Textbook(s): F. Kasch. Modules and Rings. Academic Press, 1982.

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Vize 2 FN Final 3 BNS BNS VZ * 0.40 + FN * 0.60 4 BUT Bütünleme Notu 5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60

Further Notes About Assessment Methods

1 Midterm Exam Final Exam

Assessment Criteria

%40 (Midterm examination) +%60 (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 4 56 Preparations before/after weekly lectures 14 5 70 Preparation for midterm exam 1 20 20 Preparation for final exam 1 25 25 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 175

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 PO.12 PO.13 LO.1 3 4 5 3 4 3 4 LO.2 5 5 4 3 4 3 4 LO.3 4 5 4 3 4 3 4 LO.4 4 5 4 3 4 3 4 LO.5 4 5 4 3 4 3 4