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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 1034 BASIC ALGEBRAIC STRUCTURES COMPULSORY 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR NOYAN FEVZI ER

Offered to

Mathematics (English) Mathematics (Evening)

Course Objective

This course aims to give the fundamental concepts of number theory and algebra.

Learning Outcomes of the Course Unit

1   A basic knowledge of groups, rings and fields will be acquired. 2   A basic understanding of such concepts as subgroup, cyclic group, order, normality, factor group, homomorphism will be developed. 3   Some familiarity with the concept of a ring and basic examples and types of rings (e.g. integral domains, polynomial rings, matrix rings, fields, etc) will be developed. 4   Skills for proof-making in algebra will be improved. 5   Basic applications of algebra will be learned.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Division algorithm, existence of greatest common divisor 2 Euclidean algorithm, fundamental theorem of arithmetic, moduler arithmetic. 3 Binary operations 4 Groups and subgroups 5 Permutation groups and their direct products 6 Group homomorphisms and isomorphisms 7 Rings 8 Ring homomorphisms and isomorphisms 9 Midterm 10 Integral domains 11 Fields 12 Polynomial rings 13 Divisibility in polynomial rings 14 Ideals

Recomended or Required Reading

Textbook(s): A First Course in Abstract Algebra-7Th Ed. J.Fraleigh.

Planned Learning Activities and Teaching Methods

Lectur Notes Presentations Problem Solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

%50 success rate on each of the midterms, final and the make-up.

Language of Instruction

English

Course Policies and Rules

As described in the syllabus announced for each semester.

Contact Details for the Lecturer(s)

noyan.er@deu.edu.tr

Office Hours

As announced by the instructor during the first week of the semester.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 16 4 64 Preparations before/after weekly lectures 16 3 48 Preparation for midterm exam 1 25 25 Preparation for final exam 1 26 26 Final 1 1 1 Midterm 1 1 1 TOTAL WORKLOAD (hours) 165

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