COURSE UNIT TITLE

: INTRODUCTION TO ALGEBRA

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
ELECTIVE

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR HASIBE SEVGI MORALI

Offered to

Mathematics Teacher Education

Course Objective

The aim of this course is to provide students to learn binary operations, group definition and basic features; subgroups, permutation groups, cyclic groups, n-gen symmetry group, cyclic permutations, even and odd permutations, homomorphisms, Kosets and Lagrange theorem, isomorphism theorems, effects on a set of groups, rings, maximal ideals, ring homomorphisms, arithmetic in rings, polynomial rings,; Fields, Burnside theorem and its applications, p-groups and related theorems, A n simplicity for n> 4.

Learning Outcomes of the Course Unit

1   To be able to know the definition and properties of groups. To be able to know the concepts of subgroup, cyclic group, make operations and proofs, give examples. To be able to know the concept of permutation, recognize cyclic, even and odd permutations. To be able to know the properties of symmetric groups and various examples.
2   To be able to know cosets and Lagrange's theorem, their application areas, to be able to do exercises. To be able to know the properties of group homomorphisms and isomorphisms, related theorems, to be able to prove them.
3   To be able to know the concepts of ring and sub-ring, Polynomial rings.
4   To be able to know Fields, Burnside Theorem and its applications.
5   To be able to know P-groups and prove related theorems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Groups, properties of groups, sub groups and examples
2 Cyclic groups
3 Permutations and symmetric groups
4 Examples of permutation groups, exercises
5 Cosets, Lagrange Theorem
6 Group homomorphisms, isomorphisims
7 Isomorphism theorems, proofs and exercises
8 Course overview, evaluation and midterm examination
9 Rings, subrings, examples
10 Prime and maximal ideals
11 Ring Homomorphisms, polinomial rings
12 Fields, Burnside Theorem
13 p-groups
14 Simplicity of for n>4
15 Final Exam

Recomended or Required Reading

Çallıalp, F. (1995), Cebir, Sakarya Üniversitesi Matbaası, Sakarya.

Planned Learning Activities and Teaching Methods

Lecture, Discussion, Question-answer, Group work

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Midterm
2 FN Semester final exam
3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60
4 BUT Make-up note
5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Midterm and final exams are determined according to the weekly course content within the scope of the learning outcomes of the course.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

sevgi.morali@deu.deu.tr
Cahit Arf Building Office:226
Phone: 3012422

Office Hours

Thursday 13.30-15.00

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 1 13
Preparation for midterm exam 1 6 6
Preparation for final exam 1 6 6
Preparing assignments 1 6 6
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 74

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1543323
LO.2543323
LO.3543323
LO.4543323
LO.5543323

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

Copyright 2015 DEÜ. BİD

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