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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS LME 3008 INTRODUCTION TO ALGEBRA COMPULSORY 3 0 0 3

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR HASIBE SEVGI MORALI

Offered to

Mathematics Teacher Education

Course Objective

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   Group definition, properties. Subgroup, knowing cyclic group concepts, doing operations and proofs, giving examples.To know the concept of permutation, recognition of double, single parmutations. To know properties of symmetric groups and various examples; Cosets and Lagrange Theorem. 2   To be able to know and demonstrate the properties of group homomorphisms and isomorphisms, related theorems 3   Rings, subrings and polynomial rings 4   Fields, Burnside Theorem and applications, 5   p-groups, 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 *** 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

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

To be announced.

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) TOTAL WORKLOAD (hours) 0

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 PO.14 PO.15 PO.16 PO.17 PO.18 LO.1 5 4 3 3 2 3 LO.2 5 4 3 3 2 3 LO.3 5 4 3 3 2 3 LO.4 5 4 3 3 2 3 LO.5 5 4 3 3 2 3