COURSE UNIT TITLE

: ALGEBRA I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3055 ALGEBRA I COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR SALAHATTIN ÖZDEMIR

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This aim of this course (and the course MAT3046 Algebra II) is to learn the basic concepts of algebra, the classical topics: Groups, Rings and Fields. We shall concentrate on groups in this course and continue the other topics in the course MAT3046 Algebra II. We shall study some more topics about groups, rings and fields that are covered in the course "Basic Algebraic Structures".

Learning Outcomes of the Course Unit

1   Dihedal groups, permutations groups and other basic examples of groups with their structure should be known.
2   The structure of cyclic groups should be known.
3   Quotient groups (=factor groups) and Homomorphism Theorems should be known.
4   The structure of finitely generated abelian groups should be known.
5   Groups actions, the main role of groups everywhere, 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 Motivating questions for algebra, a historical introduction. The classical topics of algebra: Groups, Rings and Fields.
2 Symmetries.
3 Permutations. Divisibility in Integers. Moduler arithmetic.
4 Polynomials over a field.
5 Elementary properties of groups. Subgroups.
6 The structure of cyclic groups.
7 Group of Permutations. Dihedral groups.
8 Product of groups. Semidirect products.
9 The structure of finitely generated abelian groups. Midterm.
10 Cosets and The Theorem of Lagrange.
11 Quotient groups (=factor groups) and Homomorphisms.
12 Isomorphism Theorems.
13 Group action on a set.
14 Applications of G-sets to counting. Burnside's Formula.

Recomended or Required Reading

Textbook:

John B. Fraleigh and Neal Brand. A First Course in Abstract Algebra, 8th edition. Pearson, 2020.

Supplementary textbooks:

[1] Frederick M. Goodman. Algebra, Abstract and Concrete, online edition 2.6 :
http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm


[2] William J. Gilbert and W. Keith Nicholson. Modern Algebra with Applications. Second edition. John Wiley & Sons, 2004.

[3] Joseph A. Gallian. Contemporary Abstract Algebra. Ninth edition. Cengage Learning, 2017.

[4] Michael Artin. Algebra. Second edition, Pearson, 2010.

[5] Joseph J. Rotman. A First Course in Abstract Algebra with Applications. Third edition, Pearson, 2006.

[6] David S. Dummit and Richard M. Foote. Abstract Algebra. Third edition. John Wiley & Sons, 2004.

[7] M. A. Armstrong. Groups and Symmetry. Springer, 1988.

[8] Nathan C. Carter. Visual Group Theory Mathematical Association of America, 2009.

[9] David W. Farmer. Groups and Symmetry, A Guide to Discovering Mathematics. AMS, 1996.

[10] Elbert A. Walker. Introduction to Abstract Algebra. Random House/Birkhauser, 1987. Online available:
http://emmy.nmsu.edu/~elbert/

[11] John Stillwell. Elements of Algebra. Springer, 1994.

[12] Robert H. Redfield. Abstract Algebra, A Concrete Introduction. Pearson, 2001.

[13] Israel Kleiner. A History of Abstract Algebra. Birkha user, 2007.

[14] Halil Ibrahim Karakaş. Cebir Dersleri. TÜBA Ders Kitapları Dizisi Sayı 4, 2008.

Planned Learning Activities and Teaching Methods

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + FIN * 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

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-posta : salahattin.ozdemir@deu.edu.tr
Ofis: (232) 301 86 08

Office Hours

Tuesday, 15.00 - 16.00

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 4 56
Preparation for midterm exam 1 25 25
Preparation for final exam 1 30 30
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 171

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.13453434
LO.25543434
LO.34543434
LO.44543434
LO.54543434

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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