COURSE UNIT TITLE

: ALGEBRA II

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3046 ALGEBRA II ELECTIVE 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

The aim of this course (and the course MAT3055 Algebra I) is to learn the basic concepts of algebra, the classical topics: Groups, Rings and Fields. In the course MAT3055 Algebra I, we have concentrated on groups. Now we shall study rings and fields in this course MAT3046 Algebra II. The main aim of this course is to study Galois Theory of Fields. We shall start with the classical algebra problem: finding a formula for the roots of polynomial equations. This question leads to Galois theory. We shall follow this historical motivation to understand how algebra evolved as it is today. We shall continue to 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   Rings, Integral domains and fields with the basic examples should be known.
2   Ideals, homomorphisms and quotient rings should be known.
3   Euclidean domains, principal ideal domains, unique factorization domains should be known.
4   Field extensions should be known.
5   Splitting fields and automorphisms of fields 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 Rings, integral domains and fields.
2 The field of quotients of an integral domain.
3 Rings of polynomials. Factorization of polynomials over a field.
4 Ideals. Homomorphisms and Quotient Rings.
5 Prime and maximal ideals.
6 Principal Ideal Domains. Euclidean Domains. Unique Factorization Domains.
7 Problem solving.
8 Field Extensions.
9 Algebraic Extensions.
10 Finite Fields.
11 Automorphism of Fields.
12 Splitting Fields.
13 Separable Extensions.
14 Introduction to Galois Theory.

Recomended or Required Reading

Textbook:

John B. Fraleigh and Neal Brand. A First Course in Abstract Algebra.
Eighth edition. Pearson, 2021.

Supplementary textbooks:

[1] Frederick M. Goodman. Algebra, Abstract and Concrete, Stressing Symmetry. Pearson, 2003. 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 I brahim Karakas . Cebir Dersleri. TU BA Ders Kitapları Dizisi Sayı 4, 2008.

Planned Learning Activities and Teaching Methods

Lecture notes, presentations, problem solving, discussions and exams

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

None

Assessment Criteria

The passing grade will be evaluated as 40% midterm exam and 60% final exam. Class participation is important.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: salahattin.ozdemir@deu.edu.tr
Phone: (232) 301 8608
Office: B 351/1

Office Hours

To be announced.

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 20 20
Preparation for final exam 1 40 40
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 176

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