FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 306 | Course Introduction and Application Information

Course Name
Abstract Algebra
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 306
Spring
3
0
3
7

Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery face to face
Teaching Methods and Techniques of the Course Discussion
Problem Solving
Q&A
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives To provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics and to study of certain structures called groups, rings, fields and some related structures.
Learning Outcomes The students who succeeded in this course;
  • will be able to define algebraic structures.
  • will be able to construct substructures.
  • will be able to analyze a given structure in detail.
  • will be able to develop new structures based on given structures.
  • will be able to compare structures.
Course Description In this course, the basic pillars of modern mathematics will be introduced and analyzed. These structures include groups, rings, fields, any mapping between them and their substructures.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Binary operations, isomorphic binary operations A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (sections 2 and 3).
2 Groups, subgroups A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (sections 4 and 5).
3 Groups, subgroups A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (sections 4 and 5).
4 Cyclic groups A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (section 6).
5 Groups of permutations, Cosets and Lagrange's theorem A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (section 8 and 10).
6 Midterm 1
7 Normal subgroups and factor groups A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (sections 13 and 14).
8 Groups homomorphisms and the isomophsim theorems A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (sections 13 and 14).
9 Rings and fields A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (section 18).
10 Midterm 2
11 Integral Domains, Fermat’s and Euler’s theorems A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (section 19 and 20).
12 Factorization A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (section 22 and 23).
13 Ideals and factor rings A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (section 26).
14 Prime and maximal ideals A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904. (section 27).
15 Semester review
16 Final exam

 

Course Notes/Textbooks

A First Course in Abstract Algebra” by J. B. Fraleigh, Addison Wesley, 2003, ISBN-13:9780201763904.

 
Suggested Readings/Materials

“Abstract Algebra: A first course” by D. Saracino, Waveland,Waveland Pr Inc; 2nd edition  2008, ISBN-13:978-1577665366

“Topics in Algebra” by I.N. Herstein, Wiley.1975,ISBN-13:978-0471010906

“Algebra” by M. Artin,Prentice Hall India Learning Private Limited; 2 edition (2011),ISBN-13:978-8120343290

“Introduction to Abstract Algebra” by J.D.H. Smith, CRC.Chapman and Hall/CRC;1st edition,2008,ISBN-13: 978-1420063714

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
50
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
2
50
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
14
5
70
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
27
54
Final Exam
1
38
38
    Total
210

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.

X
2

To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.

3

To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.

X
4

To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.

5

To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.

X
6

To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.

7

To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.

8

To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.

9

To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.

10

To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.

11

To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.

X
12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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