|
Week
|
Topics
|
Study Metarials
|
|
1
|
Binary Operations
|
R1: Fundamentals of Abstract Algebra, Section 1.6
|
|
2
|
Elementary Properties of Groups
|
R1: Fundamentals of Abstract Algebra, Section 2.1
|
|
3
|
Permutation Groups
|
R1: Fundamentals of Abstract Algebra, Section 3.1
|
|
4
|
Subgroups
|
R1: Fundamentals of Abstract Algebra, Section 4.1
|
|
5
|
Cyclic Groups
|
R1: Fundamentals of Abstract Algebra, Section 4.2
|
|
6
|
Lagrange`s Theorem
|
R1: Fundamentals of Abstract Algebra, Section 4.3
|
|
7
|
Normal Subgroups and Quotient Groups
|
R1: Fundamentals of Abstract Algebra, Section 4.4
|
|
8
|
Homomorphisms of Groups
|
R1: Fundamentals of Abstract Algebra, Section 5.1
|
|
9
|
Isomorphism and Correspondance Theorems
|
R1: Fundamentals of Abstract Algebra, Section 5.2
|
|
10
|
Dihedral and Quaternion Groups
|
R1: Fundamentals of Abstract Algebra, Section 5.3
|
|
11
|
External and Internal Direct Product
|
R1: Fundamentals of Abstract Algebra, Section 6.1
|
|
12
|
Conjugacy Classes
|
R1: Fundamentals of Abstract Algebra, Section 7.1
|
|
13
|
Cauchy`s Theorem and p-groups
|
R1: Fundamentals of Abstract Algebra, Section 7.2
|
|
14
|
Sylow Theorems
|
R1: Fundamentals of Abstract Algebra, Section 7.3
|
|
Prerequisites
|
-
|
|
Language of Instruction
|
English
|
|
Responsible
|
Assoc. Prof. Dr. Faruk KARAASLAN
|
|
Instructors
|
-
|
|
Assistants
|
-
|
|
Resources
|
R1: D. S. Malik, John N. Mordeson, M.K. Sen, Fundamentals of Abstract Algebra , McGraw-Hill, 1997
|
|
Supplementary Book
|
R1: Fraleigh, John B. (2014). A First Course in Abstract Algebra (7th Edition). Pearson Education Limited, England.
R2: Herstein, I. N. (1996). Abstract Algebra (3rd Edition). Prentice-Hall, Inc, New Jersey.
|
|
Goals
|
To teach fundamental concepts related to group theory and their properties in detailed.
|
|
Content
|
Binary operations, groups, subgroups, cyclic groups, normal subgroups and quotient groups, external and internal direct product of groups, homomorphism and isomorphism of groups, conjugate classes, Sylow theorems.
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
To have a grasp of theoretical and applied knowledge in main fields of mathematics
|
3
|
|
2
|
To have the ability of abstract thinking
|
3
|
|
3
|
To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps
|
3
|
|
4
|
To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life
|
-
|
|
5
|
To have the qualification of studying independently in a problem or a project requiring mathematical knowledge
|
2
|
|
6
|
To be able to work compatibly and effectively in national and international groups and take responsibility
|
-
|
|
7
|
To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge
|
-
|
|
8
|
To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge
|
-
|
|
9
|
To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
|
-
|
|
10
|
To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally
|
-
|
|
11
|
To be able to produce projects and arrange activities with awareness of social responsibility
|
-
|
|
12
|
To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level
|
-
|
|
13
|
To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results
|
-
|
|
14
|
To have the awareness of acting compatible with social, scientific, cultural and ethical values
|
-
|