COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Transformation Semigroups * MTS   223 3 2 2 3

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Hayrullah AYIK
Instructors
Prof.Dr.HAYRULLAH AYIK1. Öğretim Grup:A
 
Assistants
Goals
The aim of this course is to teach full transformation semigroups, some special transformation semigroups and partial transformation semigroups.
Content
Full transformation semigroups , its some special subsemigroups (symmetric group, singular transformations semigroup , order-preserving transformations semigroup , etc), partial transformation semigroups , its some special subsemigroups (strictly partial transformation semigroups, 1-1 partial transformations semigroup, partial order-preserving transformations semigroup , etc),

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Definition and basic properties of symmetric groups Review of the relevant pages from sources
2 Definition and basic properties of full transformation semigroups. Review of the relevant pages from sources
3 Comparison of the symmetric group and full transformation semigroup Review of the relevant pages from sources
4 Properties of some special transformation semigroups Review of the relevant pages from sourcesReview of the relevant pages from sources
5 Properties of elements of some special transformation semigroups Review of the relevant pages from sources
6 Factorization in full transformation semigroups Review of the relevant pages from sources
7 Properties of factorization in full transformation semigroups Review of the relevant pages from sources
8 Midterm exam Review of the topics discussed in the lecture notes and sources
9 Generating set of some special transformation semigroups. Review of the relevant pages from sources
10 Properties of generating set of some special transformation semigroups. Review of the relevant pages from sources
11 Definition and basic properties of partial transformation semigroups. Review of the relevant pages from sources
12 Comparison of the full transformation semigroups and partial transformation semigroup Review of the relevant pages from sourcesReview of the relevant pages from sources
13 Generating set of partial transformation semigroups. Review of the relevant pages from sources
14 Idempotent generating sets Review of the relevant pages from sources
15 Nilpotent generating sets Review of the relevant pages from sources
16-17 Final Exam Review of the topics discussed in the lecture notes and sources

Recommended or Required Reading
TextbookAll articles about the topics.
Additional Resources
Classical Finite Transformation Semigroups, Ganyushkin, Olexandr, Mazorchuk, Volodymyr