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About the Course

Department Profile
Course unit title Level of course unit Course unit code Type of course unit Semester of course unit Local credit ECTS credit Syllabus
TOPOLOGY- I First cycle MAT 549 1 7.50 7.50 Print
   
Description of course unit
Prerequisites and course requisities None
Language of instruction Turkish
Coordinator PROF. DR. MEHMET BARAN
Lecturer(s) PROF. DR. MEHMET BARAN
Teaching assitant(s) PROF. DR. MUAMMER KULA
Mode of delivery Face to face
Course objective To teach basic concepts in Topology, to create the ability of Mathematical idea and commend, to help to gain the basic topological knowledge and ability for their later educations.
Course description Infinite product spaces, metric product spaces, first countable spaces and second countable spaces, separable spaces, lindelöf’s spaces, separation axioms, Urysohn’s lemma and metrization theorem.

Course contents
1 Infinite product spaces
2 metric product spaces
3 examples, theorems
4 first countable spaces and second countable spaces
5 examples, theorems
6 separable spaces
7 examples, theorems
8 Midterm Exam
9 lindelöf’s spaces
10 separation axioms
11 examples, theorems
12 Urysohn’s lemma and metrization theorem
13 examples, theorems
14 Discussion of homework
15 Final Exam
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Learning outcomes of the course unit
1 To understand Initial and final topologies
2 To learn the concepts of quotient topology and product topology,
3 To learn the concepts countable spaces, separable spaces and Lindelöf spaces
4 To find the relationship between separation axioms (T0 and T1 spaces)
5 To find the relationship between separation axioms (T2 and T3 spaces)
6 To interprete Urysohn’s Lemma, Tietz extension theorem and Urysohn’s metrization theorem
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10

*Contribution level of the course unit to the key learning outcomes
1 have advanced theoretical and practical knowledge in the field of natural sciences that builds upon their secondary education and is supported by textbooks, course materials and other scientific resources presenting up-to-date information.
2 Make use of theoretical and practical knowledge acquired in the field of mathematics and natural science and chemistry.
3 The ability to have scientific and ethical values.
4 To solve unexpected problems in related applications of chemistry field.
5 The ability to plan and manage activities required for professional development.
6 Critically evaluate the accuracy and relevancy of knowledge and skills acquired; to define andassess learning needs; and to direct learning processes.
7 The ability to offer solutions to problems.
8 The ability of sharing their opinions or solutionoffers to the problems to specialists or non-specialists, supporting these with qualitative and quantitative data.
9 The ability to have enough competency in a foreign language to follow the literature in chemistry and communicate with their pers.
10 The ability to use computer software and communication and information technologies required in the field of chemistry competently and use theseto access scientific resources
11 The ability to comply with social, scientific and ethical values in the process of collecting, interpreting and using data and reporting the results in the field of chemistry
12 Awareness of the environmental protection and work/laboratory safety.
13 Have the skills towork in interdisciplinary subjects
14 To have skills to use modern devices required for the practices.
15 To have competency in keeping up with global innovations and developments in chemistry and in related fields.
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Number of stars refer to level of contribution from 1 (the least) to 5 (the most)

Planned learning activities, teaching methods and ECTS work load
  Quantity Time (hour) Quantity*Time (hour)
Lectures (face to face teaching) 14 3 42
Study hours out of classroom (study before and after the class) 14 3 42
Homework 0 0 0
Presentation / seminar 2 2 4
Quiz 0 0 0
Preparation for midterm exams 8 2 16
Midterm exams 1 2 2
Project (term paper) 0 0 0
Laboratuar 0 0 0
Field study 0 0 0
Preparation for final exam 14 3 42
Final exam 1 2 2
Research 14 3 42
Total work load     192
ECTS     7.50

Assessment methods and criteria
Evaluation during semester Quantity Percentage
Midterm exam 1 40
Quiz 0 0
Homework 0 0
Semester total   40
Contribution ratio of evaluation during semester to success   40
Contribution ratio of final exam to success   60
General total   100

Recommended and required reading
Textbook • G. Preuss, Foundations of Topology, Kluwer Academik Publisher, 2002. • O., Mucuk, Topoloji ve Kategori, Nobel Yayın, 2010.
Additional references • S., Lipshutz, General Topology, Mcgraw-Hill, 1965.

Files related to the course unit