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Course Description Course Name : General Topology Course Code : MT 342 Course Type : Compulsory Level of Course : First Cycle Year of Study : 3 Course Semester : Spring (16 Weeks) ECTS : 5 Name of Lecturer(s) : Prof.Dr. DOĞAN DÖNMEZ Learning Outcomes of the Course : Can decide whether a given structure a topology on a set Can determine the continuity of a function on a topological space They realize that there is no difference between topological spaces which are equivalent under homeomorphisms Can apply some arguments in analysis to topological spaces Can define metric spaces and state some basic concepts in metric spaces Can show that every metric space is a topological space Can find interior, closure, exterior and boundary of a set in a topological space CAn explain and prove of the basic theorems in topology and use them for solving mathematical problems Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To teach the students the basic concepts in general topology, continuity and homeomorphisms in topological spaces and to give basic properties of metric spaces. Course Contents : Definition of topology, interior, exterior, boundary and derived set of a set in a topological space, bases, Hausdorff spaces and product spaces, continuity and homeomorphisms and metric spaces. Language of Instruction : Turkish Work Place : Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Review of some basic concepts and definition of topological space Reading the relevant parts of the textbook and recommended texts Lecture and discussion 2 Topology of the real line, open and closed sets Reading the relevant parts of the textbook and recommended texts Lecture and discussion 3 Closure and properties of closure Reading the relevant parts of the textbook and recommended texts Lecture and discussion 4 Interior, exterior and boundary of a set in a topological space Reading the relevant parts of the textbook and recommended texts Lecture and discussion 5 Relative topology and properties Reading the relevant parts of the textbook and recommended texts Lecture and discussion 6 Topologies induced by functions Reading the relevant parts of the textbook and recommended texts Lecture and discussion 7 Bases and Neighbourhood bases Reading the relevant parts of the textbook and recommended texts Lecture and discussion 8 Midterm Exam review Written exam 9 Product topology and some examples Reading the relevant parts of the textbook and recommended texts Lecture and discussion 10 Continuity and continuity at a point Reading the relevant parts of the textbook and recommended texts Lecture and discussion 11 Some examples about continuity and homeomorphisms Reading the relevant parts of the textbook and recommended texts Lecture and discussion 12 Properties of homeomorphisms and some examples Reading the relevant parts of the textbook and recommended texts Lecture and discussion 13 Hausdorff spaces and their properties Reading the relevant parts of the textbook and recommended texts Lecture and discussion 14 Metric spaces and some properties Reading the relevant parts of the textbook and recommended texts Lecture and discussion 15 Continuity in metric spaces and some examples Reading the relevant parts of the textbook and recommended texts Lecture and discussion 16/17 Final-exam Review of the topics discussed in the lecture notes and sources Written examination   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Genel Topoloji, Author: Ali Bülbül  An introduction to metric and topologic spacces, Author. W.A.Sutherland  Analiz IV, Author: Ali Nesin Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 90     Homeworks/Projects/Others 0 10 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Is able to prove Mathematical facts encountered in secondary school. 5 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 5 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 1 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 1 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 1 6 Expresses clearly the relationship between objects while constructing a model 3 7 Draws mathematical models such as formulas, graphs and tables and explains them 5 8 Is able to mathematically reorganize, analyze and model problems encountered. 3 9 Knows at least one computer programming language 3 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 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 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 3 42 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 119 Total Workload / 25 (h): 4.76 ECTS Credit: 5