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Course Description Course Name : Topological Spaces Course Code : MT 442 Course Type : Optional Level of Course : First Cycle Year of Study : 4 Course Semester : Spring (16 Weeks) ECTS : 5 Name of Lecturer(s) : Learning Outcomes of the Course : Is able to define the first and second countable spaces. Understands the convergence of a squence, a net and a filter in a topological space. Establishes a relationship between convergence in analysis and topology. Is able to define Hausdorff, regular and normal space. Understands compact space. Becomes aware of the basic theorems about compact spaces. Understands the relationship between compactness and convergence. Improves the ability of abstract thinking. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To inform the student on countability,convergence, seperation axioms and compactness in topological spaces. Course Contents : Countability topological spaces, convergence, separation axioms, compactness. Language of Instruction : Turkish Work Place : Faculty of Science Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Review of some topological concepts. The concept of neighborhood. First countable spaces. Review of the relevant pages from sources Lecture and discussion 2 The second countable spaces. Separable spaces. Problem solving. Review of the relevant pages from sources Lecture and discussion 3 Convergence of sequences. Sequential continuity. Problem solving. Review of the relevant pages from sources Lecture and discussion 4 Nets and Convergence. Filters and convergence. Review of the relevant pages from sources Lecture and discussion 5 Problem solving. T0 and T1-spaces. Review of the relevant pages from sources Lecture and discussion 6 T2 (Hausdorff), regular, T3-spaces. Review of the relevant pages from sources Lecture and discussion 7 Problem solving Review of the relevant pages from sources Lecture and discussion 8 Mid-term exam Review of topics discussed in the lecture notes and sources Written exam 9 Completely regular, normal and T4-spaces. Review of the relevant pages from sources Lecture and discussion 10 Cover and compact spaces. Finite intersection property Review of the relevant pages from sources Lecture and discussion 11 The relationship between the finite intersection property and compactness. Heine-Borel Theorem. Review of the relevant pages from sources Lecture and discussion 12 The relationship between compactness and Hausdorff spaces. Review of the relevant pages from sources Lecture and discussion 13 Important basic properties of compact spaces. Review of the relevant pages from sources Lecture and discussion 14 Locally compact spaces Review of the relevant pages from sources Lecture and discussion 15 Problem solving Review of the relevant pages from sources Lecture and discussion 16/17 Final exam review of topics discussed in the lecture notes and sources Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Genel Topoloji, Author: Ali Bülbül 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 1 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 2 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 2 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 4 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 1 15 15     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 15 15 Total Workload: 129 Total Workload / 25 (h): 5.16 ECTS Credit: 5