1 Faculty of Sciences & InformationTechnological Department: Mathematics COURSE SYLLABUS Short Description Student s Copy One copy of this course syllabus is provided to each student registered in this course. It should be kept secure and retained for future use.
2 I. Course Information 1. Course Title : General Topology-1 2. Corse Code : Credit Hours : 3 4. Prerequisite : None 5. Corequisite : None 2. Instructor Information 1. Instructor : Prof. Ass. Dr. Walid Abdu mohammad Saeed 2. Office : 238-D 3. Phone : Office Hours :Sun 2-3 and 4-5.5, Thu2-3 and 4-5.5, Tu2-3 and Class Time and Place 1. Class Days and Time : Wedn 4-7 PM 2. Class Location : 3. Lab Days and Time : 303 h 4. Lab Location : Course Policies University regulations are applied to this course, regarding Class Attendance; Punctuality, Exam, Makeup Exams; Absence with permission; Penalties for Cheating; and Policies for Assignment and Projects. Students Should be aware of all those in addition to other rules and regulations. 5. Resources Main Reference Text Book: 1. Bert Mendelson. Introduction to Topology. Third Edition(1990). 2. Paul E. Long. An Introduction General Topology. (1986). 3. William J. Pervin. Foundations of General Topology.(1985). Additional Reference (s): 1. William J. Pervin. A Basic course in Algebraic Topology.William J.(1991 Pervin 2. M. A. Armstrong Basic Topology(1983)
3 5. Course Description and Purpose 1. General topology- 3 Credits 2. Course Description: This course covers steps for preparing background foundations of general topology and metric, Product Spaces in Matric Spaces and topology Spaces, Continuity in Matric Spaces and Topology Spaces and matrically Equivalent and Topology Homeomorhpism, Identifiction topology and Quotint Spaces, convergence in Matric Spaces and topology Spaces, Complete and Compactness in Matric Spaces and topology Spaces,Propertices of topological and topological non Uniform Spaces and homotopy Groups. 3. Purpose: The purpose pf the course is to achieving the following purposes: 1. To undertand the main consept of topological spaces and metric 2. Explain the relationship between topological spaces and metric spaces and how to find it. 3. Discuss and illustrat the travel from the metric spaces(special) to topological spaces(general). 4. Provide students with the basic ideas of properties the sets and spaces from interior and exterior. 5. Provide students with the basic ideas of properties of topological and non-topological. 7. Course Learning Outcomes Upon successful completion of this course, the learner should be able to: A- Knowledge and understanding (students should - Be able to distinguish between different metric spaces and topological - Be able to prepare information of metric spaces and topological spaces. - Be able to analyze solving problems of metric spaces and topological - Understand to solving problems of metric spaces and topological - Understand the steps of solving problems in metric spaces and topological - Understand the contribution format in proof state theorems. - Be able to use activity-based to solving problems of metric spaces and topological spaces. - Use information techniques to state and proof of theorms. - Be able to use different methods to proof theorems and solving problems.
4 B- Intellectual skills with ability to:- - Apply the basic principles solving problems of metric spaces and topological spaces.. - Apply the information techniques to state and proof of theorms. - Prepare of metric spaces and topological - Prepare a contribution format in proof state theorems. - Use activity based to solving problems of metric spaces and topological spaces.. C- Subject Specific Skills: At the end of the course, students will be able to: - Realize the cost classification for managerial purpose. - Realize the relevant cost and benefits for decision making purpose. D- Transferable skills with ability to:- - Display an integrated approach for the development of financial and non financial data for managerial purpose. - Provide decision makers with useful information and help them in analyzing and interpreting the components of managerial reports. 8. Methods Of Teaching The methods of instruction may include, but are not limited to: 1. Lectures 2. Discussion and problem solving 3. Brainstorming 4. Individual assignments 5. Case Study 6. Asking students to ive a presentation in a specific subject or problem related to the course 7. Lecturing using PowerPoint Presentations, mixed with discussion with students 8. Asking students to prepare a term paper about a subject or a problem related to the course, and discuss it in the class. 9. Course Learning Assessment/Evaluation The following methods of learning assessment will be used in this course: A Assessment Weight Description 3 Tests - Multiple choice questions 30% - First Exam and - State and Proof Research proposal - Short answers 30% - Second Exam and - Essay Questions Research proposal - Problem solving 40% - Final Exam - Explanations Total 100%
5 10. Course Schedule/Calendar Wk No. 1, 2,3 3, ,8 9, ,13 14,15 Topic Backgroud and Foundation of Topology Spaces and metric spaces SetTheory,RelationTheory,Functions Theory, Introduction of Matric Space and topology Spaces. Product Spaces Matric Space and topology Spaces Finite Product, Product Infariant Properties, Matric Product, Tichonov Theorem. Continuity of Matric Spaces and Topology Spaces Continuous Functios, non- Continuous Functios, matrically Equivalent and Topology Homeomorhpism Identifiction topology and Quotint Spaces Relative Topology, Identifiction topology Spaces and Quotint Spaces First Exam and Research proposal Convergence of Matric Spaces and Topology Spaces Sequences, Couchy sequences, Completions, Convergence in first countable spaces, Subsequences Filters and Net Glimpse,Resutling of Axioms Separation. Compact in Matric Spaces and Topology Spaces Compact topological spaces, Compact metric spaces, Compact subset of the real line and R n, Property of Compactness, Sequential compact Second Exam and Research Proposal Uniform Spaces Quasi Unifomization, Unifomization, Uniform continuity, Completeness and Compactness, Proximity Spaces. Homotopy Group Homotopy Path,Topological Groups, The fundamental Homotopy Groups. Assignments/ workshops due date Homewoek Research Ch 6,9,10 Research Ch 6,9,10 Reference in the textbook CLO Ch 1,2,3,4,5 1-5 Ch 5,8 5,8 Ch 2,4, 5,,8,9 2,4,5, 8,9 Ch 3,7 3,7 Ch (2-10) 2-10 Ch 7 7 Ch 4,5,8 4,5,8 Ch (2-10) 2-10 Ch Ch 4 4
6 16 Final Test Special Equipment or Supplies Personal Computer Ch 1-to- Ch
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