MATH 540—FALL 2009 Mathematics 540: Topology Instructor: Dr. Chris Thron Office: TAMUCT North Campus 16B Phone: 512.293.0715 (cell) Email: firstname.lastname@example.org Skype: chris.thron Google chat: email@example.com Office Hours: Mondays- 1:15 – 3 pm Tuesdays 3 – 4:30 pm, 7:15 – 8 pm (Virtual on odd weeks) Wednesdays 1:15 – 3 pm (Virtual on even weeks) Thursdays 3 – 4:30 pm, 7:15 – 8 pm Saturdays- Virtual 8 – 10 pm Virtual office hours: Contact via Google chat. 1.0 Course Overview A first graduate course in topology is often considered foundational for graduate study in mathematics. It extends many of the concepts in a study of the topology of the real line to the more general context of topological spaces. Though primarily intended for graduate students, advanced undergraduate mathematics majors provisionally admitted to the graduate program may also enroll in the course. The course topics include the theoretical development of open and closed sets, interior, closure, boundary, neighborhoods, continuous functions, separation, subspaces, compactness, connectedness, and continua. Prerequisite: Math 409 (Advanced Analysis). Students mayl be asked to demonstrate competence in prerequisite material that is essential for success in this course. 2.0 Competency Goal Statements Students will: Students will demonstrate knowledge of fundamental definitions and theorems by repeating them. Students will demonstrate the ability to prove mathematical theorems related to the material. Students will demonstrate an understanding of the theoretical aspects of the course by applying them to related problems. Students will demonstrate the ability to apply the material in the course to investigate mathematical questions. 3.0 Required Materials Topology Without Tears, Online textbook (see http://uob-community.ballarat.edu.au/~smorris/topology.htm for instructions on obtaining) 4.0 Course Requirements Reading Comprehension (12%). You are expected to read the textbook outside of class and answer questions posed by the instructor. Your answers must be posted on MATH 540—FALL 2009 Blackboard before the next class period. Problems and proofs (24%) These will be submitted approximately weekly via Blackboard. Midterm tests (32% total). There are three midterm tests. Tests will closely follow the homework. Students will be allowed to make their own cheat sheet as per instructor’s guidelines. Cheat sheets are handed in with the exam Final exam: (32%). Half of the final will cover the last 4 chapters, and half of the final is cumulative. Your lowest test grade will be replaced with your grade on the cumulative portion of the final. 5.0 Grading Criteria Rubric and Conversion Reading Comprehension (150 points) 12% 80-100%=A Problems and Proofs (300 points) 24% 70- 79%= B Midterm Exam 1 (200 points) 16% 60- 69%= C Midterm Exam 2 (200 points) 16% 50- 59%= D Final Exam (400 points) 32% Below 50 % F TOTAL (1250 points) 100% Scoring for each of these categories is as follows: Reading Comprehension assignments (on a more-or-less weekly basis) will be worth 10-20 points if complete, and a random sample of the questions is found to be accurate. Partial credit may be given for incomplete assignments. Each Problems and Proofs assignment will be assigned 40 points if complete, and a random sample of the problems is found to be correct. Partial credit may be given to partially complete or partially correct assignments. Exams will be a combination of multiple-choice, diagram, and short-answer questions at the instructor’s discretion. The instructor reserves the right to determine the relative proportion of these questions, to provide best coverage of the material. In addition to the point values given above, up to 25 points (2%) extra credit may be given at instructor’s discretion for additional class or take-home activities. Course Calendar FALL 2009 Comprehension Questions are due the day before class by midnight (via Blackboard). Computation problems are due every Sunday by midnight (via Blackboard) Wk # Ch(s) Topics 1 1 Topological Spaces 2 2 The Euclidean Topology 3 -- Set theory 4 --- Proofs 5 -- Review and TEST over first 4 weeks 6 3 Limit Points 7 3 Limit Points 8 4 Homeomorphisms MATH 540—FALL 2009 9 4 Homeomorphisms 10 5 Continuous Mappings 11 5 Continuous Mappings 12 --- Review and TEST 3-5 13 6 Metric Spaces 14 6 Metric Spaces 15 6 Metric Spaces and Review 6.0 Drop Policy If you discover that you need to drop this class, you must go to the Records Office and ask for the necessary paperwork. Professors cannot drop students; this is always the responsibility of the student. The Records Office will give a deadline by which the form must be returned, completed and signed. Once you return the signed form to the records office and wait 24 hours, you must go into Duck Trax and confirm that you are no longer enrolled. If you are still enrolled, FOLLOW-UP with the records office immediately. You are to attend class until the procedure is complete to avoid penalty for absence. Should you miss the deadline or fail to follow the procedure, you will receive an F in the course. 8.0 Academic Honesty (Tarleton State University Catalog, p. 37) Texas A&M University Central Texas expects all students to maintain high standards of personal and scholarly conduct. Students guilty of academic dishonestly are subject to disciplinary action. Academic dishonesty includes, but is not limited to, cheating on an examination or other academic work, plagiarism, collusion, and the abuse of resource materials. The faculty member is responsible for initiating action for each case of academic dishonesty. 9.0 . Disability Services If you have or believe you have a disability, may wish to self-identify. You can do so by providing documentation to Sarina Swindell, the Assistant to the President for Diversity and External Education Initiatives. Students are encouraged to seek information about accommodations to help assure success in this class. Please contact Sarina Swindell, at firstname.lastname@example.org, 254-519-5711 or KLLN Room 104C. 10. Library Services INFORMATION LITERACY focuses on research skills which prepare individuals to live and work in an information-centered society. Librarians will work with students in the development of critical reasoning, ethical use of information, and the appropriate use of secondary research techniques. Help may include, yet is not limited to: exploration of information resources such as library collections and services, identification of subject databases and scholarly journals, and execution of effective search strategies. Library resources are outlined and accessed at http://www.tarleton.edu/centraltexas/departments/library/ 11. Grading Policies MATH 540—FALL 2009 Regular attendance is extremely important to your success in this course. If you are absent, it is your responsibility to find out what material was covered. In general, makeup work is not accepted. I compensate for this by dropping the three lowest comprehension question grades, the two lowest homeworks, and the lowest midterm test. Exceptions to this policy may be made at the instructor's discretion in case of: Prolonged illness Death in the immediate family Legal proceedings MATH 540—FALL 2009 Appendix: Course Philosophy A. Instructor Goals You may have heard that topology is what shows that a coffee cup is the same as a donut. One branch of topology does indeed have something to do with shapes. However, the topology that we’ll talk (called point-set topology) about is more like the study of fabric – the fabric (detailed structure) of mathematical spaces, and showing that different mathematical spaces have the same “fabric”. For instance, we think that three-dimensional space is essentially “different” from two dimensional space, while the surface of a globe is somehow similar to two-dimensional space. Topology can be used to make these ideas precise. This kind of topology (point-set topology) is not a subject of active research. However, it is fundamental for rigorous arguments in analysis (real analysis, complex analysis, differential equations, and so on). Topology is a very particular subject. You might say that topology is the grammar of analysis. In topology you need to learn to make very exact statements, and very precise arguments. This is one of the main goals of the course – to get you to “talk” real mathematics. B. Course Methodology In most courses, there are these common components: A) Reading the textbook B) Lecture C) Homework Problems D) Projects and Lab exercises E) Quizzes or Tests A. I assign reading, and I ask reading comprehension questions. You are to do the reading outside of class, and post the answers to the reading comprehension questions on Blackboard. B. I won't do much “lecturing” in this course. In class, I will give sufficient background to work the problems, and will work problems that students are having trouble with. C. In this course, Homework is central. When you get right down to it, doing math means being able to do the problems. If you can't do the problems, then you can't do math. Homework will be graded partly for completion grade, partly for content. Homework will be due every week via Blackboard. E. Midterm tests will be every 5 weeks (weeks 5, 10, 15). Each test will cover about 4 chapters. The final exam is cumulative. C. Instructor Responsibilities: Post necessary study materials on Blackboard Respond effectively to all email requests within 36 hours Return all papers no more than 1 week after they are handed in Make all grades available to students via Blackboard after each midterm test. D. Student Responsibilities: The student is solely responsible for: MATH 540—FALL 2009 Completing each assignment by the specified due date. Obtaining assignments and other information for classes from which they are absent. If necessary materials are missing from Blackboard, requesting the instructor to put them up. Utilizing, as needed, all available study-aid options (including meeting with the instructor, referring to outside texts, etc.) to resolve any questions that they might have regarding course material. Giving as much of an effort as it takes to pass this course. You should expect to spend two hours outside of class for every in-class hour. If your background is weak, you may have to spend more time than this. Saving all graded work. If there is a dispute about grades, no recorded grade will be changed unless the paper in question is produced.
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