Math 540 Topology Fall 09 by FWvp68C


									                                                                             MATH 540—FALL 2009

                                    Mathematics 540: Topology

Instructor:   Dr. Chris Thron
Office:       TAMUCT North Campus 16B
Phone:               512.293.0715 (cell)
Skype:               chris.thron
Google chat:
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
     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
 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,
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

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
      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
 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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