Math 470 - Topology

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Inga Johnson
Associate Professor
Department of Mathematics
Willamette University
Ford 212
ijohnson(at)willamette(dot)edu
503.370.6551

Math 470 - Topology - Syllabus
Class Meetings: T/Th 9:40-11:10 in Ford 201

Course Goals: To understand introductory concepts, calculations and questions about topological invariants, knot theory, classification of surfaces, homotopy theory, and point set topology. To increase proof writing ability (increased clarity and sophistication). To increase ability to communicate mathematics orally and in writing.

Textbooks: Topology NOW!   by Robert Messer & Philip Straffin.
Textbook website.

Homework: The homework for this course will be due in class on Tuesday. The weekly homework assignments will be posted on the course schedule. Your homework must be written up using LaTeX. An introduction to LaTeX and information about how to download it can be found here. You may include figures in your homework by hand or by including the images into your LaTeX file.

Late Homework policy: You may turn in ONE homework assignment late (within one week of when it was due) with no penalty. All late homework assignments should be clearly labeled with the phrase "Late Math 470 HW" at the top of the first page. Any late assignment turned in without this phrase might be lost, or confused with garbage and accidentally thrown out. Any additional late homework assignment that is turned in will be accepted and corrected at my discretion.

Email Recaps: For each class period two students will be assigned to compose and send an email to the class list that includes (1) a recap or summary of the main ideas presented in class and (2) a study guide for the concepts/examples that were skipped but are relevant to the material covered. The recap and study guide should be explanations in your own words. (Do not copy my words or the book's explanations.) This email should tie into previous material covered (when applicable) and include questions that the class or the email composer has regarding current, previous or upcoming material. This summary will be read by all class participants prior to the next class period and serve as the basis for the opening questions of the next class. If it is clear that all students are thoughtfully composing, reading and thinking about the recap emails between class sessions in preparation for the next class there will be no need for quizzes.

The two students assigned for each class period should coordinate which part of the class material they will summarize or meet to jointly compose the message together. The email summary of Tuesday's class must be sent by Wednesday evening before 5PM. The email summary of Thursday's class must be sent by Sunday night.

The instructional goal behind the Email Recaps is to encourage and ensure all students are regularly reviewing and engaging with the material presented in class and reading the book in addition to completing the homework assignments.

Study Habits for Success: I recommend the following study habits to increase your likelihood of success in this class.

1. Before a given class period skim the section of the textbook that will be covered. Look for big picture ideas, definitions that may seem complicated, important examples that you may want to ask about in class. Math textbooks are often more difficult to read than other texts. It is often necessary to read the mathematics several times before the ideas are clear. This skim should serve as your first pass at the material. A slightly fuzzy picture of the material is OK at this point.
2. During class you will see some of the material from the textbook for a second time and some new material that is not in the text. Please feel free to ask questions during class that relate to the material presented.
3. After class, review your notes and reread the section of the textbook that was covered in class. This third pass of the material should solidify all important concepts.
4. Work on the homework problems. Don't expect to be able to sit down and complete all the problems in an hour. Some of the problems will require repeated attempts before you find the solution. I highly recommend starting early and spending many short periods of time on the homework problems that stump you. Coming back to a problem multiple times, even if only for 20 minutes, often leads to deeper understanding and breakthroughs. Extended study sessions working on problems for hours and hours without breaks often leads to frustration, exhaustion and decreased ability for new problem-solving ideas or breakthroughs in understanding.
5. If you still feel shaky with the material after these three passes and are unable to complete any of the homework problems, please come to see me in office hours as soon as possible.

Math Colloquium: You are encouraged to go to many of the Math Department Colloquia this semester, and as part of the course you are required to go to four. Attendance will be taken in Colloquium. If your schedule conflicts with all the Colloquia scheduled, please see me for an alternate reading and writing assignment.

Midterm Exams, and Final Exam: There will be two midterm exams and a final exam. These exams will be taken individually to test your concept understanding, mathematical literacy, and proof writing abilities over the topics covered thus far in the course. The final will be comprehensive. The dates and times of midterm and final exams will posted on the course schedule.

Final Project: Interested students may submit a written request to complete a final course project in lieu of taking the final exam. This request must be received before Thanksgiving Break and only students with a current course grade of B or higher are eligible to submit a request. The project request should outline the topic to be studied, include a list of possible sources and describe a written and oral component that will be completed before the time of the final examination. I will suggest ideas for project topics throughout the semester. Final Projects will be graded out of 150 points.

Special Note: If you have a documented disability and anticipate needing accommodations in this course, please make arrangements to meet with me within the first two weeks of the semester. Please request that a Disability Services staff person send me the appropriate forms verifying your disability and specifying the accommodation you will need. If your disability allows for extra time on an exam you must remind me of your needs at least one week before the exam and send me an email reminder at least three days before the exam to ensure appropriate accommodations have been made.

Academic Honesty: In accordance with Willamette University CLA catalog: ``Plagiarism and cheating are offenses against the integrity of the courses in which they occur and against the College community as a whole... Ignorance of what constitutes plagiarism shall not be considered a valid defense." For further information about the Willamette University academic honesty policy please refer to the CLA catalog.

On homework: It is appropriate and very helpful to have study groups for homework. Sharing ideas and approaches is a good way to learn. However, all students must find their own phrasing and wording for the written homework. Copied homework will earn a grade of zero for all parties involved.