Math 490
Introduction to Topology
Course Information
Lecture: Tuesday and Thursday 1:00pm–2:20pm
East Hall 4088 (Map)
Professor: Jenny Wilson
Email: jchw@umich.edu
Office Hours: Tuesdays 9:00am–11:00am and 5:00pm–6:00pm
Office: East Hall 3863 (Map)
Course Assistant: Colby Kelln
Email: ckelln "at" umich.edu
Office Hours: Wednesdays 7:00pm–8:00pm
Location: East Hall Math Common Room (Map)
Course Material: The course will investigate ideas relating to open sets, compactness, connectedness, and convergence of sequences in metric spaces and abstract topological spaces. See the LSA course listings for more details.
IBL: Our course will use an
Grades will be made available through Canvas.
Textbook: This course has no assigned textbook. Material will be developed through worksheets. Please be sure to make careful notes on the work done in class and save your worksheets and their solutions, as these will be your main study resource!
| Grading Scheme: | ||
| Homework | 30% | |
| Class Participation | 15% | |
| Quizzes | 10% | |
| Midterm Exam | 15% | (Tuesday 23 October, in class) |
| Final Exam | 30% | (Wednesday 19 December, 1:30pm–3:30pm) |
Attendance policy: Attendance in class is required. From the date a student registers for the class, s/he may miss two classes, but each subsequent unexcused absence will result in a penalty of 5% of the final grade. If you must miss a class, please inform Jenny as early as possible.
Class conduct: Class discussions, class presentations, and small group-work are major components of this course. Students are expected to be active participants in the classroom, and are expected to conduct themselves with professionalism and respect for their classmates. Our goal is to create a supportive class environment where students are comfortable testing ideas, and both offering and receiving constructive criticism from peers.
Homework policy: Homework assignments will be posted to the course webpage. Homework is due Thursdays, and collected at the beginning of class. Late homework is generally not accepted except under extenuating circumstances. Your homework solutions should be neat, legible, and stapled. Use of books or online references is strongly discouraged. You may work in groups and discuss homework problems with other students, but your solutions must be written up independently and in your own words. Please put away any notes from discussions with classmates or other sources while you write up your solutions, to ensure you fully understand and can reproduce the arguments.
Each student's two lowest homework scores will be dropped.
Quizzes: There will be regular short quizzes throughout the quarter, usually on Tuesdays. Quizzes will typically be about 10-12 minutes. I will give advance notice about each quiz and hints about what it will cover. The quizzes are intended to encourage the class to regularly review the material, to provide practice for the exams, and to give feedback (both to you the student, and to me the teacher) about your progress, early on and in a lower stakes setting than the exams.
Each student's two lowest quiz scores will be dropped.
Academic integrity: Students are expected to know and to uphold the LSA Community Standards of Academic Integrity.
Students with documented disabilities: If you might need an academic accommodation based on the impact of a disability, please get in touch with Jenny, and contact the Office of Services for Students with Disabilities (SSD) (734-763-3000) as soon as you can. SSD typically recommends accommodations through a Verified Individualized Services and Accommodations (VISA) form. Any information you provide is private and confidential. Please note that University Policy is two weeks’ prior notice for any academic accommodation.
Homework
| Homework 0 | Due: Thursday 6 September 2018 | |
| Homework 1 | Due: Thursday 13 September 2018 | |
| Homework 2 | Due: Thursday 20 September 2018 | |
| Homework 3 | Due: Thursday 27 September 2018 | |
| Homework 4 | Due: Thursday 4 October 2018 | |
| Homework 5 | Due: Thursday 11 October 2018 | |
| Homework 6 | Due: Thursday 18 October 2018 |
| No homework due Thursday 25 October 2018. Happy studying! |
| Homework 7 | Due: Thursday 1 November 2018 | |
| Homework 8 | Due: Thursday 8 November 2018 | |
| Homework 9 | Due: Thursday 15 November 2018 |
| No homework due Thursday 22 November 2018. Happy Thanksgiving! |
| Homework 10 | Due: Thursday 29 November 2018 | |
| Homework 11 | Due: Thursday 6 December 2018 |
Worksheets
| Worksheet 1 | 4 September 2018 | |
| Worksheet 2 | 6 September 2018 | |
| Worksheet 3 | 11–13 September 2018 | |
| Worksheet 4 | 13–25 September 2018 | |
| Worksheet 5 | 25 September – 2 October 2018 | |
| Worksheet 6 | 4–9 October 2018 | |
| Worksheet 7 | 11 October 2018 | |
| Worksheet 8 | 18–25 October 2018 | |
| Worksheet 9 | 30 October – 1 November 2018 | |
| Bonus Worksheet | 1 November 2018 | |
| Worksheet 10 | 1–6 November 2018 | |
| Bonus Worksheet | 6 November 2018 | |
| Worksheet 11 | 8–13 November 2018 | |
| Bonus Worksheet | 13 November 2018 | |
| Worksheet 12 | 20–29 November 2018 | |
| Bonus Worksheet | 20 November 2018 | |
| Worksheet 13 | 4–6 December 2018 | |
| Worksheet 14 | 6–11 December 2018 |
Quizzes
| Quiz 1 | Tuesday 11 September 2018 | (Solutions) | |
| Quiz 2 | Tuesday 18 September 2018 | (Solutions) | |
| Quiz 3 | Tuesday 25 September 2018 | (Solutions) | |
| Quiz 4 | Tuesday 2 October 2018 | (Solutions) | |
| Quiz 5 | Tuesday 9 October 2018 | (Solutions) | |
| Quiz 6 | Tuesday 30 October 2018 | (Solutions) | |
| Quiz 7 | Tuesday 6 November 2018 | (Solutions) | |
| Quiz 8 | Tuesday 13 November 2018 | (Solutions) | |
| Quiz 9 | Tuesday 20 November 2018 | (Solutions) | |
| Quiz 10 | Tuesday 4 December 2018 | (Solutions) |
Exams
The course will have a closed-book midterm exam and a closed-book final exam.
The midterm will be held in-class on 23 October 2018, and cover material up to and including Worksheet #7 and Homework #6. Some practice material is available:
| Practice Midterm | (Solutions) |
| Additional Practice Problems |
The midterm and its solutions are now available:
| Midterm | (Solutions) |
Our final exam will be held Wednesday 19 December from 1:30pm–3:30pm. It is a comprehensive exam, covering material from the entire semester, but with more emphasis on material since the midterm.
The exam is closed-book, but each student may bring in a single double-sided standard-size (8.5"x11") hand-written sheet of paper.
Some additional practice material is available:
| Additional Practice Problems |
The final exam and its solutions are now available:
| Final Exam | (Solutions) |
Optional Reading
The following reading is strictly optional: it is not related to the course material and will not be discussed in the course. These are articles on math education and learning psychology which may be of interest to math students.
Dweck - Beliefs about intelligence (Nature.com)
Kimball and Smith - The myth of 'I'm bad at math' (The Atlantic)
Tough - Who gets to graduate (New York Times Magazine)
Paul - How to be a better test-taker (New York Times)
Boaler - Timed tests and the development of math anxiety (Education Week)
Parker - Learn math without fear (Stanford Report)
Steele - Thin ice: stereotype threat and black college students (The Atlantic)
Vedantam - How stereotypes can drive women to quit science (NPR)
Stroessner and Good - Stereotype threat: an overview (University of Arizona)
Lockhart - A mathematician's lament (Mathematical Association of America)
Duchin - The sexual politics of genius (Tufts University)
Campus Resources for Wellbeing
As a student, you may experience personal challenges that impacts your ability to participate or impacts your academic performance in our class. These could include anxiety, depression, interpersonal or sexual violence, difficulty eating or sleeping, loss, and/or alcohol or drug problems. The University of Michigan provides a number of resources available to all enrolled students.- Counseling and Psychological Services (CAPS)
- University Health Service 24-hour Nurse Line (734-764-8320)
- Psychiatric Emergency Service (PES) (734-936-5900)
- Sexual Assault Prevention and Awareness Center (SAPAC)
(24-hour Crisis Line: 734-936-3333) - University Psychology Clinic (evaluation and therapy)
- Services for Students with Disabilities (SSD)
- Campus Mind Works (mental health education and drop-in wellness groups
for students with a diagnosed mental health disorder) - Resources for eating disorders
- Resources for alcohol and other drugs
- Addiction Center and Collegiate Recovery Program
- Wolverine Support Networks
(peer-facilitated group meetings and community events) - UHS Wellness Coaching
- MiTalk
- Helping a friend
- Resources for financial needs and medical assistance
- National Suicide Prevention Lifeline (1-800-273-8255)
- Substance Abuse and Mental Health Services Administration Helpline (1-800-662-4357)
- Trevor Project Lifeline (24-hour chat or phone
1-866-488-7386),
and the Trans Lifeline (877-565-8860)