Math 590
Introduction to Topology
Course Information
Lecture: Monday, Wednesday, Friday 12:00pm–12:50pm
East Hall 3096 (Map)
Professor: Jenny Wilson
Email: jchw@umich.edu
Office Hours: Mondays 10:30–11:30am and Wednesdays 2:00–4:00pm
Office: East Hall 3863 (Map)
Course Description:
This course covers the fundamentals of general (point-set) topology. Topics include metric spaces, topological spaces, continuous functions and homeomorphisms, separation axioms, quotient and product topology, compactness, and connectedness. We may also cover some topics in algebraic topology as time permits.
See the LSA course listings for more details.
Grades will be made available through Canvas.
Textbook: Topology (James Munkres)
| Grading Scheme: | ||
| Homework | 40% | |
| Quizzes | 10% | |
| Midterm | 15% | (Wednesday 13 March, in class) |
| Final Exam | 35% | (Monday 29 April, 1:30pm–3:30pm) |
Homework overview: Homework assignments will be posted to the course webpage. Homework is due Fridays, and collected at the beginning of class. Your homework solutions should be neat, legible, and stapled.
Each student's two lowest homework scores will be dropped.
You are encouraged but not required to write your solutions using LaTeX. If you do typeset your solutions, it is likely easiest to draw images by hand on a separate sheet of paper and reference them in your typed solutions.
Homework collaboration policy: 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.
You are welcome to use other texts and online resources to review the mathematical theory or computational techniques we cover. You may not, however, seek out solutions to specific homework problems. Outside sources should be used to improve your understanding of the material, not as a shortcut to finish assignments with an incomplete understanding. Use your discretion.
You are expected to put away any notes from discussions with classmates or other sources while you write up your homework solutions, to ensure you fully understand and can reproduce the arguments.
The homework is your foremost resource for practice with the course material, and for feedback on your work. Doing the homework thoughtfully is essential to your success in this class.
Late homework policy: Each student is permitted to drop their two lowest homework scores to allow for circumstances such as the occasional illness or overscheduled week. Late homework is generally not accepted, except under extenuating circumstances such as medical issues that impact more than two weeks of the semester.
Quizzes:
There will be frequent short quizzes throughout the quarter, usually on Wednesdays. 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 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 the University Policy is two weeks’ prior notice for any academic accommodation.
Homework
| Homework 1 | Due: Friday 11 January 2019 | |
| Homework 2 | Due: Friday 18 January 2019 | |
| Homework 3 | Due: Friday 25 January 2019 | |
| Homework 4 | Due: Friday 1 February 2019 | |
| Homework 5 | Due: Friday 8 February 2019 | |
| Homework 6 | Due: Friday 15 February 2019 | |
| Homework 7 | Due: Friday 22 February 2019 | |
| Homework 8 | Due: Friday 1 March 2019 | |
| Homework 9 | Due: Friday 15 March 2019 | |
| Homework 10 | Due: Friday 22 March 2019 | |
| Homework 11 | Due: Friday 29 March 2019 | |
| Homework 12 | Due: Friday 5 April 2019 | |
| Homework 13 | Due: Friday 12 April 2019 | |
| Homework 14 | Due: Friday 19 April 2019 |
Quizzes
| Quiz 1 | Wednesday 16 January 2019 | (Solutions) | |
| Quiz 2 | Postponed: Friday 1 February 2019 | (Solutions) | |
| Quiz 3 | Wednesday 6 February 2019 | (Solutions) | |
| Quiz 4 | Wednesday 13 February 2019 | (Solutions) | |
| Quiz 5 | Wednesday 27 February 2019 | (Solutions) | |
| Quiz 6 | Wednesday 20 March 2019 | (Solutions) | |
| Quiz 7 | Wednesday 10 April 2019 | (Solutions) | |
| Quiz 8 | Wednesday 17 April 2019 | (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 Wednesday 13 March.
| Midterm Review Problems | (Selected Solutions) |
The midterm and its solutions are now available:
| Midterm | (Solutions) |
The final exam will be held on Monday 29 April from 1:30pm–3:30pm.
| Final Review Problems | (Selected Solutions) |
The exam is closed-book, but each student may bring in a single double-sided standard-size (8.5"x11") sheet of notes, which they must prepare themselves, either by hand-writing or typing in at least 12-point font.
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)