Math 490
Introduction to Topology
Course Information
Lecture Section 1:
Tuesday and Thursday 1:00pm–2:20pm
Mason Hall 2325
Professor: Sarah Koch
Email: kochsc@umich.edu
Office Hours: Mondays 7pm–8pm, Thursdays 2:45pm–3:45pm and 8:45–9:45pm (Zoom), Fridays 3pm–4pm.
Worksheet Hours: Tuesdays and Thursdays 10pm–11:30pm (Zoom)
Office: East Hall 3855
Tuesday and Thursday 1:00pm–2:20pm
East Hall 4464
Professor: Jenny Wilson
Email: jchw@umich.edu
Office Hours: Tuesdays 9:30am–11:30am, Fridays 4pm–5pm
Office: East Hall 3863
Course Assistant: Madhav Krishna
Email: kmadhav -at- umich.edu
Office Hours: Mondays 2pm–3pm
Location: East Hall Upper Math Atrium
Course Assistant: Zhe Zhang
Email: zhezxz -at- umich.edu
Office Hours: Tuesday 3:30pm–5:30pm (Zoom)
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.
Previous years’ webpages:
(2018) http://www.math.lsa.umich.edu/~jchw/2018Math490.html
(2019) http://www.math.lsa.umich.edu/~jchw/2019Math490.html
Textbook: This course has no assigned textbook. Students will develop the class material through guided worksheets. Because the objectives of the course are problem-solving and self-led discovery of the material, students are asked not to use outside sources.
| Grading Scheme: | ||
| Homework | 30% | |
| Class Participation | 15% | |
| Quizzes | 10% | |
| Midterm Exam | 15% | (Tues 26 Oct 2021, in class) |
| Final Exam | 30% | (Thurs 16 Dec 2021, 4pm–6pm) |
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 3% of the final grade. If you must miss a class, please inform your instructor as early as possible. Circumstances such as illness, job interviews, religious observances, certain university-sponsored events, etc, usually constitute "excused" absences and do not typically count toward the two missed classes, provided your instructor is informed in advance when possible.
Office hours: Students from any section may attend the office hours of either instructor or course assistant.
Office hours take place in-person unless noted. Virtual office hours will take place in the Math 490 Zoom room. See the Canvas course front page for the password.
Math 490 Zoom room
https://umich.zoom.us/j/91012200668
Meeting ID: 910 1220 0668
Worksheet hours: Starting 21 September, Sarah will host "worksheet hours" Tuesday and Thursday evenings over Zoom from 10pm–11:30pm. These are not office hours, instead, they are a way for students to discuss the worksheets. In particular, if a student is absent from class, these worksheet hours are an opportunity to go over the material they missed.
Class conduct: Class discussions 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: Each week, students will be asked to write up and submit one or more problems from the latest in-class worksheet(s), along with some additional homework problems. Homework assignments will be posted to the course webpage. Homework is due Fridays at 8pm, and collected through Gradescope. See the Gradescope instructions below. Your homework solutions should be neat and legible.
Students may not consult books or online references for their homework. You may work in groups and discuss homework problems with other students, but all solutions (worksheet and homework) must be written up independently and in your own words. You must put away any notes from discussions with classmates or office hours 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 between 10-15 minutes. Students will receive 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 or Sarah as soon as possible. Requests for accommodations by persons with disabilities may be made by contacting the Services for Students with Disabilities (SSD) Office located at G664 Haven Hall. The SSD phone number is 734-763-3000 and their website is ssd.umich.edu. Once your eligibility for an accommodation has been determined, this information will be reflected in SSD's Accommodate system. Please note that under most circumstances University Policy is two weeks’ prior notice for any academic accommodation.
Homework
| Homework 0 | Due: Friday 3 September 2021, 5pm | |
| Homework 1 | Due: Friday 10 September 2021, 8pm | |
| Homework 2 | Due: Friday 17 September 2021, 8pm | |
| Homework 3 | Due: Friday 24 September 2021, 8pm | |
| Homework 4 | Due: Friday 1 October 2021, 8pm | |
| Homework 5 | Due: Friday 8 October 2021, 8pm | |
| Homework 6 | Due: Friday 15 October 2021, 8pm | |
| Homework 7 | Due: Friday 22 October 2021, 8pm | |
| Homework 8 | Due: Friday 29 October 2021, 8pm | |
| Homework 9 | Due: Friday 5 November 2021, 8pm | |
| Homework 10 | Due: Friday 12 November 2021, 8pm | |
| Homework 11 | Due: Friday 19 November 2021, 8pm |
| Homework 12 | Due: Friday 3 December 2021, 8pm | |
| Homework 13 | Due: Friday 10 December 2021, 8pm |
Worksheets
| Worksheet 1 | 31 August 2021 | |
| Worksheet 2 | 2 September 2021 | |
| Worksheet 3 | 9 September 2021 | |
| Worksheet 4 | 14 September 2021 | |
| Worksheet 5 | 21 September 2021 | |
| Worksheet 6 | 28 September 2021 | |
| Worksheet 7 | 5 October 2021 | |
| Worksheet 8 | 12 October 2021 | |
| Worksheet 9 | 14 October 2021 | |
| Worksheet 10 | 21 October 2021 | |
| Worksheet 11 | 2 November 2021 | |
| Worksheet 12 | 4 November 2021 | |
| Worksheet 13 | 9 November 2021 | |
| Worksheet 14 | 16 November 2021 | |
| Worksheet 15 | 18 November 2021 | |
| Worksheet 16 | 23 November 2021 | |
| Worksheet 17 | 2 December 2021 |
Quizzes
| Quiz 1 | Tuesday 7 September 2021 | (Solutions) |
| Quiz 2 | Tuesday 14 September 2021 | (Solutions) |
| Quiz 3 | Tuesday 21 September 2021 | (Solutions) |
| Quiz 4 | Tuesday 28 September 2021 | (Solutions) |
| Quiz 5 | Tuesday 5 October 2021 | (Solutions) |
| Quiz 6 | Tuesday 12 October 2021 | (Solutions) |
| Quiz 7 | Tuesday 9 November 2021 | (Solutions) |
| Quiz 8 | Tuesday 16 November 2021 | (Solutions) |
| Quiz 9 | Tuesday 23 November 2021 | (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 Tuesday 26 October, and cover material up to and including Worksheet 8 and Homework 7.
The exam is closed-book, but each student may bring in a single double-sided standard-size (8.5"x11") sheet of notes. Each student must handwrite or typeset their own sheet of notes. Typewritten notes have a minimum of 12pt font.
Some practice material is available:
| 2018 Practice Midterm | (Solutions) | |
| 2018 Midterm | (Solutions) | |
| 2019 Midterm | (Solutions) |
This year's midterm and solutions are now available.
| 2021 Midterm | (Solutions) |
Our final exam will be held Thursday 16 December 4pm to 6pm.
It is a comprehensive exam, covering material from the entire semester, but with more emphasis on material since the midterm.
The final exam is closed-book, but each student may bring in a single double-sided standard-size (8.5"x11") sheet of notes. Each student must handwrite or typeset their own sheet of notes. Typewritten notes have a minimum of 12pt font.
In addition to the Review Package, some previous years' finals are available:
| 2018 Final Exam | (Solutions) | |
| 2019 Final Exam | (Solutions) |
This year's final exam and solutions are now available.
| 2021 Final | (Solutions) |
Gradescope Instructions
Gradescope is an online platform for grading homework and exams. Your work is still being graded by a human on the Math 490 instructional team, but Gradescope streamlines the process. Gradescope is designed around grading best-practices, for example, the solutions are anonymized for the grader, points are assigned according to a rubric that we set, and Gradescope allows the grader to give more detailed feedback more efficiently.
You can find instructions and trouble-shooting advice at the Gradescope student centre and Gradescope help page.
How to set up a Gradescope account. Gradescope synchronizes with Canvas to create our course roster. Students should receive an email from Gradescope with information on how to create their log-in credentials. If you have not received this email by Thursday 2 September, contact Jenny or Sarah.
How to upload an assignment or test. To upload an assignment, you must:
Note: This final step is important! The grader will not see your solution to a question if it is not properly selected.
This video explains the homework submission process.
Resubmission. If you find a mistake in your solution, it is possible to resubmit it anytime before the deadline passes. In Gradescope, click on your assignment, and you will see a "resubmit" button in the bottom right corner. Unfortunately, to make any changes to your solution you must re-upload your whole solution and repeat the page selection process.
How to produce a pdf of your homework. If you write your homework solutions by hand, you can "scan" your solutions to create a pdf. Gradescope has recommendations for apps you can use to produce a pdf with a smartphone. To create legible scans, it is best to write with a dark pencil or pen.
Please preview your scan before you upload it to ensure it is clearly readable.
You can also complete your homework on a computer, using software such as LaTeX. If you do use LaTeX, it may be easiest to draw figures separately by hand and scan or photograph them. You can add graphics to a LaTex document by using the graphicx package, or use software to collate the pdf files after your LaTeX document is complete.
Viewing your graded assignment. Once your work is graded and the grades are "published", you will be able to log into Gradescope to see your graded solutions. Click on the name of your assignment to see a problem-by-problem breakdown of your score. Click on an individual problem to see your solution, the complete grading rubric, and any comments from the grader.
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)
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)
- UM Psychiatry resources for COVID-19, including advice for college students
- Advice from UCSF on coping during COVID-19