Math 490: Introduction to Topology (Fall 2023)

Department of Mathematics
University of Michigan

Math 490: Introduction to Topology

Fall 2023

Lecture Section 1:
Tuesdays and Thursdays at 1:00-2:30pm
Location: East Hall 3088
Instructor: Nir Gadish
Email: gadish@umich.edu
Office: East Hall 3827
Office hours: Tuesdays, Wednesdays, and Thursdays at 5:30pm-6:30pm

Lecture Section 2:
Tuesdays and Thursdays at 1:00-2:30pm
Location: East Hall 2866
Instructor: Linh Truong
Email: tlinh@umich.edu
Office: East Hall 4842
Office hours: Mondays 10:30am-12:30pm
Syllabus

Course Assistant and Grader: Akash Narayanan
Email: anaray@umich.edu

Course Information:
This course is an introduction to point-set topology. 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.

Our course will use Inquiry-Based Learning (IBL). During each class, students will work on exercises together in small groups. Development of collaboration and mathematical communication skills is an overarching goal of the course.


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.

Homework

Homework 1, due Sept 8 at 8pm
Homework 2, due Sept 15 at 8pm
Homework 3, due Sept 22 at 8pm
Homework 4, due Sept 29 at 8pm
Homework 5, due Oct 6 at 8pm
Homework 6, due Oct 13 at 8pm
Homework 7, due Oct 20 at 8pm
Homework 8, due Nov 3 at 8pm
Homework 9, due Nov 10 at 8pm
Homework 10, due Nov 17 at 8pm
Homework 11, due Dec 1 at 8pm

Worksheets

Worksheet 1, Aug 29
Worksheet 2, Aug 31
Worksheet 3, Sept 7
Worksheet 4, Sept 14
Worksheet 5, Sept 21
Worksheet 6, Sept 26
Worksheet 7, Oct 3
Worksheet 8, Oct 10
Worksheet 9, Oct 17
Worksheet 10, Oct 26
Worksheet 11, Oct 31
Worksheet 12, Nov 2
Worksheet 13, Nov 7
Worksheet 14, Nov 9
Worksheet 15, Nov 14
Worksheet 16, Nov 16
Worksheet 17, Nov 21
Worksheet 18, Nov 28
Worksheet 19, Nov 30
Worksheet 20, Dec 5

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, October 24, 2023.
Some practice material is available here.

Our final exam will be held Tuesday, December 12, 2023 at 1:30pm–3:30pm.

Grading Scheme:
Homework    30%
Class Participation    15%
Quizzes 10%
Midterm Exam 15% (Tuesday, October 24, 2023, in class)
Final Exam 30%    (Tuesday, December 12, 2023 at 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 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.

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 your professor 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.


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 your instructor.

How to upload an assignment or test. To upload an assignment, you must:

  • Produce a legible pdf of your solutions. Be sure that the solutions are well labeled.
  • Upload the pdf to Gradescope by the deadline.
  • Select the page(s) that contain the solution to each of the assigned problems.
    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.