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 9:30am–11:30am and Wednesdays 5:30pm–6:30pm
Office: East Hall 3863 (Map)

Course Assistant: Alex Wang
Email: alxwang "at" umich.edu
Office Hours: Mondays 6pm–7pm
Location: EH 1866

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 Inquiry-Based Learning (IBL) format. For a portion of 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. The group discussions are an opportunity for students to practice conveying mathematical ideas clearly, precisely, and effectively.

Course Webpage: http://www.math.lsa.umich.edu/~jchw/2019Math490.html
Grades will be made available through Canvas.

Previous years’ webpages:
(2018) http://www.math.lsa.umich.edu/~jchw/2018Math490.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% (Tuesday 22 October, in class)
Final Exam 30%    (Wednesday 18 December, 10:30am–12:30pm)

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. Circumstances such as illness, job interviews, certain university-sponsored events, etc, usually constitute "excused" absences and do not typically count toward the two missed classes, provided Jenny is informed in advance when possible.

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.

Worksheet solutions: Students will be assigned, on a rotating basis, the job of writing up or editing selected solutions to the worksheet problems they worked out with their groups. I will distribute their solutions to the class. Students are responsible for the correctness of their solutions keys.

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. Students are asked not to use books or online references. 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 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. 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 5 September 2019           
Homework 1     Due: Thursday 12 September 2019           
Homework 2     Due: Thursday 19 September 2019           
Homework 3     Due: Thursday 26 September 2019           
Homework 4     Due: Thursday 3 October 2019           
Homework 5     Due: Thursday 10 October 2019           
Homework 6     Due: Thursday 17 October 2019           
No homework due Thursday 24 October 2019. Happy studying!           
Homework 7     Due: Thursday 31 October 2019           
Homework 8     Due: Thursday 7 November 2019           
Homework 9     Due: Thursday 14 November 2019           
Homework 10     Due: Thursday 21 November 2019           
Homework 11     Due: Tuesday 3 December 2019           


Worksheets

Instructions for submission of worksheet solutions
Worksheet 1     3 September 2019           
Worksheet 2     5 September 2019           
Worksheet 3     12 September 2019           
Worksheet 4     17 September 2019           
Worksheet 5     24 September 2019           
Worksheet 6     26 September 2019           
Worksheet 7     3 October 2019           
Worksheet 8     10 October 2019           
Worksheet 9     10 October 2019           
Worksheet 10     24 October 2019           
Worksheet 11     29 October 2019           
Worksheet 12     31 October 2019           
Worksheet 13     7 November 2019           
Worksheet 14     12 November 2019           
Worksheet 15     14 November 2019           
Worksheet 16     21 November 2019           
Worksheet 17     26 November 2019           
Worksheet 18     5 December 2019           
Review Problems     10 December 2019           


Quizzes

Quiz 1     Tuesday 10 September 2019     (Solutions)
Quiz 2     Tuesday 17 September 2019     (Solutions)
Quiz 3     Tuesday 24 September 2019     (Solutions)
Quiz 4     Tuesday 1 October 2019     (Solutions)
Quiz 5     Tuesday 8 October 2019     (Solutions)
Quiz 6     Tuesday 29 October 2019     (Solutions)
Quiz 7     Tuesday 5 November 2019     (Solutions)
Quiz 8     Tuesday 12 November 2019     (Solutions)
Quiz 9     Tuesday 19 November 2019     (Solutions)
Quiz 10     Tuesday 26 November 2019     (Solutions)
Quiz 11     Thursday 5 December 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 22 October 2019, and cover material up to and including Worksheet #9 and Homework #6. Some practice material is available:

2018 Practice Midterm     (Solutions)          
2018 Midterm     (Solutions)          
Additional Practice Problems               

The midterm and its solutions are now available:
Midterm     (Solutions)          


Our final exam will be held Wednesday 18 December from 10:30am–12:30pm. 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, last year's final is available:
2018 Final Exam     (Solutions)          

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.

Some non-university resources:



















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