Math 442: Introduction to Algebraic Topology
Spring 2024
Instructor: Kristen Hendricks
Email: kristen. hendricks at rutgers.edu
Office Hours: M 2-3 and F 9-10 over Zoom via Canvas Integration. I also plan to eat lunch in the Livingston Dining Hall Mondays right after class and you are welcome to discuss math with me there.
Location and Time: MTh 10:20-11:40 AM in TIL-252.
Content: This course is a first look at algebraic topology. We will discuss CW complexes, the fundamental group, covering spaces, plane curves, and basic homology and cohomology. Near the end of term we may discuss some special topics according to student interest (with knot theory and vector bundles as the two most likely options).
Text: A. Hatcher, Algebraic Topology. Available free of charge online. It may also be helpful to read Munkres’ discussion of the same topics..
Notes: Lecture notes will be made available here sometime by the day before each lecture, and updated shortly after lecture with any typo corrections or other changes.
Homework: Homework will be assigned weekly and due on Mondays at 5 pm. Homework will be collected via a mirror site on Canvas; the relevant Assignment will remain open for submission until 6 pm, to account for the possibility of technical difficulties, and will then close. The first homework is due January 29. There will be twelve homeworks in total. No late homework will be accepted, but your lowest two homework scores will be dropped in computing your grade.
You are encouraged to work together on your homework. However, you must write up all solutions in your own words, and credit all your collaborators. You are also welcome to use any resources on the Internet that you want – in particular, you are welcome to read the Math Stack Exchange and/or Math Overflow discussions of problems in Hatcher. A good rule of thumb is that you should try to solve every problem yourself for at least half an hour, then ask a classmate or me for thoughts, then try looking online for discussion of the problem.
A subset of the homework will be graded carefully, and some points will be given for completeness of the rest of the assignment. There will be one point of extra credit on each homework possible for quality of presentation -- typesetting your work is always enough to earn this, but the grader may also choose to award it for handwritten work that is tidy and has well-drawn figures. Homework solutions will be posted online promptly.
Exams: There will be an eighty-minute midterm exam in class on Thursday, March 21. There will also be a final exam scheduled by the registrar. Exams will be taken closed book and closed notes. If you miss the midterm exam for a documented good reason, such as serious illness or other comparable emergency, your grade will be based on your final and homework scores. Make-up finals will only be given in extreme cases. In exam circumstances and otherwise, students are expected to be familiar with and abide by the href = "http://academicintegrity.rutgers.edu/academic-integrity-at-rutgers">academic integrity policy.
Disability Accomodations: If you need accommodations for the course, please bring me a Letter of Accommodations as early in the term as possible. There are detailed instructions on how to do this in the University Resources section of this syllabus.
Grading: Grades will be computed as follows:
A reasonable curve will be applied to the composite numerical scores. The bar for an A will not be set higher than an overall 90% in the course.
Schedule: We will cover most of Chapters 0-2 of Hatcher, and part of Chapter 3, followed by some special topics. Precise reading will be posted as we go along. Reading the textbook is strongly recommended.
Assignments
Homework 1. Due January 29 at 5 pm.
Exam Materials
University-Level Resources
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