AMAT 342 : Elementary Topology

Fall 2021, Class #1886

Monday, Wednesday 10:10-11:30 on Zoom

Last revision: 8/16

Instructor: Michael Lesnick
mlesnick [at] albany [dot] [the usual thing]
Office Hours: Monday, Wednesday 4:30-5:30, and by appointment
Office Hours Locations: Massry B014, B003, and B125 (see Blackboard for schedule)

I typically respond to emails within a day (two days on the weekend).

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Prerequisites:
AMAT 214, AMAT 220, and (especially) AMAT 299.
IMPORTANT: You cannot take this course without my permission if you have not passed all of the prerequisites.

About this Course:
This course will introduce some of the key ideas of topology. Topology studies the properties of geometric objects that are preserved under "continuous deformations." Informally speaking, continous deformations include bending, twisting, and stretching of the object, but not tearing or puncturing.

Topology is one of the major areas of modern mathematics. It is a beautiful subject in its own right and it plays an important role in other parts of mathematics, the sciences, and engineering.

Topics may include: Course Logistics:
As of now, the plan is to conduct the course in a fully in-person format. Masks are required at all times. Course materials will be hosted on Blackboard.

Course Materials:
There is no required textbook. I will provide readible handwritten lecture notes. I will also provide concise typed notes summarizing the main definitions and ideas.

Supplemental Materials (Not Required):
For those looking to explore course topics in more depth, there are many good textbooks on topology, though some are pitched at a somewhat higher level than this course. Two standard choices are "Topology" by Munkres, and "Basic Topology" by Armstrong.

For those interested in learning about applications of topology to the sciences, I recommend "Topological Data Analysis for Genomics and Evolution: Topology in Biology" by Blumberg and Rabadan. The first half of the book is an accessible introduction to applied topology.

Exams:
My tentative plan is to have in-class exams on the folowing days:
Midterm I: Wednesday, September 29,
Midterm II: Wednesday, November 3,
Final: TBD.

Exam rules: For each exam, you will be allowed to prepare one page of handwritten notes, front and back, to use during the exam. During the exam, no use of any other materials (inlcuding the internet, phone, etc.) will be allowed.

Homework:
Homework will be assigned semi-regularly. In addition, we may occasionally have quizzes. Homeworks and quizzes will be weighted equally. The lowest two scores among the homework and quizzes will be dropped. Homework is to be handed in at the beginning of class on the day it is due (you will have a 5 minute grace period), and this rule will be enforced strictly. Tentatively, homework handed in at most one day late may be accepted with a 30% penalaty, or at most two days late with a 50% penalty. You may discuss homework with your classmates, but homework must be written up on your own.

Grading:
The class will use the university's A-E grading scheme.

30%: Homework
20%: Midterm I
20%: Midterm II
25%: Final
5%: Class engagement/effort.

Each homework will be weighted equally. The lowest two homework scores will be dropped. The midterm and final may be curved, but not downward.

The engagement/effort score will take into account attendance, participation in class, and participation in office hours. Students do not need to engage in all of these ways to have a high engagement/effort score, but should actively engage through some of these avenues.

Expectations:
Topology is a fun and fascinating subject, but it is also a challenging one. The material is inherently very abstract, and it takes time and careful thought to become comfortable with the ideas. As a first eposure to topology, this class tries to introduce the ideas in a gentle, friendly way. Still, most students will find the material to be a good challenge, and to have a good experience in this class, they will need to put in substantial work. As a rough estimate, I expect students to put in at least 8-10 hours of work per week on this course, aside from time spent in class. This time should be spent reading the notes, doing homework, visiting office hours, discussing the material with your classmates, and thinking about the material on your own.

Pandemic-Related Challenges:
The pandemic creates a complex and ever-evolving set of difficulties for students. I am mindful of this. If you are dealing with issues created or exacerbated by the pandemic that risk getting in the way of your being a focused, active participant in this class, I encourage you to discuss this with me.

Academic Regulations:
Naturally, SUNY Albany's Undergraduate Academic Regulations apply to this course, and students are expected to be familiar with these. The regulations concern academic integrity and missing/rescheduling exams, among other things. Students should also be aware of the University's Medical Excuse Policy.

There will be no leeway on missed exams or last-minute exam rescheduling, except as noted in the regulations. If you anticipate an issue with the timing of an exam, please let me know as soon as possible.

Cheating: Cases of cheating are a major headache for an instructor, typically creating hours of extra work to resolve. Know that it is often a lot easier to detect cheating than students realize. If you are caught cheating, your grade will pay a heavy price, and there is a good possibility that you will fail the course. Cheating may also be reported to the university, as described in the Academic Regulations.