AMAT 342 : Elementary Topology

Fall 2023, Class #1740

Monday, Wednesday 3:00-4:20 Arts and Sciences B15

Instructor: Michael Lesnick
mlesnick [at] albany [dot] [the usual thing]
Office Hours: Monday, Wednesday 4:30-5:30, and by appointment
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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 introduces some of the key ideas of topology. Topology studies the properties of geometric objects that are preserved under "continuous deformations." Informally speaking, continious 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:
The course will be conducted in a fully in-person format. Course materials will be hosted on Brightspace.

Course Materials:
There is no required textbook. I will provide readable handwritten lecture notes. These will be the main course reference. I will also provide concise typed notes summarizing the main 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 Rábadan. 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 following days:
Midterm I: Wednesday, September 27,
Midterm II: Wednesday, November 1,
Final: December 11, 3:30 p.m.

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 (including 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. Tentatively, homework handed in at most one day late may be accepted with a 30% penalty, 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.

25%: Homework/Quizzes
20%: Midterm I
20%: Midterm II
30%: 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 exposure to topology, this class tries to introduce the ideas in a gentle, friendly way. Still, most students will find the material to be challenging, 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 7-10 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.

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. 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 it is possibile that you will fail the course. Cheating may also be reported to the university, as described in the Academic Regulations.