## Faculty of Science Course Syllabus

Department of Mathematics & Statistics

## MATH 4180/5180: Algebraic Topology (Winter 2023)

**Instructor:** Theo Johnson-Freyd, theojf@dal.ca.

**Lectures:** Tuesdays and Thursdays, 10:05-11:25 Atlantic Time. LSC C234.

**Office Hours:** Tuesdays and Wednesdays 15:35-16:55 Atlantic Time, or by appointment. Chase 214.

**Course website:** http://categorified.net/23Winter5180/.

This course is governed by the academic rules and regulations set forth in the University Calendar and by the Senate.

### Course Description

An introduction to algebraic topology including the following topics: the definitions, properties and methods of computation of the fundamental group of a topological space; simplicial, singular and cellular homology groups; basic properties and methods of computation of homology groups; a selection of application such as the classification of surfaces and fixed point theorems.

### Prerequisites

Group Theory (MATH 3031 or equivalent).

Students are encouraged to review some basic category theory and point-set topology. An excellent resource for such a review is the book *Topology: A Categorical Approach* by Tai-Danae Bradley, Tyler Bryson, and John Terilla.

### Course materials

The main textbook for the class is **Algebraic Topology** by Allen Hatcher. It is freely available from the author's website.

Homework, notes, and so on will be available on the Course Content page. Lectures will be delivered in person.

### Course Assessment

Weekly homework assignments will be drawn from the exercises in each section of the textbook. I encourage you to work together to complete your homework assignments. Studies have shown that social ties are a main predictor of success in STEM classes. Although you are encouraged to work together, the homework you submit must be written by you individually. There are many online resources offering solutions to homework at all levels. If you choose to use such resources, please be cautious: they often provide too detailed an answer, and students can trick themselves into thinking that they understand more than they do by copying those answers.

Graduate students (enrolled in 5180) must each give a short (15-20 minutes) presentation sometime during the semester, based on one of the "Additional Topics" sections of the textbook; please confirm topic and presentation date with the instructor. Undergraduate students (enrolled in 4180) are encouraged to give a presentation for extra credit.

There will be a final exam. There will not be a midterm.

#### Component weighting

#### Math 4180

**Homework:** 70%.

**Final exam:** 30% .

Conversion of numerical grades to Final Letter Grades follows the Dalhousie Common Grade Scale:

**A+** (90-100)

**A** (85-89)

**A-** (80-84)

**B+** (77-79)

**B** (73-76)

**B-** (70-72)

**C+** (65-69)

**C** (60-64)

**C-** (55-59)

**D** (50-54)

**F** (<50)

#### Math 5180

**Homework:** 50%.

**Presentation:** 20%.

**Final exam:** 30%.

Conversion of numerical grades to Final Letter Grades follows the Dalhousie FGS Common Grade Scale:

**A+** (90-100)

**A** (85-89)

**A-** (80-84)

**B+** (77-79)

**B** (73-76)

**B-** (70-72)

**F** (<70)