## Faculty of Science Course Syllabus

Department of Mathematics & Statistics

## MATH 3032: Abstract Algebra II (Winter 2023)

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

**Lectures:** Tuesdays and Thursdays, 11:35-12:55 Atlantic Time. LSC C202.

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

**Course website:** http://categorified.net/23Winter3032/.

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

### Course Description

Rings, fields, integral domains, Fermat's theorem, Euler's theorem, ideals, quotient rings, prime and maximal ideals, factorization of polynomials, GrÃ¶bner bases, Unique Factorization Domains, Euclidean Domains and Gaussian integers, and applications as time allows.

### Prerequisites

Group Theory (MATH 3031 or equivalent).

### Course materials

The main textbook for the class is **Abstract Algebra:
Theory and Applications** by Thomas W. Judson. It is freely available from the author's website. We will focus primarily on chapters 16, 17, and 18. Additional material will be drawn from *A First Course In Abstract Algebra* by John B. Fraleigh; specifically, the section on Gröbner bases, but students are not expected to purchase a copy of that book. Brief introductions to other topics in commutative algebra will be included as time permits.

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

### Course Assessment

#### Weekly homework assignments: 50%.

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.

Students will be allowed to drop one homework score for any reason. In the case of further extenuating circumstances, students should consult with the instructor.

#### Exams: 50%

There will be one midterm exam and one final exam. Both exams will be delivered in-person. Students may bring prepared (paper!) notes with them, but may not use electronic resources during the exam. The midterm will be worth 20% of the final grade, and the final will be worth 30% of the final grade.

#### 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)