### Course Overview

This page focuses on the course *18.703 Modern Algebra* as it was taught by Prof. James McKernan in Spring 2013.

This is a first course in abstract algebra. The focus of the course is on traditional algebra topics that have found the greatest application in science and engineering, as well as in mathematics.

### Course Outcomes

#### Course Goals for Students

Students will learn the definition and basic properties of groups, permutation groups, groups of small order, cosets, Lagrange’s theorem, the classification of finite abelian groups, normal subgroups, quotient groups, simple groups and the Sylow Theorems. Students will also learn the definition of rings, basic properties of rings, ideals, quotient rings, integral domains, fields of fractions, unique factorization domains and principal ideal domains, and the classification of finite fields.

### Curriculum Information

#### Prerequisites

Calculus II GIR

Any of the following courses at MIT will prepare you for 18.703:

*18.02 Calculus**18.022 Calculus**18.024 Calculus with Theory**18.02A Calculus**CC.1802 Calculus**CC.182A Calculus**ES.1802 Calculus**ES.182A Calculus*

#### Requirements Satisfied

This course has similar content to *18.702 Algebra II*, and at most one of the subjects can be counted toward an undergraduate major or minor in mathematics.

#### Offered

Every spring semester

### Assessment

The students’ grades were based on the following activities:

- 50% Homework; Late problem sets are not accepted; however, the lowest problem set score will be dropped.
- 20% Midterm exams (10% each)
- 30% Final exam

### Student Information

#### Enrollment

11 students this year. Enrollment has varied each year from ~10 students to 30 students.

#### Typical Student Background

This course is intended for math majors and anyone interested in the applications of abstract algebra, perhaps someone interested in theoretical computer science.

### How Student Time Was Spent

During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:

#### Lecture

- Met 2 times per week for 1.5 hours per session; 24 sessions total.
- The final exam was held during Finals Week, in one 3-hour session.

#### Out of Class

- Read the assigned sections in the textbook
- Work on homework assignments
- Study for the exams