Instructor Insights

Instructor Insights pages are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.

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:

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

The Classroom

  • A small classroom with tables, chairs, and several chalkboards.

    Room 1 of 1

    Lecture

    A small classroom with several chalkboards was used for this course.

 

Assessment

The students' grades were based on the following activities:

The color used on the preceding chart which represents the percentage of the total grade contributed by homework. 50% Homework; Late problem sets are not accepted; however, the lowest problem set score will be dropped.
The color used on the preceding chart which represents the percentage of the total grade contributed by midterm exams. 20% Midterm exams (10% each)
 

Student Information

11 students took this course in Spring 2013.

Enrollment

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

3 hours per week
  • 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

9 hours per week
 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. Lecture session held. No session scheduled. Lecture session held. No classes throughout MIT.
2 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
3 No classes throughout MIT. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
4 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
5 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
6 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
7 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
8 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT.
9 No session scheduled. Lecture session held. No session scheduled. Lecture session held; midterm exam held. No session scheduled.
10 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
11 No classes throughout MIT. No classes throughout MIT. No session scheduled. Lecture session held; assignment due date. No classes throughout MIT.
12 No session scheduled. Lecture session held. No classes throughout MIT. Lecture session held; assignment due date. No session scheduled.
13 No session scheduled. Lecture session held. No session scheduled. Lecture session held; midterm exam held. No session scheduled.
14 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No session scheduled.
15 No session scheduled. Lecture session held. No session scheduled. Lecture session held; assignment due date. No classes throughout MIT.
16 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT; final exam held. No classes throughout MIT.
Displays the color and pattern used on the preceding table to indicate dates when classes are not held at MIT. No classes throughout MIT
Displays the color used on the preceding table to indicate dates when lecture sessions are held. Lecture session
Displays the symbol used on the preceding table to indicate dates when exams are held. Exam
Displays the color used on the preceding table to indicate dates when no class session is scheduled. No class session scheduled
Displays the symbol used on the preceding table to indicate dates when assignments are due. Assignment due date