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 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.
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
Every spring semester
The students' grades were based on the following activities:
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.
During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:
- 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