Math 31 - Fall 2006
Dartmouth College
home
general information
homework
office hours
professor
| course
description |
textbook |
exams |
| scheduled lectures |
homework policy |
disabilities |
| grades |
honor principle |
religious observances |
Math 31 is an introductory course in algebraic structures: Nonempty sets with at least
one operation. Abstract Algebra is the branch of mathematics that studies sets, (e.g. integers)
where one can add one or more operations, (e.g. addition and multiplication) and some axioms
(e.g. commutatitivity, associativity, etc.). The main algebraic structures studied in Math 31
are groups, rings and fields. In Math 22 you already learned about vector spaces, another example
of an algebraic structure.
Historically, algebraic structures arose first in some other field of mathematics.
In the nineteeth century they were specified aximatically and studied in their own right in
abstract algebra. Because of these origins, abstract algebra has numerous and fruitful connections to
all other branches of mathematics.
Abstract algebra has many applications to other fields of science for example chemistry and physics.
Other applications include digital cryptography and error correction.