|
|
Mathematics Department |
The Mathematics Department has reorganised its 300 level algebra classes in order to clarify their different purposes and emphasize their different teaching styles.
There are three ``entry level" algebra classes with 200 level prerequisites
MAT 318 involves writing a project, while MAT 312 involves work with computers. The other three classes are more theoretical with a considerable emphasis on proofs.
A list of the classes in approximate order of difficulty follows.
MAT 318: Classical Algebra. An examination of algebra from a historical perspective. Topics include Euclid's algorithm, congruences and the unsolvability of the three ``great problems" (trisecting the angle, squaring the circle and solving quintics). All students write an extended project, on topics ranging from the quaternions to Pascal's triangle. Fall and Spring Mandatory Prerequisite: MAT 211 or AMS 210.
MAT 312: Applied Algebra. Applications of conguence arithmetic to cryptography and applications of group theory to the theory of error-correcting codes. Students participate in computer workshops that illustrate these applications. Crosslisted with AMS 351. Fall and Spring Mandatory Prerequisites: MAT 203 or 205 or AMS 261, and MAT 211 or AMS 210.
MAT 310: Linear Algebra. Develops the basic theory of vector spaces and linear transformations. Together with MAT 320, it is a core course for the mathematics major in which students are taught how to write proofs. Fall and Spring Mandatory Prerequisites: MAT 203 or 205 or AMS 261, and MAT 211 or AMS 210.
MAT 313: Abstract Algebra. Describes the basic properties of groups, rings and fields. Students are expected to have taken either MAT 312 and 318, which provide relevant examples of the general theory, or MAT 310 which gives experience with the theoretical development of algebraic structure. Fall only Mandatory Prerequisites: MAT 318 or 312 or 310 or permission of the instructor.
MAT 311: Number Theory. The fascinating properties of numbers are one of the main driving forces of mathematics. This course discusses some accessible parts of number theory such as continued fractions, quadratic residues, and properties of prime numbers. In order for this course to be to cover some interesting material, students are expected to know congruence arithmetic before they start. Spring only Mandatory Prerequisites: MAT 318 or 312 or 313 or permission of the instructor.