This course provides a rigorous introduction to the fundamental structures of algebra: integers, polynomials, rings, fields, and groups. It is a cornerstone course for math majors, and is part of a two-semester sequence leading to Math 334. The fall semester is designed to introduce the objects of study and introduce students to the vocabulary and methodology of abstract algebra. The spring semester covers advanced topics that build on this introductory material.
The course has a strong focus on learning how to write clear and precise
mathematical definitions and proofs. In many ways, it is a writing class, with frequent
assignments involving student writing of proofs, and in-depth feedback on the mathematical
content and style of these proofs.
Math majors are required to take Math 333 as well as one of Math
334 or Math 318.
Prerequisites:
Math 215 (Linear Algebra), and either Math
121 or Math 216 or consent of instructor.
Who should take this course?
All math majors and minors
Chemistry majors (or anyone else) interested in studying the mathematics of symmetry
Physics majors interested in applications of symmetries in theoretical physics
Computer science majors interested in computer arithmetic, error-correcting codes, or
cryptography
Prospective high school teachers
Anyone interested in number theory
Anyone interested in exploring the formal or conceptual side of mathematics in depth
Topics covered:
Algebra of the integers: modular arithmetic, primes, divisibility, factoring
Algebra of polynomials: congruence, irreducibles, divisibility, factoring
Introduction to rings
Introduction to fields
Introduction to groups
For detailed information about Math 333 this year, please consult the list of Fall Courses and Spring Courses linked to the Mathematics and Statistics Home Page.