MME529 On-Line Materials -- Numbers, Polynomials and Algebraic Structures

This page contains materials related to the course MME 529, "Numbers, Polynomials and Algebraic Structures".

Course Description

The course will begin with the most familiar algebraic structures: the integers. After dealing with such issues as prime factorization, modular arithmetic and multiplicative functions, we will see many of the same ideas again in our study of polynomial rings. These two families of examples (subrings of the field of complex numbers and various polynomial rings) will motivate us to introduce abstractions that enable us to approach definitions, theorems, and algorithms from a unified perspective. At each stage, we will take time to explore open-ended projects, we will discuss current applications, and we will creatively develop pedagogical building blocks for later use in the classroom. Some topics to be covered include:

• the Fundamental Theorem of Arithmetic
• the Fundamental Theorem of Algebra
• multiplicative functions
• RSA cryptography
• error-detection schemes for ISBN numbers and postal money orders, etc.
• the error-correcting codes used in CDs, DVDs and MP3s
• repeating decimal patterns in rational numbers
• Weird dice
• Galois fields

Text: Contemporary Abstract Algebra, Seventh (or later) Edition by Joseph Gallian Brooks/Cole, Cengage Learning, 2010.