57091/49995 Algebra for High School Teachers, Fall 2008

This course is offered in support of our Master's program for secondary teachers and it will become one of the core courses for the program. This is a gentle introduction into modern algebra with an emphasis on connections to high-school curriculum, problem-solving, examples, and applications. The topics covered may include:
• Induction (Fibonacci numbers and Hanoi Towers)
• Newton's Binomial Formula
• Complex Numbers and Trigonometry (De Moivre's Theorem, complex exponentiation, Euler's Theorem, roots of unity), Quaternions and Octonians
• Integers and Divisibility, Congruences (Fermat's Little Theorem, Wilson's Theorem, Chinese Remainder Theorem, Dates and Days)
• Error-Correcting Codes, Primality Testing, Introduction into Public-Key Cryptology
• Introduction into Group Theory (symmetry and groups of motion, permutations, integers mod m),
• Introduction into Ring Theory (integers mod m and polynomials; irreducible polynomials)
• Geometric Constructions
• Fields (definition and examples)

There are no formal prerequisites. It is expected though that the undergraduate students registering for this course are integrated math majors who have completed courses in Discrete Math, Fundamental Concepts of Algebra, and Fundamental Concepts of Geometry. Please talk to me if you are thinking about registering for the course or have already registered.

Jenya Soprunova, soprunova@math.kent.edu
Office hours: TBA in MSB 219 (cancellations will be announced here)
Telephone: (330)672-9086
FAX: (330)672-2209

Lecture: W 4:25 - 7:05 in MSB 211

Statement on academic dishonesty