57091 Algebra for High School Teachers, Stark, Fall 2008 - Spring 2009
Course Description
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)
Contact information
| Class schedule
Mondays (5:05-7:35) Rm 306 Main Hall:
Nov 10, 17, 24;
Dec 1, 8, 15;
Jan 12, 26;
Feb 2, 9, 16
Saturdays: (9:30-12:15) Rm 007 Library:
Nov 22,
Dec 13,
Jan 24,
Feb 7
Syllabus
Textbook
Homework
You will be assigned weekly homework which I will collect every Monday.
Exams
Midterm: Dec 15th, in class
Final presentations: Feb 9 and 16, in class
Grading
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