Description: Do you really understand how numbers work? We are so accustomed to our base-10 positional notation system that it’s hard to make our brains work in any other way; but, think about what mathematics must have been like before Leonardo Fibonacci introduced the Hindu-Arabic numeral system to Europe in the 13th century. Can you imagine doing arithmetic with only Roman numerals and no zero? (Try it. I bet you’ll be converting numbers to decimal without even thinking about it.) In this class we’ll explore how numbers, specifically integers, work, and with that understanding, we’ll learn to solve some hard math problems with ease.
- Week 1 – The Basics: Primes, Divisibility Rules, Exponents, Prime Factorization, Fundamental Theorem of Arithmetic, Counting Factors
- Week 2 – Systems of Numeration, Place Value, Binary, and Other Number Bases
- Week 3 – Base Number Arithmetic and the Units Digit
- Week 4 – Modular Arithmetic
- Week 5 – Diophantine Equations
- Week 6 – Review and Practice
Homework: Math is not a spectator sport. You never really know if you truly understand math until you solve problems. Practice is essential, hence twenty to thirty minutes of homework three times a week and a desire to improve will be the key to getting the most out of this course.
Prerequisites: Students should be advanced in mathematical reasoning beyond grade level and must be fluent with basic pre-algebra skills such as fractions, decimals, percents, and ratios. Algebra is not a prerequisite, but students should have some experience solving basic linear equations and working with square roots and exponents.
Instructor: Jolene Gleason