From Babylonians to Binary: A History of Counting (Full Course)

The objective of this course is to cultivate a knowledge of past and present uses of number systems beyond our everyday base-10 system. Students will learn about the birth of these systems, the different purposes and cultures around their use, and how to calculate numbers in them.

Students will be able to answer the following questions (and more) for each class.

Day 0: Did you know that not everyone uses the 10 digits that we do and take for granted? Let's take a look at how number systems in other bases work so we can count and calculate numbers like a Babylonian, a computer, or (maybe?) a panda!

Day 1. Egyptian Hieroglyphics: How did Egyptians represent numbers? What do we have that they didn’t? How did they construct large numbers? How did they subtract numbers or calculate fractions?

Day 2. Babylonian Cuneiform: What was different about how place value was represented? What did they use in place of zero? Why do some believe that trigonometry would be easier if we used a base system like the one the Babylonians did?

Day 3. Roman Numerals: How were Roman numerals similar to Egyptian numerals? What was unique in the addition and subtraction properties used to determine a number’s value? What other
conventions were used for very large numbers? Why do we still see these numbers on clocks and other places today?

Day 4. Maya Vigesimals: What calendar did the Mayans actually live by? How could they build a whole number system with just three symbols? What does “zero” mean, and just as importantly, what does it do?

Day 5. Ancient Chinese: What alternative did the Chinese have to a number’s position alone to indicate place value? The Chinese are obviously still here--why has their numerical writing system
all but disappeared?

Day 6. Computer Binary: How does one translate to English a message in binary such as 01100001 01101100 01101100 00100000 01111001 01101111 01110101 01110010 00100000 01100010 01100001 01110011 01100101? What is the genius of binary and higher-base numbers for programming and coding?

Day 7. Hindu-Arabic Numbers: How did we come to use the Hindu-Arabic numerals and
the base-10 number system? What are its inherent advantages and disadvantages to other bases?

Mr. Kelsey is a professional math, philosophy, logic, and language tutor, writer, and super-learning advocate. He is certified through the Praxis II (5161) exam to teach high school mathematics (pre-algebra through calculus), but his range of subjects has included ACT/SAT test prep, college-level mathematics, science, logic, foreign languages, and philosophy. 

As of March of 2019, Kelsey has had over 1000 registered tutoring hours on top of 3+ years of experience teaching in the classroom. This background, coupled with a bent for lifelong learning, has given him a knack for finding and rounding out students' weak spots and boosting their confidence in themselves. I've helped many students find the joy in learning math, language, and philosophy by helping them "crack the code" and dissolve the illusion so often impressed on us that everything about these subjects is difficult, complicated, or even impenetrable. It's not.

Please see his Teacher Bio below for details.

Additional practice problems following each lesson are posted in the class forum for students to complete and check for understanding. Completed assignments should be uploaded and directly sent to me through the Outschool messages tool in the classroom.

A check for understanding (CFU, or "Mastery Check") will be given in the final lesson, as well as the end of each individual lesson, to review material and test for student comprehension. The final CFU will be given in the form of a review and challenge to the students in the form of a game show-like quiz.

1 hour 50 minutes per week in class, and an estimated 1 - 2 hours per week outside of class.