A History of Computation

Since elementary school, we have known how to add, subtract, multiply and divide, and as soon as we were able to use calculators, life got even easier. But just why do we calculate the way we do, and just how does our calculator do things, especially when we move beyond simple arithmetic into square roots, trigonometry, and logarithms and exponentials. And just how did we compute back before the invention of computers and electronic calculators?

The aim of this course is to take a tour through the history of how we have computed, from the most ancient times to today. First, we will look at some of the different ways of representing numbers through the ages, including some that never really took off but have interesting features. Second, we will look at how to do addition, subtraction, multiplication and division, first using counters, then later with positional notation and other variants. We will look at many different ways of doing basic arithmetic. For example, we will see ten (!) different ways of performing subtraction using positional notation. Third, we will look at various of the tools used through the ages to help us with calculation, from the sand table and abacus through to mechanical adding machines, then analog and digital calculators and computers. Finally, time permitting, we will look at some of the ways developed to find square roots, evaluate trigonometric functions, use logarithms and exponentials, see how some electronic calculators work, think about high precision arithmetic, then finish off with a discussion of pi through the millenia.