Samuel Dodds

The 'Things of Mathematics' are its tools. The purpose of this course is to analyze and build some of the things that have built mathematics. Tools such as the abacus, astrolabe, sextant, sector, slide rule, planimeter, and others were ancestors of the earliest computers, such as the difference engine and the differential analyzer, which were special-purpose and mechanical. In this course, we rediscover how mathematics was literally 'handled' by earlier people. The course content extends across traditional divisions in mathematics (arithmetic, algebra, geometry, trigonometry, calculus). It also compares systems of notation and calculation, incorporating perspectives on mathematical cognition from psychology and anthropology. The focus of this course is making as the means to engage with mathematical concepts. Standard textbook-type excerpts will be used to convey the needed mathematical background. There will also be readings to give historical context to each tool and related mathematical topic. In order to revisit fundamental mathematics in a rigorous way, we will examine, understand, and actually build devices such as those mentioned. The sharing of student work and experience gained in the making process will be a consistent component of this course. A main component of student work is the making of math tools via given instructions. There will also be in-class problem solving activities to gain math facility, and there will be weekly readings for background accompanied by short comprehension quizzes.