The World of Numbers: From Euclid to the Information Age
Block 1: Amelia Taylor
Block 2: Rodney James
This two-block course fulfills the Critical Perspectives: The West in Time and Critical Perspectives: Quantitative Reasoning requirements.
Numbers are as fundamental to humans as are language and music. People have been writing numbers for as long as there has been writing. In our course, we will trace the use of numbers from the ancient civilizations of the Middle East, Egypt, and Mesopotamia through the axiomatic deductive approach taken by the Greek and Hellenistic civilizations all the while observing the many influences from around the world. We will progress to Newton and new insights into infinite processes, and what we now call calculus eventually reaching the twentieth century discussing notions of infinity and Fermat’s Last Theorem.
The way that people think about numbers has evolved over time: natural numbers, prime numbers, rational numbers, real numbers, complex numbers. Similarly, our ability to calculate has evolved: the Peruvian quipu, the Chinese abacus, the modern microprocessor. Using the concept of number to model the world is a fundamental human activity and we will explore its role in everything from foundations of society, to shifting ideas about risk, to computers. We will discover how numbers are both endlessly useful and fascinating.
In our historical journey through the development of numbers, we will consider epistemology (what is truth? how do we know what we know?), the role of mathematics in art and architecture, and the prominence of mathematics in religion and calendrical systems. We will read from a wide range of sources as well as study contemporary plays and film. Along the way, we will also delve into the mathematics of other cultures and make comparisons to the Western tradition. In this course students will read, write, calculate, prove and philosophize!
A two-block course with a unique instructor each block; one grade will be given for the course as a whole.
• There will be occasional afternoon problem sessions.
• The class will spend Week 1 of Block 2 at the Baca Campus in the Sangre de Cristo mountains.
• There is no formal mathematical prerequisite, however, experience and comfort with arithmetic and elementary algebra is strongly recommended.