Counting Badly and Brilliantly (E100)

Summary

How many prime numbers are there less than some given integer?
How many molecules of CO2 are there in the atmosphere?
How many more microscopic states are there in a cup of water than in a chunk of ice?

Experimentally, the question of counting is always at the fore, whether in the context of counting CO2 molecules in the atmosphere, as pioneered by Caltech’s own David Keeling, or counting the number of mRNA (transcriptomes), proteins (proteome), or metabolites (metabolome) in living cells.

This course will consider a series of case studies in counting, beginning with the 18th century efforts to count molecule, showcasing simultaneous efforts to count prime numbers and the rise of the entropy concept in the 19th century. One of the most important parts of this course will be to dig deeply into the questions of estimation and approximation. The goal is to force students to rethink their own understanding of what we mean by an equals sign and why we have other symbols such as approximately equal to or asymptotically equal to.

Schedule

This course is offered in the Spring term of the 2025–26 academic year. We will meet every Monday for a one hour discussion at Chen Neuroscience Research Building, Room 100. Assigned reading will be posted on the Syllabus page.