Sparks Short Courses

Sparks Short Courses (a.k.a., "Sparks") are small-group, low-unit pass/fail courses for first-year undergraduates. The goal of each Spark is to share a spark -- a spark of insight, a spark of creativity, a spark of inspiration -- that speaks to the heart of a field or research area in which the faculty instructor is engaged. Sparks are intended to help undergraduates early in their Caltech experience to connect individually with faculty and to experience the same thrill of discovery that drew faculty into their own fields of interest.

Since enrollment in each Spark is limited, early registration is recommended.

Enrollment in Sparks Short Courses is limited to First-Year Undergraduates. Other students must contact instructors for permission.

Units for the course: 0.5-0.5-1

Grading Scheme: Pass/fail

Days/times: First Monday of classes – 3/31 @ 2:00pm

Room: Chen 100

Experimentally, the question of counting is always at the fore, whether in the context of counting 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.

How many prime numbers are there less than some given integer? This course will consider a series of case studies in counting, beginning with the 18th century efforts to count molecules, 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.