You probably grew up hearing about how quickly the world’s population is expanding. Billions of humans now inhabit most every corner of the globe, one of fastest explosions of life in known natural history. While it may seem that growth and busts of populations are essentially random - especially when it comes to humans, who in theory have the power to choose how quickly their community changes - there is an entire suite of mathematical tools and techniques dedicated to describing and predicting how human numbers will change. Part of this is a country’s census, whose job it is to figure out how a country has and will change in terms of its people and their characteristics. In addition to large-scale, decadal censuses, more frequent data is collected and used to predict everything from the population density in a crowded city to the life expectancy in 2075. Beyond predicting quantitative outcomes, the mathematics and statistics employed in demographic modeling play a large role in how people are treated: for example, which districts receive funding at what levels, and what new public programs are developed. In this course, we’ll cover the bread and butter of demography, and use demographic data to explore how many humans there are and where they live. Given that 2020 marked an important Census milestone, this course will be a fun introduction to using the data generated by this program. Census data are used to justify and explain trends in human communities. Once informed about how to use these data, you’ll see how important and ubiquitous the Census is!

How can we use math to discover patterns in nature? Why might some patterns be difficult to decode, while others are more obvious? You may have learned about Bayes' Theorem in a high school statistics course. It turns out that this theorem has inspired (and largely enabled) a whole subfield of mathematics and statistics: Bayesian Analysis. In this course, we’ll go through the basics of Bayesian Analysis, an increasingly popular framework used in scientific research and as an underpinning for machine learning. We will demystify the relatively intuitive idea behind Bayesian Analysis, which will equip you for college courses in math and computer science. The fun part, though, will be diving into application areas in biology, including bacterial genetics and habitat modeling. Students of this course will gain solid mathematical skills while trying your hand at the wide world of mathematical biology.