Fibonacci's rabbits and Darwin's elephants: integer sequences for evolutionary biology
Course Description
What is the population size trajectory of a family of rabbits that follows particular rules for population growth? This question, posed by Leonardo Fibonacci in 1202, can be viewed not only as a touchstone of mathematics, but also as an early moment in the mathematical modeling of biological populations. Centuries later, in the 1859 Origin of Species—with no apparent knowledge of Fibonacci—Charles Darwin would ask a mathematically similar question about a population of elephants. In this seminar, students will analyze integer sequences that, like the Fibonacci sequence, connect to problems in mathematical biology. The biological topics that we will examine emerge from population dynamics, population genetics, and the study of evolutionary trees. The mathematical analysis will include combinatorial enumerations, recurrences, generating functions, and bijections. Through the investigation of biologically-linked integer sequences, students will develop an appreciation for the interface of mathematics and evolutionary biology.
Meet the Instructor: Noah Rosenberg
“So many areas of mathematics have applications in biology—combinatorics, dynamical systems, mathematical statistics, and probability, to name a few. The art of mathematical biology involves uncovering links between problems in biology and tools from math—often revealing interesting mathematics in the process. As a mathematical evolutionary biologist with an undergraduate degree in math and a PhD in biology, I delight in finding these connections, and I hope to share that enthusiasm in this course.”
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