Jonathan Tannenhauser
Lecturer in Mathematics
Background in theoretical particle physics, focusing on a conjectured equivalence between certain quantum field theories and certain string theories.
Professor Tannenhauser's background is in theoretical particle physics, where his work has focused on the the AdS/CFT correspondence, a conjectured equivalence between certain quantum field theories and certain string theories. More recently he has become interested in applying computational and statistical tools to the genomics of birdsong. The goal is to pinpoint which genes are expressed in a singing bird's brain and how the expression pattern changes over the course of brain development.
Education
- A.B., Harvard University
- M.A., University of California (Berkeley)
- Ph.D., University of California (Berkeley)
Currently teaching
Probability
MATH220
Probability is the mathematics of uncertainty. We begin by developing the basic tools of probability theory, including counting techniques, conditional probability, and Bayes's Theorem. We then survey several of the most common discrete and continuous probability distributions (binomial, Poisson, uniform, normal, and exponential, among others) and discuss mathematical modeling using these distributions. Often we cannot calculate probabilities exactly, and we need to approximate them. A powerful tool here is the Central Limit Theorem, which provides the link between probability and statistics. Another strategy when exact results are unavailable is simulation. We examine Markov chain Monte Carlo methods, which offer a means of simulating from complicated distributions.
(MATH 220 and STAT 220 are cross-listed courses.)-
This course examines the number 𝝅 from various points of view in pure and applied mathematics. Topics may include: (1) Geometry: Archimedes’ estimates; volume and surface area of spheres in arbitrary dimensions; Buffon’s needle (and noodle); Galperin’s colliding balls; the isoperimetric inequality; triangles in spherical and hyperbolic geometry; Descartes’s theorem on total angular defect (discrete Gauss-Bonnet). (2) Digit hunting: Viète’s infinite product; Wallis’s product and related ideas (the Gaussian integral and its multidimensional extension, saddle point approximation, Stirling’s approximation); the Leibniz-Gregory formula and Machin-type formulae; spigot algorithms and the Bailey-Borwein-Plouffe formula; elliptic integrals, the arithmetic-geometric mean, and the Brent-Salamin algorithm. (3) Analysis: complex exponentials; Fourier series; the Riemann zeta function, dilogarithms, Bernoulli numbers, and applications to number theory (means of arithmetic functions). (4) Algebra: the irrationality and transcendence of e and 𝝅.