STATS 405 / ECON 405 is a very accelerated introduction to mathematical statistics that requires complete fluency with advanced differential calculus. The purpose of the course is to provide students with a deep theoretical understanding of the foundations of statistical inference. Topics include probability theory, experimental and theoretical derivation of sampling distributions, hypothesis testing, and properties of estimators including maximum likelihood and method of moments. In practice most students enrolling in STATS 405 / ECON 405 have experience in advanced calculus beyond the required MATH 116, are typically planning to enroll subsequently in STATS 406 / ECON 406, and often are considering graduate study in economics or statistics. Students looking for a general, less mathematical treatment are urged to consider instead STATS 404 / ECON 404, which covers the same material.