This course is a mathematical introduction to probability theory, covering random variables, moments, multivariate distributions, law of large numbers, central limit theorem, and large deviations.
Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.
This course will cover important topics in linear algebra not usually discussed in a first-semester course, featuring a mixture of theory and applications.
Mathematical logic and proof, mathematical induction, counting methods, recurrence relations, algorithms and complexity, graph theory and graph algorithms.
Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series
Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.
This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.
