This course will cover the basics of knot theory. A (mathematical) knot can be thought of as a piece of string which has been knotted (in the traditional sense) with its ends glued. Two knots are the "same" if one can be moved through space to look exactly like the other (without breaking the gluing). An essential question in knot theory is to be able to distinguish different knots. Answering this question proves challenging and the attempt to address it has inspired beautiful mathematics for hundreds of years, and continues today.
The lectures will focus on an introduction of modern data science techniques and the foundational mathematical concepts in linear algebra, probability, and basic optimization related with these techniques. Sufficient case studies with real-world data sets will be provided to illustrate how to use the learned techniques and how to choose an appropriate model.
This course is an introduction to theoretical statistics for students with a background in probability. A mathematical formalism for inference on experimental data will be developed.
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.
MATH 3215, MATH 3235, and MATH 3670 are mutually exclusive; students may not hold credit for more than one of these courses.
Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.
MATH 3215, MATH 3235, and MATH 3670 are mutually exclusive; students may not hold credit for more than one of these courses.
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.
An introduction to proofs in advanced mathematics, intended as a transition to upper division courses including MATH 4107, 4150 and 4317. Fundamentals of mathematical abstraction including sets, logic, equivalence relations, and functions. Thorough development of the basic proof techniques: direct, contrapositive, existence, contradiction, and induction. Introduction to proofs in analysis and algebra.
