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.
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.