MATH 3094-001: Knot Theory
Instructor: Katie Hall
Prerequisites: MATH 2710/W or 2142Q is preferred. Linear algebra and some familiarity with proofs and/or mathematical maturity is necessary. Email instructor with a description of your mathematical background for a permission number.
The objectives are this course are twofold: First, students will learn how to distinguish knots using both basic knot invariants like 3-coloring and more compli- cated invariants like knot polynomials. They will learn how to determine properties of a knot, for example, whether a knot has an alternating knot diagram, from these invariants. Students will also learn about surfaces, including the classification of orientable and non- orientable surfaces. Finally, we will tie these ideas together to see what surfaces we can get from knots.
Second, this class will introduce students to potentially new proof techniques including how to write an appropriately rigorous proof in a very visual area of math.
MATH 3094-002: Mathematics for Machine Learning
Prerequisites: MATH 2110Q, MATH 2210Q, and MATH 2710/W, or permission of the instructor. Email one of the instructors for a permission number.
Machine Learning is a “hot topic” that brings together ideas from computer science, statistics, and mathematics to extract structures from large data sets. As a branch of artificial intelligence, it has applications in building automated systems, identifying patterns and making decisions. Some typical problems in machine learning include image recognition, fraud detection and extracting meaning from text.
Machine Learning uses mathematics as its basic language and main resource of important techniques. In order to exploit the immense possibilities of Machine Learning, a thorough mathematical understanding of many of these techniques is necessary.
In this course we will discuss the mathematical foundations of key algorithms in Machine Learning, and, through lab projects, apply these algorithms to some real world data. This course will incorporate computer work in Python. Necessary programming skills will be taught as part of the course.