Listed in: Mathematics and Statistics, as MATH-279
Miriam Kuzbary (Section 01)
Knots appear throughout history and in many aspects of our lives. In ancient times, multiple civilizations used them to record data such as in Andean South America and East Asia while in other parts of the world like Northeast Africa and Southwest Asia, knots were more often used in spiritual and religious applications. Knots have other real-world applications even now, such as in sailing, rock climbing, protein folding, and string theory! These days, knot theory is a rich and active area of research involving questions of interest both to mathematicians and to researchers outside of mathematics, and many of these questions boil down to a single essential query: how can we tell when two knots are different? In this course we will begin the study of mathematical knots starting with this question. In order to answer it, we will construct tools called knot invariants and use them to investigate when knots can and cannot be distinguished from each other. Along the way, we will get a taste of some introductory topics in topology, combinatorics, algebra, and analysis including colorings, polynomials, surfaces, and graphs. At the end of the course, there will be a final project which can include interdisciplinary work.
Spring Semester. Professor Kuzbary
How to handle overenrollment: Preference is given to math majors
Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: problem sets, in-class quizzes or exams, take-home exams, reading and writing of mathematical proofs, use of computational software, final project with writing and oral presentation component.
Course Materials