In the final day we will have a guest lecture and, depending on the number of students, we will have five/ten-minute presentations by the participants on topics related to knot theory.
Examples of the problems we face are the following: (i) if we are given a knot, is it unknottable or is the knot irremovable? (ii) How do we distinguish knots among themselves? (iii) How do we look for new knots? (iv) Can we classify knots? (v) How is the pure mathematical theory related to other areas of science? We will see instances of all these, and more, questions in the academy. In this Math Academy our focus will be to see what a knot means mathematically and what are the kind of questions we, as mathematicians, try to answer. Knot theory itself has its beginnings in physics and not in pure mathematics!
A particular example is DNA Knotting or Protein Knotting in biology.
Of course, the process of knotting an object that is similar to a string and study the knot that results goes beyond tying rope and is a very natural process that appears in several branches of mathematics and science. If you have had the chance of practicing rock climbing you might have heard about the eight knot or the square knot, and if you ever gloss over books of knots for camping or used in the navy or for sailing you will find a great number of different knots, that look different and that require different rules to be created. An example of this process that is well know to all of us is tying our shoelaces or tying a tie. Instructor: Malors Espinosa Lara, PhD candidate, Department of MathematicsĬourse Description: We usually think of a knot as the result of manipulating a string in specific ways and then pulling the ends of it to make the knot tight. Classes and office hours will be conducted live over Zoom and require participants to have access to a device with a microphone and camera. This will provide the same number of contact hours as our usual one-week format. At 3pm each day we will regroup for an office hour when students can ask questions about the problems. The format of the program has been modified by spreading it out over two weeks and providing a break during the day to work on problems away from the screen. Math Academy will be run online in summer 2021. The topic will be creative, fun, and somewhat abstract in other words, what mathematicians consider “real math.” Math Academy includes both lecture-style teaching and significant time devoted to independent and small-group problem-solving. Each two-week term is a standalone special topics course that goes in-depth on a single topic. The program is typically run during the summer. Students are accepted into the program on the basis of their solutions to a problem set which is aimed at highlighting their ability to think mathematically and creatively rather than testing for specific curricular knowledge. Math Academy is a challenging, two-week, intensive, enrichment experience for students in grades 9-12 with very strong mathematical thinking ability. Please note: for summer 2021 this program will be offered in a modified online format.
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