## Math Academy

*Please note: for summer 2021 this program will be offered in a modified online format. *

## Details

Math Academy is a challenging, two-week, intensive, enrichment experience for students in grades 9-12 with very strong mathematical thinking ability. 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. The program is typically run during the summer. Each two-week term is a standalone special topics course that goes in-depth on a single topic. 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.

Math Academy will be run online in summer 2021. 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. At 3pm each day we will regroup for an office hour when students can ask questions about the problems. This will provide the same number of contact hours as our usual one-week format. Classes and office hours will be conducted live over Zoom and require participants to have access to a device with a microphone and camera.

## Summer 2021 Online Program

July 19 - 30, 2021 (two weeks)

Class: 11am-1pm Monday to Friday

Office Hour: 3pm-4pm Monday to Friday

Instructor: Malors Espinosa Lara, PhD candidate, Department of Mathematics

Course Title: *Knot Theory*

Course 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. An example of this process that is well know to all of us is tying our shoelaces or tying a tie. 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.

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. A particular example is DNA Knotting or Protein Knotting in biology. Knot theory itself has its beginnings in physics and not in pure mathematics!

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. 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 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. Also, we will solve several problem sheets related to the theory we are studying and read material from papers and science magazines related to this beautiful area of mathematics.

## Cost

The cost of the program is $400+tax for the 2 week term.

Bursaries are available. Please wait until you've been accepted into Math Academy before requesting a bursary here.

## Location

Summer 2021 Math Academy will be offered online.

## Apply

Students must first apply for the program and be accepted in order to register. Successful applicants will be informed of their acceptance as soon as possible. Round 2 Application Deadline: Monday May 17th, 2021.

Application for 2021 Summer Math Academy is now closed.