Think Like a Mathematician: Explorations in Math
It is impossible to be a mathematician without being a poet in your soul.
Sofya Kovalevskaya, Russian mathematician who made noteworthy contributions to analysis, partial differential equations and mechanics.
May 8-28, 2022
For Ei ATS Scholars (and equivalent);
Students in Grades 8/9/10 in 2022-23
This course will be a unique opportunity for students to explore and learn mathematical concepts rarely offered at the middle to high school level. Students will delve into rigorous and proof-oriented mathematical explorations spanning several topics of current interest. Some of the topics likely to be discussed include:
Proofs vs Conjectures. Techniques of Proofs (such as induction, pigeonhole principle, recursion) in Algebra, Geometry, Combinatorics; Proofs of impossibilities! Importance of using cross domain techniques (such as using Algebra in geometry and vice versa)
Number Theory and its use in modern day cryptography
The wonderful world of Probability; winning and losing in lotteries and in gambling bets
Introduction to Combinatorics, game theory and search and sort algorithms.
The course will use lectures, problem sessions, demonstrations, and exploratory research to engage students. The problems and puzzles will be at the level of international Olympiads. There will be graded levels of problems so that every student can find his or her own rhythm and pace in tackling these problems.
The goal of the course is to shape and attune the students’ minds towards mature mathematical reasoning and get them to start thinking like mathematicians. We expect that students going through this course, when confronted with challenging unfamiliar problems, will be able to marshal their own mental resources and come up with ways of tackling these.
For a student with a passion for math and the willingness to embrace such challenges without fear, this is an environment to build confidence.