Seminar

Linear Algebra ∩ Calculus ≠ Empty Set

Abstract:

Integration by parts is one of the most time-consuming methods of integration that we learn in calculus, second only to the dreaded trig-substitution. However, in certain settings, we can speed up the process by using tools from linear algebra. By considering functions as vectors, we can find a basis for a subspace that allows us to compute integrals via a simple matrix multiplica-tion. Will this discovery lead to a paradigm shift in integration techniques? No! But it is an interesting intersection of ideas. Food and drinks will be provided!

What is dimension?

Curves are dimension $1$, surfaces have dimension $2$, but fractals have non-integer dimensions. But what is this ``dimension''? What does it really mean for the West coast of Britain to have dimension 1.25? After defining the Hausdorff dimension, I will compute that of some household fractals such as Cantor's set, Koch snowflake, and Sierpinski carpet. Expect to get your black-and-white copies of some fractals!