# A Tough-looking Integral

I recently came across an integral that at first seemed “impossible”. The integral is . This was the problem A4 on the 1969 Putnam. I naturally tried to rewrite as , because this is the general technique to integrate : . What makes things difficult here is that is the product of two functions of…

# Groups and Homomorphisms

One often sees that proving theorems about groups and related structures can involve clever reasoning and ingenuity. I will be collecting, when possible, problems which use such reasoning, because what is more disorienting than not being able to re-use a clever method you discovered a few weeks ago? Problem 1: Show that has the same number…

# Results about Finite-Dimensional Linear Spaces

Just like my page for recording the results I encounter about multiplicative functions, along with their proofs, I intend to update this page with basic results about linear spaces (mostly finite-dimensional). I will try to explicitly state the linear algebra theorems I make use of in my proofs. Result 1: If is a finite-dimensional vector space,…

# Nonlinear Time Series Analysis

I am attending a short workshop from 30th April to 4th May on the topic of Nonlinear Time Series Analysis organized by the Indian Institute of Sciences, Bangalore. The course is being taught by Professor Marco Bittelli of the University of Bologna. I intend to keep (very brief) summaries of what is covered each day as it…

# Teaching my sister

This summer I have been “tutoring” my sister Prarthana (9th grader), in mathematics and physics (and chemistry, despite my own scholarly-lessness in it!). To see how she is progressing, I thought it would be good to see how she approaches problems in timed assessments. I will be updating this post with the assessments I prepare…