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…

Results about Multiplicative functions

I will be regularly updating this post with results, along with my proofs of them, that I encounter about multiplicative functions, in particular involving the Dirichlet product. A multiplicative function is such that for , , where . The Dirichlet product of two arithmetical functions (functions that take operate in the integer domain)  is . Result 1:…