Like the many before me who have tried, I hope to make math-averse and math-agnostic people fall in love with this beautiful subject. This was the original purpose of the blog, with the first few posts written for a broad audience, but the scope of the blog has changed over the course of its run. It now functions as a personal math diary. I often revisit my own posts for reference (how was this thing defined again?), to reflect on pedagogical aspects (I remember this being confusing…), or for an ego-boost (look how far I’ve come!!).
The rest of my blog assumes familiarity with basic linear algebra (as it pertains to $\mathbb R^n$). If you are coming from an undergraduate engineering background, you might want to get a feel for higher dimensions and the geometric structures that can be defined on a vector space. Hilbert spaces is a good next stop, so are the posts that define abstract vector spaces and reconcile it with the familiar program of matrix multiplication ; see the linear algebra tag for more. Note that posts are displayed in reverse chronological order, and therefore in reverse order of mathematical maturity!
Much of what I’ve posted since was motivated by a desire to understand manifolds (in particular, Lie groups ). My post on vector fields on manifolds has received critical acclaim among the 2 or 3 people who’ve read it closely. I am quite fond of this one that discusses various constructions involving Lie groups, such as quotients, products, and Riemannian metrics . Recently, I have been learning about harmonic analysis , mechanics , and fiber bundles . In the distant future, I’d like to get into the business of making math visualizations, and maybe a podcast?
About Me
This blog is maintained by Shiraz Khan (me). I have a PhD in Aero/Astro from Purdue University and did my undergrad at IIT Madras. During the week, I work as a research scientist at a robotics startup located near Boston. My research is broadly in the area of control theory and state estimation , and I spent two productive years working on Lie groups alongside Gregory S. Chirikjian . Besides being a math fanatic, I am an amateur musician, and have been rekindling my love of cryptic crosswords lately. You may reach me at this email address or leave a comment on one of my posts!