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. 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 , fiber bundles , and robotics . 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 in 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!
See Also
Here’s an assortment of pure and applied math content that I’ve enjoyed and/or continue to learn from:
- The Bright Side of Mathematics ’ excellent math lectures and explainers
- Keenan Crane’s lectures on exterior calculus
- The Joy of Abstraction (an accessible intro to category theory) and Category Theory in Context (a very well-paced textbook on category theory with plenty of examples)
- Pieter van Goor’s blog on matrix Lie groups, it’s a treasure-trove of formulae for $SO(n)$ and $SE(n)$
- Blogs by Terence Tao, John Baez, and Tai-Danae Bradley
- My Favorite Theorem (podcast)
- John M. Lee and Stephen Bruce Sontz ’s books on differential geometry
- Peter Winkler’s puzzle book , which first sparked my joy for math
AI Disclaimer
None of the content on my blog is LLM-generated, although once or twice I have asked an LLM: Do you see any errors/notational inconsistencies on this blog?, to which I have only ever received false positive responses. The logo on my homepage and its animation were created without LLMs as well (I learnt whatever minimal JS was needed to make it work). The logo is a 2-dimensional damped harmonic oscillator, a reference to the Lorenz attractor , and also has a hidden ‘S’ in it! Some of the recent CSS additions to my blog (like the post hover effect) were LLM-generated; that’s just me being lazy.
I expect to make light use of LLMs to make my life a little bit easier, in terms of maintenance and upkeep of the blog. However, using an LLM to generate the content on this blog would defeat the whole purpose of this endeavor.