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. The scope of the blog has changed dramatically over the course of its run, however. It now functions (in part) 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 $\mathbb R^n$). Once that is attained, you may 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, but arguably the most illuminating posts here are those that define an abstract vector space 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 thus in reverse order of mathematical maturity.
Much of what I 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 have 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 and mechanics . In the distant future, I’d like to get into the business of making math visualizations.
About Me
This blog is maintained by me, an aerospace engineer by training. My research is broadly in the area of control theory . 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.