Geometric Algebra
This post revisits the exterior product, forms and exterior derivative which was previously discussed in my vector spaces writeup. Revisting this section was necessary before coming to terms with the covariant exterior derivative when thinking about connections on fiber bundles which is discussed the next writeup.
October 18, 2026
A tour of the data engineering landscape
Data Engineering (DE) is an interesting field of study particulary to me since it touches on both hardware and networking stacks as well as traditional software development with strong emphasis on data structures and algorithms. And although in practice, much of the tooling is plug and play, I wanted to give tour of the DE landscape and provide a motivation for why and how some of these tools are used. Coincidentally since much of this space is driven by projects which share the Apache licence, this writeup can also be seen as an overview of the Apache ecosystem.
June 12, 2026
A home network for public facing apps
In my last home server post, I discussed setting up a home server machine which featured a KVM/QEMU hypervisor and LVM for disk management. In this post I will describe a setup to host services publicly. Hosting services publicly should not be treated lightly given it requires opening the “network” door to your home allowing untrusted parties to enter. This post will outline networking segmentation, hardening techniques and network analysis tools that will increase your awareness and reduce the attack surface and blast radius in the event of an attack.
January 27, 2026
Lie theory
Lie theory marries manifolds to group theory. Groups are mathematical structures used to describe symmetries. Note, symmetries extend beyond our initial intuition of discrete rotations and reflections of shapes. Instead symmetries describe phenomena which do not change the outcome of an experimental observation. For example an experiment done today should have the same result if done tomorrow. By treating groups as manifolds we can model continuous symmetries and use our tools of differential geometry to describe these groups.
September 9, 2024
Differential Geometry
Differential geometry as the name suggests expands fundamental ideas of calculus and applies them to more complex geometric spaces. The ideas expressed in differential geometry have far reaching applications in physics since the subject matter will refine our intuition around coordinate systems and enable us to describe physics phenomena in a coordinate free manner. Applications include Einstein’s general relativity and particle physics. This write up explores these prerequiste mathematical tools.
August 19, 2024
Vector Spaces to Geometric (Exterior) Algebra
When taught linear algebra in high school or university, you begin to formulate a notion that a vector is an array of elements which we use to represent “arrows” in 2 or 3 dimensional space and matricies as two dimensional arrays performing linear transformations on these vectors, scaling or rotating them. These are introductory interpretations of vectors and linear transformations. Mathematicians treat these structures in a far more abstract sense. In this writeup I try refine my inituition on what a vector space actually is.
August 10, 2024
Introduction to sets and topologies
Modern physics relies on foundational mathemetical structures to describe nature. Topological spaces and sets are two of these fondational structures. Here I will outline topological spaces, how they are constructed from sets and some useful properties to describe them. This is the first post in my collection of notes from the lecture series: “Geometrical Anatomy of Theorectical Physics” by Frederick Schuller.
April 24, 2024
Building a home server
Finally building a dedicated home server / lab was one of my biggest, most enjoyable projects in recent years. It provided me even more experience in Linux administration as well as introduce me to a whole field of network administration and security.
February 3, 2024
Calculus overview
University mathematics was one of the most challenging, interesting and stressful periods of my life thus far. Despite this, I have fond memories of it. For this reason have compiled a short tour of my university curriculum for my personal posterity. I will focus more on the ideas within each area as opposed to the rigorous proofs and the example problems.
January 31, 2024
Towards a home computing lab with KVM and QEMU
Virtualization is one of the backbones to cloud computing. The technology enables us to use hardware more efficiently and for a wider number of applications. Understanding virtualization requires careful study of the hardware capabilities of your system, the responsibilities of operating systems as well as a bit of networking. In this post I outline a Linux based setup for hosting virtual machines. The skills developed here will serve us when building a dedicated home server later.
August 8, 2023