Pop maths: A sliver of algebraic geometry – Part 1

This 3-part series attempts to explain a classical result in algebraic geometry to a lay-audience, using only high-school level mathematics. From ancient Greece to the modern era: Cones, curves, and coordinates In the 2nd century BC, Apollonius of Perga studied and classified the so-called conic sections: geometric curves obtained by intersecting a flat 2-dimensional plane … Continue reading “Pop maths: A sliver of algebraic geometry – Part 1”

Technical problems with the site

In the last couple of weeks,¬†WP-QuickLaTeX, the WordPress plug-in I use to render LaTeX equations and diagrams, has stopped working. I have been trying to sort the issue out, but so far no luck. Both my hosting company and the plug-in developers say that everything looks fine from their end, and I’ve tried reinstalling the … Continue reading “Technical problems with the site”

Some LaTeX beginners’ mistakes and tips

I didn’t post last week and can’t really guarantee consistent posts for the rest of the month; it’s exam period now. Normal service will resume in June. For today, I’m just going to go over a few things that can make early attempts at LaTeX typesetting look much more professional. At my university, there’s virtually … Continue reading “Some LaTeX beginners’ mistakes and tips”

Elementary proof of Krull’s intersection theorem

When doing my 3rd-year project, I found I needed a classical theorem in commutative algebra called Krull’s Intersection Theorem. It turned out to be very useful; I used it in three proofs involving formal power series, and it also gave me some intuition for DVRs. However, despite being an intuitive result, the proofs I found … Continue reading “Elementary proof of Krull’s intersection theorem”

Make time to be bored

The last couple of year, I’ve increasingly scrutinized my relationship wtih technology, and the relationship we seem to cultivate in our culture. We instinctively react to its beeps and buzzes, we whip it out whenever there’s a quite moment, and we sometimes read texts out the corner of our eye during real-life conversations. It can … Continue reading “Make time to be bored”

Algebraic derivatives

In commutative algebra and algebraic geometry, a common operation is to take derivatives of polynomials. This would seem a fairly straightforward thing to do, but in commutative algebra/geometry, we study polynomials over arbitrary rings and fields, and the good old derivative from standard calculus is quite dependent on the metric structure of or , since … Continue reading “Algebraic derivatives”

The Snake Lemma in unflattering detail

“Proving the snake lemma is something that should not be done in public…” ~ Paolo Aluffi. The Snake Lemma is a theorem about exact sequences of modules, and is an important tool in homological algebra. Almost every textbook that includes the Snake Lemma leaves it as an “easy” exercise. Atiyah–MacDonald is kind enough to construct … Continue reading “The Snake Lemma in unflattering detail”

The mindset for a successful mathematics undergraduate

Hey and welcome to my new blog, where I’ll discuss mathematics I like, study skills, and the lifestyle habits that keep me productive, organized, and stress-free on my academic journey. Mathematics is a famously difficult subject to study at university, so I’m going to kick things off with some general mindset tips for fellow undergraduates … Continue reading “The mindset for a successful mathematics undergraduate”