Welcome to the blog! Posts on this blog will tagged with a level to signify how much mathematics or physics I assume the reader knows. The levels work as follows:
- Level 0: High school algebra/physics
- Level 1: Calculus/ first course in Physics with calculus
- Level 2: University-level mathematics/physics
- Level 3: Graduate-level mathematics/physics
When is a Pi not a Pi?
In this level-0 post celebrating Pi Day, we are talking all about circles in weird spaces! In particular, when is the ratio of the circumference of a circle to its diameter not equal to 3.14159(etc)? Ceci n’est pas une pi, as they say.
The Demons that Haunted Maxwell
In this level-0 post, we take a look at some interesting thought experiments in thermodynamics, in particular the various incarnations of Maxwell’s demon. These were constructed as possible ways to subvert the second law of thermodynamics, and here we will talk about why they don’t.
There’s Something About Gamma
In this level-1 post, we take a closer look at Euler’s generalization of the factorial, and see how it makes sense even when it blows up.
Black Holes Win Again!
In this level 0 post, we take a look at one of the contributions of recent Nobel prize-winner Sir Roger Penrose. In particular, we’ll discuss the famous spacetime diagrams which bear his name.
Root-finding Fractals II
In this level 0 post, we revisit Newton’s method and the fractals it creates, but this time, we focus on generalizations of Newton’s method. This one’s for the people who love to look at fractals.
Root-finding Fractals
In this level 0 post, we will investigate Newton’s method for finding the roots of a function. Then, we will see how this process can induce chaos and find some fractals hidden inside.
Crossing the Street – Pt. 3
In this final part to our level 2 mathematical modelling series, we move to a different way of solving our street crossing problem: numerics. We go over discretization of the problem, how to simulate it, and compare with results from part 2.
Crossing the Street – Pt. 2
In the 2nd part of this level 2 mathematical modelling series, we take a look at what sorts of analytical tools we have to address the problem of how best to cross the street.
Crossing the Street – Pt. 1
In this level 2 post, we start the process of a 3-part mathematical modelling series, which will culminate in the answer to one of the most important questions of all time: How should I cross the street?
Calculus, Combinatorics, and Cubes
In this level 0 post, we look at the discrete Fundamental Theorem of Calculus and see an application that brings together combinatorics and sums of cubes (and higher powers)
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Singular Points 