modus-ponens

[modus-ponens]

A summary sheet of some key properies of (metric and) topological spaces

[modus-ponens]

Defining the natural (b)logarithm

Hey everyone!

I’ve always wanted to have a Maths blog dedicated to interesting concepts and cool facts, so I’ve finally created one! While I wouldn’t call this blog a studyblr per se, I’ll mostly be using this blog to post about the maths I’m currently working on in uni. Unlike a typical studyblr, I’m aiming to make my posts a little more more informative and provide a little bit of context to the things I post about, just so other people might be able to understand what’s going on under the hood when it comes to maths.

As someone who has just finished their first year studying Maths at the University of Cambridge, I might also post a bit about my experience studying there as an international student, as well as my journey getting there for anyone who is considering applying.

While I’m on the break at the moment, I’ve been trying to read ahead and complete some of the problem sheets and programming tasks we’ve been set over the holidays. Some of the things I’m currently working on/reading around include:

(Convex) Optimisation

Metric & Topological Spaces

Group & Ring Theory

Programming in MATLAB & JavaScript

Quantum Mechanics

Apart from Maths, I’m also passionate about Graphic Design and Art, and might share some of my works in the future. If that sounds interesting to you, feel free to follow and/or drop a message, I’d love to get to know as many of you as possible! 

As a note, is a sideblog, so I’ll be following from my main account @blog-normal-distribution. That blog is also mostly about Maths, but also includes some miscellaneous stuff. 

Hope to see you guys soon with a new post!

[modus-ponens]

10,000 particles in a simulated simple symmetric random walk; each particle has a 1/3 probability of moving left, right, or not moving. The heights of the black bars represents the distribution of particles along the walk.

As a consequence of the central limit theorem, after a long time the distribution of the particles can be very well approximated by a normal distribution (shown in red)! The mean of this normal distribution stays at 0 while the variance is proportional to the time left running.

Programmed in javascript & ProcessingJS.

[modus-ponens]

Multiparticle system following a random walk. 

Programmed in javascript.