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TOP SAUCES
Markovian Russian Roulette
Imagine you are playing a game of Russian Roulette. This game is played, of course, with a revolver: At the start of the round, the bullets are loaded in a random order with unknown distribution, and the cylinder is cycled. The players then take turns firing the revolver. Now, a simple riddle. Assume that you…
Estimating Hash Collision Rates
It’s inconceivable that a blog titled “Hashed Potatoes” never had a post about hashes for the past few years. That changes now. Potatoes neither; but another time, perhaps? Suppose you have a registration system, and you want to set up a hashing scheme to generate a unique ID for each user. You want this ID…
Probability Theory with Linear Algebra
This post was inspired by a MathOverflow problem: Coin flipping and a recurrence relation. Let’s start by taking a look at an interesting problem from probability theory. We have 6 biased coins, each with 2 sides: heads and tails. The probability of a coin landing on heads is given as 
Balancing Chemical Equations with Linear Algebra
This post is inspired by a Kattis problem: Stoichiometry. Let’s face it. Every one of us who has learnt chemistry would’ve come across a problem like this before: 
Neural ODEs
Neural Ordinary Differential Equations (Neural ODEs) are a new and elegant type of mathematical model designed for machine learning. This model type was proposed in a 2018 paper and has caught noticeable attention ever since. The idea was mainly to unify two powerful modelling tools: Ordinary Differential Equations (ODEs) & Machine Learning. This post will…
The Mathematics of Music
What makes a piece of music sound good? What makes the pitches that we use work? What makes something consonant or dissonant? These are some interesting questions that I will explore in this post. In my earlier post on The Physics of Sound, I discussed about understanding sound as a wave, and how loudness, pitch…
The Physics of Sound
This is the first out of two posts delving into the physics and mathematics behind what makes music work. In this post, I will discuss the nature of what sound is, and where it gets it properties from. Let’s start by asking the rudimentary question, “what is sound?” Sound is Moving Air Let’s try a…
The Moods of Music Modes
The concept of modes in music have been a remarkable idea and compositional tool in music theory. While basic tonal concepts (major & minor) are on their own plenty efficacious in eliciting various emotional responses, I couldn’t help after a while but feel that they were rather limited, and I sought to read into other…
Retailer Locality Simulation
Problem Statement & Motivation In this first problem exploration, I will be using this video by TED-Ed as reference: This video introduces the concept of Hotelling’s law; a game theory law which explains why two retailers selling the same product tend to set up shop close to each other. I was motivated to make this…
The Sauce
Hey there friend, I’m GK and I hail from the small island of Singapore. I love being with people, learning and discovering more about what makes us think and feel the way we do, and providing help wherever possible. I do also enjoy delving into deconstructing systems and processes, concrete to abstract alike, as well…
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Hashed Potatoes 