Mathematics

Since elementary school, we all remember the axiom we’ve learned: you can’t divide by zero. But probably everyone has wondered — why? Let’s figure it out together. Indeed, if division is an operation that finds out how many times the divisor is contained in the divisor, wouldn’t it be logical…

In this article , we will develop a model to calculate the Probability of Default (PD) for counterparties involved in financial derivative products. The PD is a fundamental risk metric that quantifies the likelihood of a counterparty defaulting on its obligations. We will use a hypothetical dataset and consider all…

PART II: A step further — The squares of protoprime numbers — “the originators to primes” — show discernible pattern across the 8 unique sequences of protoprime numbers. With my previous article published two days ago, I introduced the term “protoprime numbers”… The concept is a simple alternative to primes — an easy-to-generate, well-ordered superset to…

We consider here the classical problem in computational geometry of determining whether a set of planar points is in general position i.e. whether any 3 of them are collinear. This question is important since many results in computational geometry rely on this notion, e.g. …

Today we are going to understand and explore the concept of decision trees, an important and versatile algorithm, that can execute tasks such as classification, regression and even multi output tasks. The structure of a decision tree is widely known even outside of the AI world. …

Often described as the most beautiful equation in mathematics, Euler’s identity is an identity usually taught in high school mathematics and is as shown above. Having an interest in mathematics, I also came across this identity some time in high school and was amazing by the way in which it…

“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”-Max Planck Today I will start with a completely new concept of Fuzzy Logic. Fuzzy Logic…

Welcome to the captivating world of calculus! Often seen as a complex and intimidating subject, calculus has an extraordinary ability to unlock the mysteries of the universe and find beauty in the most unexpected places. …

INTRODUCTION In this, we dive into the depths of Principal Component Analysis (PCA), a powerful mathematical technique for dimensionality reduction and data visualization. In this, we demystify the underlying mathematical concepts and walk you through the step-by-step process of implementing PCA. From eigenvectors to eigenvalues, covariance matrices to singular value decomposition…