In this article we will explore various algorithms for calculating the nth Fibonacci term, derive formulas for various Fibonacci sums, and turn those formulas into programs. If you are vaguely acquainted with mathematics it is likely that you have heard of the Fibonacci sequence. …

This Summer I took a course on number theory. The course was challenging but with the right study techniques, I was able to land an A in the class (>= 94%). More broadly, I want to discuss the correct study approach for performing well in proof based math classes as…

Legendre’s Formula There is a theorem in number theory known as Legendre’s Formula. It states that if N is a positive integer and p is a prime number, then the highest power of p that divides N! is given by the following formula

Introduction In this article, I will discuss performance variation, methods of practice, and the fundamental problem solving skills that I believe contribute to high performance in technical fields. These insights are informed by documented concepts in performance psychology. Performance Gradients It is typical for people to believe their skill at any task exists…

When I’m experimenting with models I typically prefer to have my math and code in the same place. Python is the language of choice for data scientists as it integrates seamlessly with Jupyter Notebook allowing for carefully placed analysis and explanations alongside code modules. However, recently I’ve been working on…

Today we will be pricing a vanilla call option using a monte carlo simulation in Python. Monte Carlo models are used by quantitative analysts to determine accurate and fair prices for securities. Typically, these models are implemented in a fast low level language such as C++. …

One of the trickiest parts about improving as a Poker player is finding high quality learning resources. There are numerous successful players over the years who have written books on their approaches to the game, yet Poker evolves so quickly that these books are often outdated within a few years. …

Traversing binary trees is a fundamental skill required for coding interviews. Today I will teach you the main ways of traversing a binary tree. Each traversal style is associated with a specific pattern. Below is a quick reference. (All code examples are worked in python) Binary Tree Traversal Cheat Sheet Traversal->PatternIn-order left/center/rightpre-order center/left/rightpost-order left/right/centerlevel-order left…

In this article, I will demonstrate a crucial mathematical concept that is essential to constructing risk management strategies in games of chance. …