As explained in the first Lecture of A Tutorial in Data Science - a 10 Lecture Series I wrote to supplement our Data Science course at Mathematics Academy to help you learn the theoretical foundations of this new science - Statistics is the study of measuring the validity of claims and...

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## Research Colloquium: SEIR Model of COVID-19 using Economic Functionality for Transmission Coefficient Dynamics

Our previous research colloquia on COVID-19 consisted of 1) a preliminary sketch of a multi-scale thermodynamics paradigm ('functional communication') developed to analyze this phenomenon and 2) a graphical analysis of the economic attributes of the meso level of the crisis. Now, we combine these...

## How to Hire the Right Math Tutor

The Three Biggest Pitfalls in Hiring a Tutor and How to Handle Them When searching for a tutor there are three major things you need to have in place to ensure a good experience. Having a good tutor can be a great benefit far more bang for your buck than classroom education, but there are three...

## Absolute Value and Square Roots

Absolute values often show up in problems involving square roots. That’s because you can’t take the square root of a negative number without introducing imaginary numbers (those involving $i = √-1$ ). Example 1: Simplify $√x²$ This problem looks deceptively simple. Many students would say the...

## Absolute Value and Logarithms

Absolute Value and Logarithms Absolute values often turn up unexpectedly in problems involving logarithms. That’s because you can’t take the log of a negative number. Let’s first review the definition of the logarithm function: Logb x = y ⇔ by = x (The double arrow is a bi-conditional, which means...

## L’Hospital’s Rule

L’Hospital’s Rule is a useful way to evaluate tricky limits. It is most often used for limits of indeterminate form. The rule is as follows: If $f(x)$ and $g(x)$ are differentiable on some interval around the number $a$ (or if $a=∞$, $f(x)$ and $g(x)$ are differentiable for all $x>ε$ for some...

## Algebraic Groups

Introduction to Algebraic Groups One of the most fundamental algebraic structures in mathematics is the group. A group is a set of elements paired with an operation that satisfies the following four conditions: I. It is closed under an operation (represented here by “+”, although it does not...

## Algebraic Rings

Introduction to Algebraic Rings An algebraic ring is one of the most fundamental algebraic structures. It builds off of the idea of algebraic groups by adding a second operation (For more information please review our article on groups). For rings we often use the notation of addition and...

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