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...
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 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 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 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...
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...
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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