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Operations Research: The Science Of Doing Better

Operations research is the art of problem-solving and decision-making. In this article, we will learn more about "The Science of Doing Better" and its endless applications. Table Of Content: Introduction What is Operations Research? Origins and development through time Operations Research...

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 $i = \sqrt{-1}$ ). Example 1: Simplify $\sqrt{x^{2}}$ This problem looks deceptively simple. Many students...

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 $a=\infty$, $f(x)$ and $g(x)$ are differentiable for all...

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...

Modular Arithmetic & Fermat’s Little Theorem

Modular arithmetic is a way of counting in which the numbers wrap around after reaching a certain value. The clock is often used as an analogy. While time always progresses forward, the 12-hour clock “resets” to 1 after passing 12 (13 o’clock is equivalent to 1 o’clock). If we replace 12 with 0,...