Our Blog

Math Resources | Math Learning | Information | Math Fun Facts

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 answer...

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...

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,...

10 Ways Tutoring Can Help You

Finding a good math tutor can be essential to your success in school. Tutoring can do much more than just improving math grades. Here are 10 ways in which you can benefit from tutoring. 1. Improve your confidence When working one-on-one outside of the classroom setting, you might find it easier to...

Find the Vertex by Using the Quadratic Formula

The Quadratic Formula is primarily used to identify the roots (\(x\)-intercepts) of a quadratic function. What many people don't know is that you can also easily find the vertex of the function by simply looking at the Quadratic Formula! Graphing Quadratic Functions When graphing quadratic...

Completing the Square

Introduction A brief discussion about what completing the square is and what we use it for. Focuses on using the technique for other reasons than solving equations. Background Math Development of the patterns we use for completing the square. This part is important since it introduces the notation...

Major Categories

Math Resource

Math Learning

Math Lectures

Math Fun Facts

Student Tips

Latest Math Blogs/Articles

Find the Vertex by Using the Quadratic Formula

The Quadratic Formula is primarily used to identify the roots (\(x\)-intercepts) of a quadratic function. What many people don't know is that you can also easily find the vertex of the function by simply looking at the Quadratic Formula! Graphing Quadratic Functions When graphing quadratic...

Completing the Square

Introduction A brief discussion about what completing the square is and what we use it for. Focuses on using the technique for other reasons than solving equations. Background Math Development of the patterns we use for completing the square. This part is important since it introduces the notation...

Cardinality and Countably Infinite Sets

Cardinality is a term used to describe the size of sets. Set A has the same cardinality as set B if a bijection exists between the two sets. We write this as |A| = |B|. One important type of cardinality is called “countably infinite.” A set A is considered to be countably infinite if a bijection...

The Quadratic Equation

The quadratic equation is always the answer. Time and time again, while tutoring students, I encounter a resistance to using an unfailing tool called the quadratic equation. This simple algebraic mathematical statement allows a student to find the roots of any clumsy second order polynomial with...

Navier-Stokes is hard?

Navier-Stokes is hard? Author: James Lowman} I was recently asked the question; "\textbf{How can the Navier-Stokes equations both describe our observable world and not be known to always have solutions in 3D?}" For those that don't know, the Navier-Stokes (NS) equations represent a mathematical...

The Natural Logarithm Rules

The natural logarithm, whose symbol is ln, is a useful tool in algebra and calculus to simplify complicated problems. In order to use the natural log, you will need to understand what ln is, what the rules for using ln are, and the useful properties of ln that you need to remember. What is the...

All Categories

Math Resources

Student Tips

Math Learning

Math Test Preps

Math Lectures

Professional Math 

Math Fun Facts

Math Blogs

Share This