Modular Arithmetic — A corollary from Fermat’s Little Theorem states that: If p is a prime number, and the number a is relatively prime to p, then

A Calculus Problem — When solving second order differential equations, we start with an auxiliary equation like the following.

A Useful Formula — Use the principle of mathematical induction to prove the above formula. Step 1: n = 1 L.H.S: = 1³ = 1 R.H.S: = (1)² = 1 Therefore, the formula is true when n = 1. Step 2: assumption for n = k

The Witch of Agnesi — To learn about the history and construction of the curve, check out this article! If you are brave enough to solve the challenge, read on! Construction and Challenge The figure above shows a circle of radius a centered at the point C = (0, a). The points (x, y) are obtained as follows…

In the realm of mathematics, the witch of Agnesi (pronounced as aɲˈɲeːzi, -eːsi; -ɛːzi) is a cubic curve that emerges from two diametric points on a circle. This intriguing curve is named after the renowned Italian mathematician Maria Gaetana Agnesi, although it was previously studied by luminaries such as Fermat…

An Elegant Geometry Puzzle — The figure composes of 5 squares with rays of triangles all pointing towards on spot. What fraction of the total area is shaded? Before I reveal the solution, here’s a big hint for those who want to try this out.

Integration by parts for inverse trig? — I found this problem on the 18.01 Practice Final, Fall 2003 exam. How would you solve this integral? When dealing with an integrand that consists of a product of two functions, one common technique is integration by parts.

A Calculus Challenge — When I first studied differential equations, it was such a breeze as it’s built on top of my pre-existing knowledge on integration in calculus. Let’s take a look and solve this problem. …

An Algebra Brain Teaser — Or not. Because it really isn’t a brain teaser if we can logically analyze the scenario. Think of the height of one whole glass as h. And the part that sticks out on top of another glass as x.