A Superficial Proof of Fermat's Last Theorem
I mentioned my interest in learning about Fermat's Last Theorem in an earlier post. As I wrote in that post, the theorem is surprisingly simple to state but the proof required …
Marriage Lemma
The Marriage Lemma is a neat result that has the following interesting formulation: Consider a group of men and women in a party. Suppose in any group of n men, there …
Mathematical Induction
The Principle of Mathematical Induction is arguably one of the most powerful techniques in mathematics. Formally, the principle asserts the following: Principle of Mathematical Induction: Consider a set of statements …
The Pigeonhole Principle
The pigeonhole principle is based on a very simple idea but is very powerful in mathematical problem solving. Here is the principle: Pigeonhole Principle: If there are objects to …
Telescoping series
One of my favourite tricks in mathematical problem solving is the idea of a telescoping series. Consider the following problem: Find the sum of This seems to lead to …
The genius of Gauss
One of the most famous stories in mathematics is related to Gauss when he was a little boy. It went as follows: "It was said that to punish the kids …
An Insightful Geometry Problem
Calculate the area of the shaded region. There are many solutions to this problem. One can divide the shaded region into triangles and sum these areas. Alternatively, one might deduct …
Fermat's last theorem
One of the most fascinating features of mathematics is that many theorems are so simple to state but so difficult to prove. A prime example is Fermat's last theorem. …
Prime numbers
Prime numbers fascinate me. They are essentially the building blocks for multiplication. Recall that a positive integer is prime if the only positive integers dividing into are none other than 1 …
Mathematics: An Art and Science
I have always maintained an interest in mathematics. In this blog, you will see some of my thoughts on this subject. Most people tend to think of mathematics as a …