## Four way valid expression

People really like to twist the numbers and digits bringing fun into life. For example, someone asks, “how much is two and two?” : the answer should be four according to basic (decimal based) arithmetic. But the same  with base three (in ternary number system) equals to 11. Two and Two also equals to Twenty Two. Similarly there are many ways you can…

## Getting Started with Measure Theory

Last year, I managed to successfully finish Metric Spaces, Basic Topology and other Analysis topics. Starting from the next semester I’ll be learning more pure mathematical topics, like Functional Analysis, Combinatorics and more. The plan is to lead myself to Combinatorics by majoring Functional Analysis and Topology. But before all those, I’ll be studying measure theory and probability this July – August. Probability…

## How Many Fishes in One Year? [A Puzzle in Making]

This is a puzzle which I told to my classmates during a talk, a few days before. I did not represent it as a puzzle, but a talk suggesting the importance of Math in general life. This is partially solved for me and I hope you will run your brain-horse to help me solve it completely. If you didn’t notice,…

## Understanding Poincaré Conjecture

Introduction & Statement of Poincaré Conjecture In 1904, the french Mathematician Henri Poincaré posed an epoch-making question in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Explanation The statement can be explained by considering the analogous two-dimensional situation. Let us think of a rubber band stretched around the…

## Some good, OK, and useless revision techniques

Exam have been haunting student since forever, and although you’re willing to do whatever you can to retain essential information, sometimes you end up spending weeks studying with useless revision techniques. We’re accustomed to employ our own techniques when it comes to studying such as making sticky notes, highlighting, or drawing charts. However, recent studies conducted in the US have…