by Ashani Dasgupta

A.M.- G.M. Inequality can be used to prove the existence of Euler Number. In this discussion, we venture into the fascinating journey from classical inequalities to modern real analysis. Watch the video A short code in Python to check boundedness of a classical... by Ashani Dasgupta

Why should we study real analysis? Once you are inside the first course of this beautiful subject, you will find hundreds of complicated theorems and formulas floating around the canvas. What makes this journey into rigorous deductive reasoning interesting is: we get... by Ashani Dasgupta

Inverse maps are very important in Real analysis. They form the backbone of the definition of continuity. Subscribe to our Youtube Channel... by Ashani Dasgupta

‘Proper’ is a heavily overloaded term, both in life and in mathematics. It may mean different stuff in different contexts. Thankfully mathematics is far less complicated that life and we can rigorously define properness. Proper Function: A continuous function \( f : X... by Ashani Dasgupta

Euclidean Spaces have a very nice property. In \( \mathbb{R}^n \) (equipped with standard Euclidean metric), every closed and bounded set is a compact set. The converse is also true. Every compact set is closed and bounded). This property is known as Heine Borel... by Ashani Dasgupta

We are interested to understand the structure of a group G (is it abelian, or a product of abelian groups, or a free group of some kind etc.). In general, this is a (very) hard question. One strategy is to let G act on some well known (topological) space. Often by...