Cryptography or Cryptology is an interesting topic in mathematics and related sciences. It is a branch in math that mostly relies on the practical application of the subject. In 2011, I came to know about this while reading the Elementary Number Theory by David M. Burton. It has a little chapter on Cryptography focused primarily…

# Math

**Mathematics Blog by Gaurav Tiwari.** This section is dedicated to exploring various mathematical concepts and theories, transcending the boundaries of traditional high school and early college curriculums.

The mathematics topics here encompass various subfields, including algebra, calculus, number theory, geometry, topology, and more.

Are you interested in maximizing profits and minimizing risks while betting on sports? Well, who isn’t? If you want to know whether a wager is worth the pursuit or not, you should be well versed with the mathematics of betting odds. Basically, there are three types of odds involved in this process: American (Moneyline) Decimal…

Abel Prize is one of the most prestigious awards given for outstanding contributions to mathematics, often considered as the Nobel Prize of Mathematics. Niels Henrik Abel Memorial Fund, established on 1 January 2002, awards the Abel Prize for outstanding scientific work in the field of mathematics. The Abel prize winners get 7.5 million Norwegian kroner (about 850,000…

Formulas are the most important part of mathematics and as we all know one is the backbone of the latter. Considering there are thousands of mathematical formulas to help people develop analytical approach and solve problems easily — there are some that go beyond. Some formulas aren’t just timesaving but those also do wonders. In…

Any integer greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. The basic ideology involved in this post is flawed and the post has now been moved to Archives. Prime Generating Formulas We all know how hard it is to predict a formula for prime numbers!…

Our reader Eswar Chellappa has sent his work on the solution of ‘3X+1’ problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years. The Collatz Conjecture can be quoted as follow: Let $\phi : \mathbb{N} \to \mathbb{N}^+$ be a function defined such that: $$\phi(x):=…

Online communities are groups of web-savvy individuals who share communal interests. A community can be developed with just a single topic or by a bunch of philosophies. A better community binds its members through substantial debates. Mathematics is a very popular communal interest and there are hundreds of online communities formed in both Q&A and…

Are you getting started with Functional Analysis? If you are, you must be looking for some of the most important definitions in Functional Analysis. In this article, I have summarized those. Functional Analysis Functional analysis is the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and…

It was mid 2012, the first time I installed TeXstudio version 2.3, on my PC. ‘Peaceful‘ was the word I used to describe it then after. TeXstudio has now gradually inched to version 2.12.22 and by time being even more peaceful and wonderful. Wonder why did I call it ‘peaceful’? Writing LaTeX is a real pain, when you are willing to…

This post explains the basic method of converting an integral equation into a corresponding differential equation.

In this article, I will teach you about Square Integrable Functions, Norms and the solution of Integral Equations by the trial method. Don’t forget to refer: Definitions and Types of Integral Equations Square Integrable function or quadratically integrable function $\mathfrak{L}_2$ function A function $y(x)$ is said to be square integrable or $\mathfrak{L}_2$ function on the…

In this article, I will explain what Integral Equations are, how they are structured and what are certain types of Integral Equations. What is an Integral Equation? An integral equation is an equation in which an unknown function appears under one or more integration signs. Any integral calculus statement like — $ y= \int_a^b \phi(x)…