# Math

All mathematics articles on Gaurav Tiwari.

This is in continuation of my article on getting started with measure theory. As a measure theory student, you may have gone through the trouble of selecting the best books on measure theory. I had the same troubles once. That’s why I have collected the 15 best measure theory books

# The Best Books on Cryptography

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

# Mathematics of Betting Odds

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

# The Area of a Circle

If you are aware of elementary facts of geometry, then you might know that the area of a circle with radius $R$ is $\pi R^2$ . The radius is actually the measure(length) of a line joining the center of circle and any point on the circumference of the

# Abel Prize Laureates

Abel prize is one of the most prestigious awards given for outstanding contribution in 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 prize amount is 6 million

# Best Time Saving Mathematics Formulas & Theorems

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

# This Prime Generating Product generates successive prime factors

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 Possible Proof of Collatz Conjecture

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

# 8 big online communities a math major should join

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

# Definitions in Functional Analysis

Linear Space or Vector Space over a field K Definition: The linear space over a field K is a non-empty set along with a function $+ : X \times X \to X$ called linear/vector addition  (or just, ‘addition‘) and another function $\cdot : K \times X \to X$ called

# Meet the Math Blogger : Josh Young from Mathematical Mischief

Every mathematics student is in his own a special case — having his own qualities and snags. A math blogger is even more special.  He is more than just a mathematician or just a blogger. A math blogger is an entertainer… a magician, who devises techniques of making math more

# TeXStudio Review: Is it the most complete LaTeX Editor?

A detailed and practical review of one of the most amazing LaTeX editors available for all desktop platforms like Windows, Mac and Linux. TeXStudio is a team project of Benito van der Zander, Jan Sundermeyer, Daniel Braun and Tim Hoffmann, forked from the TeXMaker application, a non-open source application, which open-source development stalled in 2009.

# How to change Differential Equations into Integral Equations?

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

# What’s the question, if the answer is ‘No!’

Infinitely many answers questions are possible to the answer, “No”. So, our real task should be to find one of THOSE many, which seems to be a perfect one. A simple and the first ever logical approach of giving answers to a question is to derive answers from the question, that

# Square Integrable Functions, Norms, Trial Method in 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 interval $(a,b)$ if $$\displaystyle {\int_a^b} {|y(x)|}^2 dx <\infty$$ or $$\displaystyle {\int_a^b} y(x) \bar{y}(x) dx <\infty$$. For further reading, I suggest this Wikipedia page. $y(x)$ is then also

# Definitions and Types of Integral Equations

In this article I will explain what are Integral Equations, how those 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

# 11-12-13 – Last such sequence of the century

11th December 2013 (or in short 11-12-13) is just a few hours away here. It’s the last date of the 21st century with  such an extraordinary pattern of numbers.  In any calendar of the world, such date will be seen in 22nd century after 87 years and 54 days from today

# Complete Elementary Analysis of Nested radicals

This is a continuation of the series of summer projects sponsored by department of science and technology, government of India. In this project work, I have worked to collect and expand what Ramanujan did with Nested Radicals and summarized all important facts into the one article. In the article, there