# Blog

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## Free Online Calculus Text Books

In this list, I have collected all useful and important free online calculus textbooks, mostly in downloadable pdf format. Feel free to download and use these. Elementary Calculus : An approach using infinitesimals by H. J. Keisler https://www.math.wisc.edu/~keisler/keislercalc-12-23-18.pdf Multivariable Calculus by Jim Herod and George Cain http://people.math.gatech.edu/~cain/notes/calculus.html Calculus by Gilbert Strang http://ocw.mit.edu/ans7870/textbooks/Strang/strangtext.htm Calculus Bible by…

## Dedekind’s Theory of Real Numbers

Let $\mathbf{Q}$ be the set of rational numbers. It is well known that $\mathbf{Q}$ is an ordered field and also the set $\mathbf{Q}$ is equipped with a relation called “less than” which is an order relation. Between two rational numbers there exists an infinite number of elements of $\mathbf{Q}$. Thus, the system…

## Free PDF Algebra and Topology Books for Graduates

Looking for free PDF algebra and topology books online? I have gathered a list of free e-books on Algebra, Topology, and Related Mathematics. I hope it will be very helpful to all students and teachers searching for high-quality content. If any link is broken, please email me at gaurav@gauravtiwari.org. Let’s start. Abstract Algebra Online by Prof. Beachy This…

## D’Alembert’s Ratio Test of Convergence of Series

In this article, we will formulate the D’ Alembert’s Ratio Test on convergence of a series. Let’s start. Statement of D’Alembert Ratio Test A series $\sum {u_n}$ of positive terms is convergent if from and after some fixed term $\dfrac {u_{n+1}} {u_n} < r < {1}$ , where r is a fixed…

## Jablonski Diagram – Consequences of Light Absorption

All about the Light Absorption’s theory on the basis of Jablonski diagram. According to the Grotthus – Draper Law of photo-chemical activation: Only that light which is absorbed by a system, can bring a photo-chemical change. However it is not true that all the kind of light(s) that are absorbed could bring a photo-chemical change. The…

## Essential Steps of Problem Solving in Mathematical Sciences

Problem solving is more than just finding answers. Learning how to solve problems in mathematics is simply to know what to look for. Mathematics problems often require established procedures. To become a problem solver, one must know What, When and How to apply them. To identify procedures, you have to be familiar with the different…

## A Problem (and Solution) from Bhaskaracharya’s Lilavati

I was reading a book on ancient mathematics problems from Indian mathematicians. Here I wish to share one problem from Bhaskaracharya‘s famous creation Lilavati. Who was Bhaskaracharya? Bhaskara II, who is popularly known as Bhaskaracharya, was an Indian mathematician and astronomer from the 12th century. He’s especially known for the discovery of the fundamentals of…

## Un-Popular circumstances connected with Most Popular, Theory of Relativity

Henry Poincaré was trying to save the Old classical theory of Physics by Suitable Adjustments & Modifications in it. When the experiments, like Michelson Morley Experiment, in search of the ether drift failed, it began to be increasingly realized that there was no such thing as an absolute or privileged frame of reference and that…

## The Collatz Conjecture : Unsolved but Useless

The Collatz Conjecture is one of the Unsolved problems in mathematics, especially in Number Theory. The Collatz Conjecture is also termed as 3n+1 conjecture, Ulam Conjecture, Kakutani’s Problem, Thwaites Conjecture, Hasse’s Algorithm, Syracuse Problem. Statement: Start with any positive integer. • Halve it, if it is even. Or • triple it and add 1, if…

## Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

Topic: Beta & Gamma functions The Gamma function and Beta functions belong to the category of special transcendental functions and are defined in terms of improper definite integrals. Definitions of Beta and Gamma functions are given below. But before that, let’s quote the statement of Dirichlet’s theorem so that we can work around Liouville’s extension…

## The Lindemann Theory of Unimolecular Reactions

In this article we will learn about the Lindemann Theory of Unimolecular Reactions which is also known as Lindemann-Hinshelwood mechanism. It is easy to understand a bimolecular reaction on the basis of collision theory. When two molecules A and B collide, their relative kinetic energy exceeds the threshold energy with the result that the collision…

## The Mystery of the Missing Money – One Rupee

Puzzle Two women were selling marbles in the market place — one at three for a Rupee and other at two for a Rupee. One day both of then were obliged to return home when each had thirty marbles unsold. They put together the two lots of marbles and handing them over to a friend…