Memory Methods

Memory, in human reference, is the ability to store retain and recall information when needed. Without hammering the mind in the definitions, let we look into the ten methods of boosting our memory:  1. Simple Repetition Method The classical method, very popular as in committing poems to memory by reading them over and over. 2. Full Concentration Method Concentrate on…

Free Online Calculus Text Books

Once I listed books on Algebra and Related Mathematics in this article, Since then I was receiving emails for few more related articles. I have tried to list almost all freely available Calculus texts. Here we go: Elementary Calculus : An approach using infinitesimals by H. J. Keisler Multivariable Calculus by Jim Herod and George Cain Calculus by Gilbert Strang…

Dedekind’s Theory of Real Numbers

Intro 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 of rational numbers seems…

Free Online Algebra and Topology Books

This is a brief 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(at)gauravtiwari.org. Abstract Algebra OnLine by Prof. Beachy This site contains many of the definitions and theorems from the area of…

D’ ALEMBERT’s Test of Convergence of Series

Statement 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 number. The series is divergent if $ \dfrac{u_{n+1}} {u_n} > 1$ from and after some fixed term. D’ Alembert’s Test is also known as the ratio test…

Applications of Complex Number Analysis to Divisibility Problems

Prove that $ {(x+y)}^n-x^n-y^n$ is divisible by $ xy(x+y) \times (x^2+xy+y^2)$ if $ n$ is an odd number not divisible by $ 3$ . Prove that $ {(x+y)}^n-x^n-y^n$ is divisible by $ xy(x+y) \times {(x^2+xy+y^2)}^2$ if $ n \equiv \pmod{6}1$ Solution 1.Considering the given expression as a polynomial in $ y$ , let us put $ y=0 $ . We…

Milnor wins 2011 Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2011 to John Milnor, Institute for Mathematical Sciences, Stony Brook University, New York “for pioneering discoveries in topology, geometry and algebra”. The President of the Norwegian Academy of Science and Letters, Øyvind Østerud, announced the winner of this year’s Abel Prize at the Academy in…

Consequences of Light Absorption – The Jablonski Diagram

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 absorption of light may result in…

Essential Steps of Problem Solving in Mathematical Sciences

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 problem situations. You must also be good in gathering information, extracting strategies…

Classical Theory of Raman Scattering

The classical theory of Raman effect, also called the polarizability theory, was developed by G. Placzek in 1934. I shall discuss it briefly here. It is known from electrostatics that the electric field $ E $ associated with the electromagnetic radiation induces a dipole moment $ mu $ in the molecule, given by $ \mu = \alpha E $ …….(1)…

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. Problem A beautiful maiden , with beaming eyes, asks of which is the number that multiplied by 3 , then increased by three-fourths of the product, divided by 7, diminished by one-third of the quotient, multiplied…