# Mathematics

## An Introduction to the Application of Statistics in Big Data

Abstract Statistics, in its modern sense, is a field of study that aims to analyze natural phenomena through mathematical means. As a highly diverse and versatile discipline, statistics has been developed not only in the areas of STEM subjects, but also in the spheres of social science, economics, and humanities. More recently, the use of …

## BENFORD’S LAW ON SOCIAL MEDIA

Abstract Benford\’s law, also known as the law of first digit, is practically used in various applications in order to identify the reliability of the numerical data. Therefore, this paper will review one of the decisive laws in mathematics that is still present and used in our daily life by many countries and authorized …

## Evaluation the Gaussian Integral through the use of Power Series and Master Theorem

Abstract The Gaussian Integral is an important tool, imperative to the study of probability and statistics.It and similar integrals are computed usually through the method of double integrals and spherical coordinates. This paper sets forward an avenue of exploration highlighting the versatility and applications of the Ramanujan Master Theorem, a method to find the value …

## Blaise Pascal and the Pascal Triangle

ABSTRACT Pascal’s triangle, based on the expansion of any binomial expression (x+y)ⁿ, can be used for several elements within a polytope in the modern world. Some examples include significant ties to number theories and the Fibonacci sequence. In addition, pascal triangle numbers can be the coefficients of perfect squares in polynomials. For example, the coefficient …

## Proof of Stokes Law of Viscosity Using Reynolds Law

Abstract Viscosity is basically the measure of resistance of a fluid when it is flowing, i.e. it describes the internal friction of a moving fluid. In 1851 scientist George Gabriel Stokes gave his law; after that, a lot of research was done with taking that law into account. But there are no such mathematical solutions …

## What Are Fractals and Could They Be the Key to Creating an Automated Cancer Diagnosis System?

Abstract Cancerous cells can be detected in many ways, one of which uses fractal dimension (a number that describes the complexity of a shape). We analyse the “box counting” method of finding the fractal dimension of an object and the application that this has in finding the fractal dimension of an animal cell. We review …

## The science of interaction and decision-making: Game Theory

From the very beginning, we have tried to predict the future. Prediction is a messy business, and astrologers are seldom genuine. However, scientifically speaking, prediction is absolutely essential. From weather to strategic interactions, prediction is present everywhere. It is often impossible to predict complex, real-life phenomena using simple mathematical equations. We need a new concept …

## Chaos Theory and Consciousness

Abstract Consciousness remains one of the most bizarre phenomena in the universe. Though a well-researched field, science is still to reveal the fundamental nature of consciousness. This is perhaps due to the fact that consciousness is not entirely a biological phenomenon but rather an emergent process, rising out of complex interactions between simpler parts, …

## Alternative version of Bolzano’s theorem for continuous and differentiable functions

About the Author Roberto, 19, is a med student at the University of Salerno who is really interested in science communication, especially if it’s made by young students. He is particularly keen on genetics, astrobiology and human anatomy and believes that being part of the outreach team gives him the opportunity to keep science spreading.