The Looking Glass

By Rohith-Raj Dhinakaran Game Theory, as described by Steve Levitt, delves into “strategic interactions between a small number of adversaries (2 to 3 competitors)” . It's a fascinating concept ranging from every situation like “holding the door open for someone” all the way to significant global problems such as “nuclear weapon conflicts between the USA and the Soviet Union in the late 1940’s”. I will discuss the rudiments associated with this discombobulating idea and perhaps help you understand how pertinent this is to the real world. Case 1: Static Game Static Game: This is a game that happens only once and all decisions are made simultaneously.  The most common/simple game which we relate to game theory is the “Prisoner’s Dilemma”.  Explanation of the Game: The “Prisoner's Dilemma” is a scenario which involves two prisoners who each have two options: stay silent or betray the other person. If both prisoners decide to stay silent, they will each serve one month in prison. I...

ABDULLAH ABDULLAH The Maclaurin series represent a fascinating type of series in mathematics, since they approximate complicated functions as a polynomial series. It is interesting and somewhat uncanny that a simple series of polynomial terms can exactly define a different function, albeit in a strict domain for the input of the function. The general equation for series of this type is shown below:                \(\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n \) where: \(n!\) is the factorial of n \(a\) is a chosen real or complex number \(f^{(n)}(a)\) is the nth derivative of the function \(f(x)\) evaluated at \(x = a\) What is shown above is a generalised version (Taylor series), since it includes a constant a, but for Maclaurin series, the constant a is zero.  Of course, simply showing the formula outright doesn’t help much in understanding what Maclaurin series are all about, so here are a few step by step examples that will clarif...

KRISHI SEKSARIA and TIM HIRE “To infinity and beyond” - this classic line used by Disney’s ‘Buzz Lightyear’ character is known by children throughout the world, but is it mathematically true? Is there anything beyond infinity? What is infinity? To gain an understanding about such a mind-numbingly humongous concept (infinite in size!), we must first consider the original roots of infinity in the expansive history of mathematics to discover what the concept really represents. Our journey begins in the 5th Century BCE where, in Greece, the philosopher Anaximander coined the Latin term aperion (which has connotations of ‘indefinite’ or ‘undefined’ in modern-day translations) to represent his belief that the indefinite was the source of all things, perhaps stemming from the Ancient Greek’s fascination with the seemingly endless number of stars. However, such an abstract postulation generated conflict amongst the Greeks, as such an idea could not be rationalised within the boundaries of thei...