Starting a New Publication: ScienMathic Discoveries

Before the Giants of Newton and Leibniz — Ancient Foundations of Calculus If you have taken high school calculus, you will have heard the great names of Newton and Leibniz, who independently developed calculus around the same time. While there might be controversy over who first invented the subject, we can all agree that their contributions laid the foundations upon which much…

Beginnings of Calculus — Ancient Calculus by Fermat Following yesterday’s post on Cavalieri’s Principle, we once again travel back in time to witness the humble beginnings of calculus. This time, we are looking at the work of Pierre de Fermat, his first-ever method to systematically tackle the problem of tangents. Without further ado, let’s dive in! Pierre de Fermat

University of Warwick — Assignment 2 Question 1 We use x = 1–1/t. Notice x < 1 so that 1–1/t < 0 for all t > 0. And we are done. Good job. My name is Barry and I am a mathematics student at the University of Warwick. I started this blog as a…

Real Analysis — Real Analysis At its core, real analysis is the study that formalises the behaviour of real numbers in a rigorous manner. Our analysis 2 courses at the University of Warwick started off with the basic properties of power series as well as their continuity, leading up to a discussion of the exponential…

Calculus on Twitter — Today’s Challenge After going for a 3.7k run in the morning, I came across this seemingly hard, yet surprisingly easy calculus challenge on Twitter. Give this problem a try before jumping in for the solution! Solution Don’t be daunted by this complicated-looking function. Because, fear not, we can do some tricks to simplify…

Can You Solve It? — Today’s Challenge I have recently started making a high school calculus and algebra course on Udemy. The course will consist of 6 practice tests in the areas of introductory calculus and linear algebra, each with 40 questions of varying difficulty. It will probably take me a month to finish the course and…

University of Warwick: Real Analysis — By considering the ratio of the n+1th and nth terms, we see that the ratio must be greater than or equal to e/2, which is greater than 1 as e is around 2.7. Therefore, the sequence is increasing. Hope that helps — Barry My name is Barry and I am…

University of Warwick: Real Analysis — We start off by using the inequalities proven in the lecture notes. A bit of manipulation will give us the lower and upper bound for e. By the sandwich rule, (1 + 1/n)^n approaches e as n approaches infinity. And we are done. Hope that helps — Barry. My name…

Can You Solve it in 10 Seconds? — Today’s Challenge Let’s cut to the chase of today’s geometry challenge. Can you prove that triangles with the same colour sum to one fifth of the total area of the regular decagon? Give this problem a try before jumping in for the solution! Solution