Classical Mechanics
Applications in Physics and Elastic Collisions
Bouncing balls to space
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Calculus
Solving the Dirichlet Integral
The Dirichlet integral was first solved by the brilliant Leonhard Euler, it then achieved fame with Dirichlet’s work on Fourier series…
Ramanujan
Ramanujan’s First Letter to G.H. Hardy (1913)
On or about the 31st of January 1913, mathematician G.H. Hardy (1877-1947) of Trinity College at Cambridge University received a parcel of papers from Madras, India which included a cover letter from an aspiring young Indian mathematician by the name of Srinivasa Ramanujan (1887–1920).
Group Theory
Noether’s Theorem: How Symmetry Shapes Physics
Conservation laws form the basis of theoretical physics. In 1915, Emmy Noether found their origin in the symmetries of the universe.
Vector Spaces
A Note on Reproducing Kernel Hilbert Spaces
In this article we introduce the reproducing kernel Hilbert space.
Pi
Calculating the Value of Pi: A Monte Carlo Simulation
We interact with the number π (‘pi’) everyday. Due to its fundamental involvement with circles, π has found applications in virtually every industry, ranging from sports to designing power lines and everything in between. It would, then, seem absurd that a number that is seemingly so specific and universal can
Practical Mathematics
How To Multiply Large Numbers Quickly
The Toom-Cook Algorithm
Hilbert
The Hardy-Hilbert Space of the Unit Disc and Composition Operators
The Hardy space has three equivalent definitions. Each of them emphasizes a different aspect of the space and all three of these aspects…
Geometry
Why Trisecting the Angle is Impossible
An accidental introduction to field theory.
Geometry
How They Estimated the Distance to The Moon
Two independent methods, two genius minds: How Aristarchus and Hipparchus calculated the Earth-Moon distance.
Analysis
Cantor Pairing Function
Represent an ordered pair of integers with a single integer.
Statistics
An Intuitive Explanation of Benford’s Law
A simpler way of visualising and observing Benford’s Law through the powers of two