Numerical Analysis
Cubic Polynomials - Rotation to Calculate Roots
Exploiting the amazing symmetry of cubic polynomials to quickly find the first root using Newton’s method.
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Group Theory
The Power of Invariants
We can find invariants in many branches of mathematics. Let us try to use the theory of invariants to solve a few popular brainteasers.
Applied Mathematics
Principal Component Analysis: The Basics of Dimensionality Reduction
In the era of big data, we frequently find ourselves manipulating high-dimensional data, whether it be image data (where the number of…
Erdős
A Theorem of Erdős and Szekeres
A Theorem by two mathematical greats, which anybody, no maths experience required, can understand! An amazing, and beautiful, result…
Biography
A Titan Among Men, Ron Graham
An Ode to the Beloved Mathematician
Combinatorics
A Combinatorial Curiosity
A beginner’s guide to combinatorics, and using it to solve a rather tricky question.
Number Theory
The Fibonacci Sequence and The Powers of Two
On two of the most popular and well-known patterns by humans and nature
Physics
A Brief Overview of Candidate Theories Of Everything
Microscopic strings, looped space, and eight dimensional spheres
Modular Arithmetic
Solving Infinite with Finite
Mathematics has a lot of hidden gems. Today I will try to give us a glimpse to one of the vast domain — modular arithmetics.
Geometry
The Law of Sines with Proof
It states that the ratio of any side to the opposite sine in a given triangle has a constant value.
Infinity
The Paradox of Infinity
As I finished reading The Fault in Our Stars by John Green, perhaps what stood out the most was the phrase, “Some infinities are bigger…
Calculus
Calculus and the Legend of the Founding of Carthage
How modern calculus of variations solved an ancient math problem.