Series
An Amazing Formula
Generalizing Leibniz' formula for π, the alternating harmonic series, and the Basel problem
Euler
Complex Analysis
Beyond Infinity
Analytic Continuation and its Applications in Quantum Physics
Number Theory
Transcendental Numbers
Into the Unknown
Differential Equations
Numerical Solvers for ODEs
An introduction to Euler methods
Number Theory
The Euler-Mascheroni Constant
Remember the harmonic series? More often than not, it serves as one’s first encounter with a series wherein individual terms diminish successively yet the series diverges to infinity. The below quote nicely sums the up notoriousness of the harmonic series: Today I said to my calculus students, “I know,
Euler
The Most Beautiful Equation in the World
And the Geometry of Numbers
Euler
Infinity in Numbers — Leonhard Euler
This is a story about one of the greatest minds in history, and about the mysteries and beauty surrounding his legacy. The story is about Leonhard Euler (1707–1783).
Euler
About Euler’s Identity
It is so famous and well-known, that I feel adding any praise to it would only decrease its value :) It is often cited as one of the most beautiful equations ever, by maths funs and others as well.
Euler
From Derangement To Euler’s Number
How e can rise from combinatorics
Number Theory
Another Derivation of Euler’s Fabulous Formula
Leonhard Euler (15 April 1707–18 September 1783) was a Swiss mathematician, who is considered to be one the greatest mathematicians of all…
Complex Analysis
Euler’s Fabulous Formula
Here we investigate and understand the brilliant formula which unlocks the power of complex numbers.
Number Theory
The Celebrated Harmonic Numbers and How to Approximate Them
We discuss the famous harmonic sum and describe a simple way to approximate it.