Solve hard integrals by differentiating under the integral sign

Richard Feynman, differentiating under the integral sign, Leibnitz rule, Feynman trick.

Differentiation and integration are two sides of the same coin. Sometimes we call that “coin” calculus.

One of the reasons why they are related is the fact known as the fundamental theorem of calculus which basically says that the two operations are inverses of each other. …

Proving the beautiful and incredibly useful Euler–Maclaurin summation formula — from scratch

The Euler-Maclaurin formula, Bernoulli numbers, fractional part function and Abel summation.

It is said that if the number 691 appears in your calculations, then the Bernoulli numbers are hiding somewhere.

While this is more of a joke than a truth, every time this happened to me, sure enough, I discovered the Bernoulli numbers shortly after.

At first, they were hiding in…

Can a ball be divided into a finite number of pieces such that they can be put together to yield two exact copies of the original ball?!

When I first heard about this, I literally choked on my coffee. In mathematics, theorems have to make sense because after all, we can prove them.

Therefore, when we encounter something very strange or even contra-intuitive in mathematics, we need to turn to the proof in order to understand what…

Customize your training of deep neural networks - a practical guide

Callbacks are essential when you want to control the training of a model.

And you do want to control the training…

Callbacks help us prevent overfitting, visualize our training progress, save checkpoints and much more.

TensorFlow

But why TensorFlow?

TensorFlow is the preferred deep learning API in the world by many…

Kasper Müller

Mathematician and Data Scientist interested in the mysteries of the Universe, fascinated by the human mind, music and things that I don’t understand.

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