Archive for October, 2019

The Wonders of Complex Analysis

AugustinLouis-Cauchy

Augustin-Louis Cauchy (1789–1857)

If you love mathematics and have never studied complex function theory, then you are missing something wonderful. It is one of the most beautiful branches of maths, with many amazing results. Don’t be put off by the name: complex does not mean complicated. With elementary calculus and a basic knowledge of imaginary numbers, a whole world of wonder is within your grasp.

In the early nineteenth century, Augustin-Louis Cauchy (1789–1857) constructed the foundations of what became a major new branch of mathematics, the theory of functions of a complex variable.

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Emergence of Complex Behaviour from Simple Roots

It is exhilarating to watch a large flock of birds swarming in ever-changing patterns. Swarming is an emergent behaviour, resulting from a set of simple rules followed by each individual animal, bird or fish, without any centralized control or leadership.

Flocking-Starlings-CyrilByrne

A murmuration of starlings at dusk near Ballywilliam, Co Wexford. Photograph: Cyril Byrne.

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