What did Nikolay Krasovsky Study?

Nikolay Krasovsky, born in Yekaterinburg (on the Iset River), worked in the mathematical theory of control, dynamical systems and differential games.

A Lookback at 17th Century Maths

A very good "lookback" at 17th Century maths can be found on the following website. This includes Edmonton-born Brook Taylor's treatise: "Methodus Incrementorum Directa & Inversa". Taylor was famed for the Taylor series and Taylor's theorem. John Napier's treatise on logarithms is also presented in translated form: "Mirifici Logarithmorum Canonis Descriptio".

Latin is one of the "hazards" of reading 17th Century maths. As a taster, Mirifici (above) is the plural of Mirificus (wonderful, miraculous). Canonis is the genitive of canon (referring to a catalog of sacred writings). Descriptio means simply description.

As well as discovering logarithms, John Napier was also known for inventing the so-called "Napiers Bones" which was a calculating device for multiples and quotients. It was based on lattice multiplication.

Bifurcation Theory for PyCryptonistas

What is bifurcation theory? An abstract definition is possible, but the most common usage is in dynamical systems, when a small change to parameters creates a major change to the "topology" of a solution (typically of a family of differential equations). It is informally part of the "qualitative" theory of differential equations.

Revisiting The Legendary Doob

Pick up a book on stochastic processes and you will invariably see references to the legendary Doob.

Joseph Doob was an American mathematician who developed the theory of martingales.

He was born in Cincinnati, Ohio and the family later moved to New York City.

He studied at Harvard, where is advisor as Joseph Walsh, known for the Walsh function.

Who First Conceived of Linear Programming and How did it Become Mainstream

Linear programming (LP) was first conceived in 1939 by Kantarovich, who began studies at Leningrad University (now known as the Saint Petersburg State University) at the age of 14.

He developed LP in the context of the real-world problem of optimizing production in the plywood industry.

(Quiz question - what was Kantarovich's middle name? Answer - Vitalievich).

Kantarovich published his findings in a 1939 book called "The Mathematical Method of Production Planning and Organization". He received the Nobel Prize as well as the Soviet Union's Lenin Prize (1965) and the Order of Lenin (1967), the highest civilian decoration bestowed by the Soviet Union.

Portland-Oregon born George Dantzig, whose parents were linguists (his father Tobias was also a mathematician) took Kantarovich's ideas further and developed an algorithm to address LP problems.

The so-called "simplex method" in 1948 made LP practical for use in solving real world problems. The name "simplex" refers to the shape of the search space for the feasible set.

The related theory of duality was later developed by John von Neumann.

What Pythonistas Ought to Know About NEGs

Euclidean geometry (we will call it EG) is very familiar thanks to Euclid's Elements. EG possesses the interesting fact that the sum of the angles of a triangle at up to 180 degrees, or PI radians. This property is not shared by non Euclidean geometries (we shall call it NEGs) including spherical and hyperbolic geometries.

Complex Functions need L-Series, Like Real functions need T-Series - thanks PAL!

Any mathematical programmer needs nodding acquaintance with Laurent series.

So what is a "Laurent Series"?

These super-important series are a way of expressing a complex function as a power series when a Taylor series is not possible. They are interesting in that negative exponents are part and parcel of the series.

Pierre Alphonse Laurent ("PAL") was the discoverer of the Laurent series.

He was an engineer directing operations for the enlargement of the port of Le Havre. He applied deep theoretical knowledge to practical use.

His name is also given to the polynomial known as the Laurent polynomial (characterised by terms of negative degree).