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In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

Washington, D.C. is in many ways a city of extremes. Starland Vocal Band, Marvin Gaye, Duke Ellington, Nils Lofgren, Chuck Brown, Henry Rollins, Fugazi and Trouble Funk all hail from D.C. In the early '70s, the music style go-go originated here, and has remained a local craze ever since. Dave Grohl sits down with Trouble Funk's Big Tony Fisher to talk about go-go, and explores its origins with Chuck Brown, the genre's undisputed godfather.
He also chats with Don Zientara, owner of Inner Ear Studios, which the Virginia-raised Grohl says 'produced the entire soundtrack of my youth,' as well as with members of the harDCore band Bad Brains and Ian MacKaye of Teen Idles, Minor Threat and Fugazi, who all recorded at Inner Ear over the decades. The song 'The Feast and the Famine' is recorded during this episode.

Last in series about the Nazi concentration camp looks at the fate of the remaining prisoners and their guards. Uncovers how many survivors faced appalling treatment in their home countries and how many guards escaped justice.

In the eighth episode, after two long days of closing arguments, the jury deliberates. Steven's fate hinges on whether the jury believes police misconduct may have occurred.

Rockefeller, Carnegie and Morgan team up to help elect William McKinley to the U.S. presidency by paying for his 1896 campaign, to avoid a possible attack on monopolies. However, fate intervenes when McKinley is suddenly assassinated, and vice president Theodore Roosevelt assumes the presidency and promptly begins dissolving monopolies and trusts in America. Meanwhile, Morgan buys out Carnegie Steel to make Carnegie the richest man in the world, and Henry Ford designs an affordable automobile with his Model T and starts his own business, Ford Motor Company, which sets a new business model for companies to follow.

Dr. Thomas Asbridge explains how in the thirteenth century, after almost two hundred years of Holy Wars, the titanic conflict between Christianity and Islam, known to history as The Crusades, reached a decisive and shocking conclusion – a chapter that despite its drama has been virtually forgotten. He explains how, in the end, the fate of the Holy Land was decided not on the hallowed ground of Jerusalem, but in Egypt; and how the ultimate outcome of the Crusades was dictated not by Christians, but by the Mongol successors to Genghis Khan, and by a Muslim slave – a fearsome warrior whose story is now all but lost to western history.