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.

Sagan discusses the story of the Heike crab and artificial selection of crabs resembling samurai warriors, as an opening into a larger discussion of evolution through natural selection (and the pitfalls of intelligent design). Among the topics are the development of life on the Cosmic Calendar and the Cambrian explosion; the function of DNA in growth; genetic replication, repairs, and mutation; the common biochemistry of terrestrial organisms; the creation of the molecules of life in the Miller-Urey experiment; and speculation on alien life (such as life in Jupiter's clouds). In the Cosmos Update ten years later, Sagan remarks on RNA also controlling chemical reactions and reproducing itself and the different roles of comets (potentially carrying organic molecules or causing the Cretaceous–Paleogene extinction event).

Andrew Marr tells the story of the first empires which laid the foundations for the modern world. From the Assyrians to Alexander the Great, conquerors rampaged across the Middle East and vicious wars were fought all the way from China to the Mediterranean. But this time of chaos and destruction also brought enormous progress and inspired human development. In the Middle East, the Phoenicians invented the alphabet, and one of the most powerful ideas in world history emerged: the belief in just one God. In India, the Buddha offered a radical alternative to empire building - a way of living that had no place for violence or hierarchy and was open to everyone. Great thinkers from Socrates to Confucius proposed new ideas about how to rule more wisely and live in a better society. And in Greece, democracy was born - the greatest political experiment of all. But within just a few years, its future would be under threat from invasion by an empire in the east...

Professor Brian Cox travels from the fossils of the Burgess Shale to the sands of the oldest desert in the world to show how light holds the key to our understanding of the whole universe, including our own deepest origins. To understand how light holds the key to the story of the universe; you first have to understand its peculiar properties. Brian considers how the properties of light that lend colour to desert sands and the spectrum of a rainbow can lead to profound insights into the history and evolution of our universe. Finally, with some of the world's most fascinating fossils in hand, Brian considers how but for an apparently obscure moment in the early evolutionary history of life, all the secrets of light may have remained hidden. Because although the universe is bathed in light that carries extraordinary amounts of information about where we come from, it would have remained invisible without a crucial evolutionary development that allowed us to see. Only because of that development can we now observe, capture and contemplate the incredible wonders of the universe that we inhabit.

As tuition rates spiral beyond reach and student loan debt passes $1 trillion (more than credit card debt), IVORY TOWER asks: Is college worth the cost? From the halls of Harvard, to public colleges in financial crisis, to Silicon Valley, filmmaker Andrew Rossi assembles an urgent portrait of a great American institution at the breaking point. Through interviews profiled at Arizona State, Cooper Union, and Sebastian Thrun's Udacity-among several others-IVORY TOWER reveals how colleges in the United States, long regarded as leaders in higher education, came to embrace a business model that often promotes expansion over quality learning. Along the way we also find unique programs, from Stanford to the free desert school Deep Springs to the historically black all women's college Spelman, where the potential for life-changing college experiences endure.

This series, narrated and written by Oliver Stone and co-author Peter Kuznick, will focus on human events that at the time went under reported, but crucially shaped America’s unique and complex history over the 20th and 21st century. The series is a re-examination of some of the under-reported and darkest parts of American modern history using little known documents and newly uncovered archival material. The series looks beyond official versions of events to the deeper causes and implications and explores how events from the past still have resonant themes for the present day." The fist episode examines World War II. It offers special attention to the Spanish Civil War, Roosevelt's desire to enter the war on the side of the allies, the strategic Japanese decisions that lead up to Pearl Harbor Attack, and the often overlooked role that the Soviet Union had in winning the war.