The big blue is the world's greatest wilderness, far from shore and many kilometres deep. It's a vast marine desert where there is little to eat and nowhere to hide. Yet it's home to some of the biggest and most spectacular creatures on earth. This episode reveals what it takes to survive in this savage and forbidding world. We witness feats of incredible endurance, moments of high drama and extraordinary acts of heart-wrenching self-sacrifice. Every animal in the big blue must find their own unique way to survive. Sperm whales have the largest brains in the world. They live for 80 years, and we are only now beginning to learn the extraordinary complexity of their language of clicks - thought to coordinate the whole family in everything from childcare to hunting. With special pressure-proof cameras, we witness record-breaking feats of endurance as they hunt for squid a kilometre down into the abyss. Only recently have we begun to solve the mystery of where baby turtles disappear to in their early years. They leave the crowded waters of the coast and head to the open ocean, where they use floating debris like logs as life rafts. Here they remain until adulthood, adrift on the high seas in relative safety away from coastal predators. Over half of all animals in the open ocean drift in currents. Jellyfish cross entire oceans feeding on whatever happens to tangle with their tentacles. The jelly-like Portuguese man-of-war can harness sail power to fish with its deadly tentacles. Sometimes there is a brief explosion of food in this marine desert, but ocean hunters must be fast to make the best of this bonanza. We witness super pods of up to 5,000 spinner dolphins racing to herd vast shoals of lanternfish, briefly caught at the surface where it is thought they spawn. New aerial footage reveals, for the first time, the truth to a centuries-old sailors' legend of the 'boiling seas' - the spectacular feeding frenzy of 90kg tuna and dolphins smashing through the lantern fish shoals turning the sea white with foam.

It's a timeless classic of children's literature and the third most-quoted book in English after the Bible and Shakespeare. But what lies behind the extraordinary appeal of Alice's Adventures in Wonderland to generations of adults and children alike? To mark the 150th anniversary of its publication, this documentary explores the life and imagination of the man who wrote it, the Reverend Charles Dodgson, better known as Lewis Carroll." Broadcaster and journalist Martha Kearney delves into the biographies of both Carroll himself and of the young girl, Alice Liddell, who inspired his most famous creation. Kearney's lifelong passion for Carroll's work began as a young girl, when she starred as Carroll's heroine Alice in her local village play. She discusses the book with a range of experts, biographers and distinguished cultural figures - from the actor Richard E Grant to children's author Philip Pullman - and explores with them the mystery of how a retiring, buttoned-up and meticulous mathematics don, who spent almost his entire life within the cloistered confines of Christ Church Oxford, was able to capture the world of childhood in such a captivating way

Competition to win a partner …has created some of the most extraordinary beauty and life-threatening violence anywhere in nature. Dazzling colours, elaborate dances and powerful weapons have all evolved to attract and defend a mate. The stakes could not be higher: without a mate, the journey of life ends here... sometimes literally.

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.

Iain Stewart investigates a new and controversial energy rush for the natural gas found deep underground. Getting it out of the ground involves hydraulic fracturing - or fracking. We travel to America to find to find out what it is, why it is a potential game changer and what we can learn from the US experience". Sometimes, this is right under the places people live in. He meets some of the people who have become rich from fracking as well as the communities worried about the risks. Director Jeff Wilkinson

'Flexing' is a dance style forged in far east Brooklyn, at the dead-end of a handful of subway lines. Flex dancers channel the grittiness and crime of East New York into choreographed violence with gun movements, simulated bone-breaking, and the mimicked ripping of hearts from opponent's chests. Through battles dancers gain respect, craft an artistic identity, and sometimes find a sanctuary from the poverty and violence that saturates their neighborhood. No other style of street-dance is this violent, scary, or beautifully theatrical. In this purely do-it-yourself scene, creativity and ambition bring a community together around frequent dance-battle showcases that have begun to attract an international audience and may catapult the best dancers into careers in theater or film. Following a group of dancers for over two years, Flex is Kings explores the hopes and realities of this under-acknowledged and totally unfunded group of urban artists