In the high-stakes game of big-wall climbing, the Shark’s Fin on Mount Meru may be the ultimate prize. Sitting at the headwaters of the sacred Ganges River in Northern India, the Shark’s Fin has seen more failed attempts by elite climbing teams over the past 30 years than any other ascent in the Himalayas. To undertake Meru, says Jon Krakauer, the bestselling author of Into Thin Air, "You can’t just be a good ice climber. You can’t just be good at altitude. You can’t just be a good rock climber. It’s defeated so many good climbers and maybe will defeat everybody for all time. Meru isn’t Everest. On Everest you can hire Sherpas to take most of the risks. This is a whole different kind of climbing."

Few sounds are more beautiful or moving than the underwater songs of the humpback whale. Male whales compete with their songs, which often last for 10 minutes at a time, and can be repeated for hours on end. Whales separated by thousands of miles of sea will sing almost identical songs. Researchers have found that the songs change throughout the breeding months, following a mysterious pattern repeated across the waves. Whales also use sound to hunt. To catch herring, humpback whales release a stream of bubbles to form a shimmering, circular fishing net. Emitting a repetitive loud scream, they scare the fish into a tight ball, then lunge out of the water to swallow the shoal whole. Now it seems that the long-held image of the gentle giant must change to one of a ferocious and opportunistic hunter.

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.

The Great Pyramid of Giza's construction is still shrouded in mystery, despite it being the only survivor among the Seven Wonders of the Ancient World. In Building the Great Pyramid, travel back 4,500 years with the BBC as they re-create the circumstances under which it may have been built, as well as the daily life of the population at that time. Expert archaeologists, Egyptologists, and scholars share their latest theories on what may have happened. The film combines dramatic reconstruction, location shooting and state-of-the-art CGI computer effects. Directed and written by Jonathan Stamp.

In the 1960s, US President John F Kennedy proposed landing a man on the moon before the decade was finished. This film has interviews with most of the surviving astronauts of the Apollo program who were making ready to make that great voyage with an army of experts determined to make the endeavour possible. Through training, tragedy and triumph, we follow the greatest moments of one of Humanity's great achievements. The documentary reviews both the footage and media available to the public at the time of the missions, as well as NASA films and materials which had not been opened in over 30 years.

To show what the USA can learn from rest of the world, director Michael Moore playfully visits various nations in Europe and Africa as a one-man "invader" to take their ideas and practices for America. Whether it is Italy with its generous vacation time allotments, France with its gourmet school lunches, German with its industrial policy, Norway and its prison system, Tunisia and its strongly progressive women's policy and Iceland and its strong female presence in government and business among others, Michael Moore discovers there is much that American should emulate