Troop withdrawals begin as the Americans train their ARVN allies to take over the war. Gery Benedetti patrols the hostile waters of the Mekong Delta. James Anderson leads a battalion into Cambodia after Nixon's controversial order. Don DeVore struggles to survive a fierce night attack, and Anne Purcell gets promising news about her husband.

The turmoil of 1968 helps Nixon win the presidency. Troop strength in Vietnam peaks and the draft accelerates. Karl Marlantes endures bitter jungle fighting on Hill 484, and draftee Arthur Wiknik gets a grim introduction to combat on 'Hamburger Hill'. But shortly after winning both hills, US troops abandon them.

Vintage footage from the Vietnam war is presented along with narration from both war veterans and Hollywood voice talent. The documentary follows key events and their impact on both the war effort and the American public.
The Beginning: The first episode looks at the early months of the Vietnam war from the escalation following the Gulf of Tonkin incident to the grim fighting of the Battle of Ia Drang where a few hundred American soldiers are pinned down by three battalions of North Vietnamese infantry. Using superior air power and reinforcements, the Americans fight the North Vietnamese to a draw.

Dr Hannah Fry explores a paradox at the heart of modern maths, discovered by Bertrand Russell, which undermines the very foundations of logic that all of maths is built on. These flaws suggest that maths isn't a true part of the universe but might just be a human language - fallible and imprecise. However, Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.
Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature. But if we accept that maths is part of the structure of the universe, there are two main problems: firstly, the two main theories that predict and describe the universe - quantum physics and general relativity - are actually incompatible; and secondly, most of the maths behind them suggests the likelihood of something even stranger - multiple universes.
We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.

The great flood in the Okavango turns 4,000 square miles of arid plains into a beautiful wetland. Elephant mothers guide their families on an epic trek across the harsh Kalahari Desert towards it, siphoning fresh water from stagnant pools and facing hungry lions. Hippos battle for territory, as the magical water draws in thousands of buffalo and birds, and vast clouds of dragonflies. Will the young elephant calves survive to reach this grassland paradise? The experienced mother elephants time their arrival at the delta to coincide with the lush grass produced by the great flood.
In a TV first, the programme shows the way they use their trunks to siphon clean water from the surface layers of a stagnant pool, while avoiding stirring up the muddy sediment on the bottom with their feet. Lechwe swamp deer, zebras, giraffes, crocodiles and numerous fish and thousands of birds arrive in the delta. And, in a phenomenon never before filmed in the Okavango, thousands of dragonflies appear - seemingly from nowhere - within minutes of the flood arrival, mating and laying eggs. As the flood finally reaches its peak, elephants and buffalo, near the end of their epic trek across the desert, face the final gauntlet of a hungry pride of lions. In a heart-wrenching sequence, a baby elephant is brought down by a lion in broad daylight.

What's worse for us: sugar or fat? To answer the hottest question in nutrition, twin doctors Chris and Xand Van Tulleken go on month-long high-fat and high-sugar diets. The effects on their bodies are shocking and surprising. But they also discover that in the debate about fat and sugar, the real enemy might have been hiding in plain sight.