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invent calculus provide a powerful motivation for one's own journey across the mathematical landscape.

I am certainly not advocating watering down the rigorous side of the subject. When you are learning a musical instrument you'll get nowhere without the graft of doing your scales and arpeggios. But supplement this with some of the tales of where mathematics has come from and we might be on to a more engaging approach to learning maths.

Marcus du Sautoy is Professor of Mathematics at Wadham College, Oxford. His new television series, The Story of Maths, starts on BBC4 on Monday at

principalityбАfor dessert. Even drop in the fact it is in Alaska. The overwhelming chances are you will still see a blank face before you. Perhaps it is not such a surprise. Wrangell-St Elias National Park had roughly

may say. Yellowstone, perhaps. Throw in a few clues. Mention it is so large it would swallow Switzerland whole and have room for a sizeable

Intrigued by this vast unknown, IДset off with three fellow adventure-seeking spirits to explore. After a few hours’ drive from Anchorage, we reached a

one annual visitor for every 200 acres at the last count. Stretching from the

coast to the mountainous interior of the “Last Frontier” state, it is remote and hard to access.

We encountered our first superlative beforeИwe even arrived in the park: Kelly, our weather-beaten bush pilot, was also the world’s most laconic man. As we took off and the sandbanks fell below, he gestured towards an ominous cluster of grey on the southern horizon. “There’s something of a typhoon coming in,” he told us, leaving the intercom to crackle for a moment. The plane wobbled. “I don’t think it’s going to hit us, but that explains all the wind.”

dusty airstrip alongside the state’s mighty Copper River, where the season’s first salmon were surging upstream.

America's 20 best national parks

Then Kelly fixed the Cessna 206 on its course east, threading through a mountain range that seemed never to end. His commentary turned to the

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park’s extraordinary alpine beauty, comprising nine of the 16 highest peaks in the US. Over there was the highest point of the Wrangell ranges, Mount Blackburn, and the active volcano Mount Wrangell. “We sometimes see steam coming out – glad we don’t see it too often, we live a bit too close,” said Kelly.

This was truly wild country, ripe for adventurers, where you are far more likely to meet a bear than another human. Kelly pointed at a river that only

Сone intrepid soul had navigated; an intimidating peak that only one climber had summited. We could just about make out a gravel track weaving through the bush below, too roughly hewn for most car rental companies – hence our use of the services of Wrangell Mountain Air.

иThis was the tiny hamlet of McCarthy, our base and a compelling place in its own right. As improbable as it seemed in the wilderness, it was once a boom

Soon a wide valley spread out before us and we looped over a glacier – the park is home to the highest concentration of these mighty ice rivers in North

America – before approaching another long, dry airstrip. “I usually come in the other end, but the windsock is blowing some,” Kelly explained.

It wasбАset up as fast-living and freer alternative to the rigidly regulated company town , and a cast of big characters passed through in its heyday: labourers, chancers, alpinists and bootleggers – although few larger than a 25-stone prostitute named Beef Trust who once, reputedly, plied her trade here. When the mines collapsed in 1938, it withered to a ghost town. Decades on, a few hardy souls ventured back to the area: outdoorsmen, homesteaders,

town, where money flowed easily, even in the depths of the Depression, as nearby copper mines thrived.

USA national parks: 20 fascinating facts

then tourist workers and, yes, a quota of oddballs.

We checked into Ma Johnson’s Hotel, a wonderfully authentic Wild West-

not altogether coherently on an inflatable two-man “duckie” kayak on a glacial lake. Once my co-paddler and I had established our craft was practically unsinkable, we moored with the rest of the group on an “island” – in fact an iceberg – in the middle of the lake. We toasted several capsize-free minutes in what is likely to be my only ever coffee break on a large chunk of ice, listening to cracks and splashes as the glacier thinned.

Back in McCarthy, we explored some more, sharpening our impression of an abandoned outpost. Many old wooden shacks were derelict; chassis of old pickup trucks lay rusting by the wide, dusty streets.

Today its residents are frequently outnumbered by moose, with just a few dozen hardy souls living here year-round – although the population

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swells to several hundred in the summer. One of the full-timers was our host, Neil Darish, and nobody could accuse him of being bashful about WrangellSt Elias. “More superlatives than any other national park,” he told us.

An East Coast sophisticate – a slightly incongruous find in Alaskan backcountry – Darish already seemed to own half the going concerns in town, many aimed at tourists. The fine-dining bistro, the bar where we drank,

Сand the hotel we stayed in, all belonged to him.

He had another more controversial way of shining a spotlight on his home: a pivotal role in Edge of Alaska, a reality television show that had just finished filming series two (“Hidden deep in the wilderness of Alaska is the toughest town in America: McCarthy”). Some locals welcomed the attention;

иcopper deposits, news of which landed on the radar of the Guggenheims and JP Morgan. They ploughed in vast sums, funding one of the world’s most

others derided the tabloid approach. “It’s pretty ridiculous,” one told us.

That said, the human history of the national park can be far-fetched. A man

with a suitably low-key nickname, “Tarantula” Jack Smith, bears much of the

school, bunkhouses,бАa power plant, administration buildings and one of the most advanced hospitals of its time, including the first X-ray machine in Alaska.

responsibility. A prospector in the early 20th century, he discovered huge

unlikely railways, a 196-mile track traversing raging rivers, glaciers and canyons.

We saw the legacy of the remarkable Copper-River Northwestern

Railway, as the project was known, on a guided tour of Kennecott, the

abandoned mining town the railroad was built to serve. It is an extraordinary,

evocative place, strewn with buildings in disrepair: an old company store, Д

All sprang from copper wealth, and all were deserted when the mines

shut, their decay arrested only by the extreme cold and dry of the climate. The centrepiece is the copper mill, one of theИlargest free-standing wooden buildings in the world. We followed our guide, Bryan, up to its summit, where workers would make a hair-raising commute on a “tram”, a rudimentary cable-car bringing ore down from the hills. They would cling on for the numbing return journey to the mines. Thoughtfully, the company issued a disclaimer saying it was all at their own risk.

But they got the results. Ore passing through the mill’s 14 storeys of gravity-defying timber, and the tanks of the leaching plant opposite, made the Guggenheims’ and Morgans’ “Alaska Syndicate” a fortune: $100 million in profit in little more than three decades. For context, Russia sold the whole of Alaska for $7.2 million in 1867.

Walking beyond Kennecott, we left these giant totems of the previous century behind and rejoined the wild. Spruce and cottonwood lined a path, lupins on the fringe, with the Kennicott Glacier below (a careless clerk

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caused the variant spellings of the mine and the glacier). We passed a dilapidated wooden outhouse, its door pinned with a handwritten warning, “Beware: the porcupine may actually be in the hole”, then descended to yet another ice river, the Root Glacier.

Here we donned crampons and stepped on to the ice. We crunched over the ripples, eddies and hypnotic frozen swirls, a close encounter with the Сfascinating geology of a glacier: its peaks, lakes, moraines and rivers partly

shaped by its age-old collision course with the Kennicott. In this dramatic setting, Bryan had more tales of derring-do. He picked out Mount Blackburn from the summits beyond and told us how it was first climbed by a female alpinist named Dora Keen in 1912. She had roped in local prospectors on her mission to the top, and only one had made it to the top with her. She married him later in McCarthy. “She was a badass,” said Bryan approvingly. “A real

иhad realised. When time came for a return to more mundane realities, such as paved roads and Wi-Fi, we went back to our aircraft at McCarthy airstrip. It was a still day as we took off, soaring above glacier and spruce, and leaving the mighty old copper mill on its unlikely perch in the wild.

cool chick.”

LikeбАthe landscapes, tales from these parts tend towards the epic, we

From “The Telegraph”

Д И

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APPENDIX IV

Texts to prepare for internet examinations/testing

Read the following texts and perform the tasks.

С1. Renewable energy is energy generated from natural resources. In its various forms, it derives directly from the sun, wind, rain, tides, and geothermal heat. Renewable energy is derived from natural processes that are

иthe Earth-Atmosphere system can roughly be described as the Earth's “climate”.

replenished constantly. Each of these sources has unique characteristics which influence how and where they are used.

2. The majority of renewable energy technologies are powered by the sun.

The Earth-Atmosphere system is in equilibrium so that heat radiation into

бА which is tapped by hydroelectricДprojects, and for the growth of plants used

space is equal to incoming solar radiation, the resulting level of energy within

3. The hydrosphere absorbs a major fraction of the incoming radiation.

Most radiation is absorbed at low latitudes around the equator, but this energy is dissipated around the globe in the form of winds and ocean currents. Wave motion may play a role in the process of transferring mechanical energy between the atmosphere and the ocean through wind stress. Solar energy is also responsible for the distribution of precipitation

to create biofuels.

4. While most renewable energy projects and production is large-scale, renewable technologies are also suited to small off-grid applications,

sometimes in rural and remote areas, where energy is often crucial in human development. Some renewable energy technologiesИare criticized for being

intermittent or unsightly, yet the renewable energy market continues to grow. Climate change concerns, coupled with high oil prices, peak oil, and increasing government support, are driving increasing renewable energy legislation, incentives and commercialization.

(Encyclopedia Wikipedia)

1) Define, which statement conforms to the text content.

a)The Earth “climate” constitutes the resulting level of energy solar radiation.

b)Some renewable energy technologies being criticized, the renewable energy market is increasing.

c)All renewable energy is generated by the Sun.

d)Sources of renewable energy have much in common.

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