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...world of mathematics. In this free course, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces...Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this free course, you will learn...

...world around us is enabled by what we see, hear, smell – that is, generally, perceive. There is no pun intended here: we make a lot of sense of things using our senses. Music technology, in particular, relies much on perception: if the proof of the pudding is in the eating, the ‘proof’ of music technology is in the hearing. Additionally, though, in technological...

...world engineering problem. This will exercise your mathematical abilities and, I hope, convince you of the usefulness of mathematical modelling...Engineering: The challenge of temperature: 2.1 Boiling water - Whether it's to wash clothes, make a cup of tea, or just make it safe to drink, water often has to be heated – sometimes to boiling point. There are many ways to...

...world's land area and population for various regions at the end of the twentieth century. Make rough estimates of the fraction of the land area and the fraction of the population that are in each of the following regions: (a) North America (b) Asia and Oceania (c) Europe (d) Africa. Answer (a) North America has approximately a sixth of the land area and about a twentieth...