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...concept allows us to generalise the notion of continuity. Section 2 develops the idea of sequences and convergence in metric spaces. Section 3 builds on the ideas from the first two sections to formulate a definition of continuity for functions between metric spaces...This free course contains an introduction to metric spaces and continuity. The key idea is to use three...

...concept of expectation or expected value, the familiar notion of the mean, also known as the first moment, two general definitions of moments, variance, random variables linked by linear transformation and finally, how to deal with moments all in one go, using the moment generating function...This free course looks at a number of the basic properties of statistical...

...concepts in physics, chemistry, biology and life-sciences, and Earth and environmental sciences. Across these multiple disciplines you will meet time scales that include ages, durations and rates, and size scales including distances in three dimensions, which underpin areas and volumes...Scale – dealing with the miniscule to the massive, over milliseconds to millennia...

...concept is wide ranging and has evolved over thousands of years. They can be seen on ancient cave walls, are used in therapy and they signal to us in globally understood icon. They are also a way to debate large and significant problems. This collection of films explores the concept of Rich Pictures and many ways images have evolved into communication tools... The Art of...