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# Author: Chris Sangwin

What's the integral of
x^{k}? If you're up to speed with your calculus, you can probably rattle the answer off by heart. But can you prove it? Chris Sangwin introduces an ingenious method for deriving the integral from first principles. |
Coming to think of it, is the standard formula for the integral of
x^{k} really the best one? Chris Sangwin makes an interesting case that it is not. |

In the fourth and final part of our series celebrating 300 years since Leonhard Euler's birth, we let Euler speak for himself.
Chris Sangwin takes us through excerpts of Euler's algebra text book and finds that modern teaching could have something to learn from Euler's methods. |
John Napier was a clever man indeed. Besides inventing the logarithm, he developed ingenious calculating devices that fully exploit the power of the positional system. In this article
Chris Sangwin tells you how to make your own set of Napier's bones and perform mathemagic with an interactive checker board. |

Calculus is a collection of tools, such as differentiation and integration, for solving problems in mathematics which involve "rates of change" and "areas". In the second of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us how to move on from first principles to differentiation as we know and love it! |
Calculus is a collection of tools, such as differentiation and integration, for solving problems in mathematics which involve "rates of change" and "areas". In the first of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us about these tools - without doubt, the some of the most important in all of mathematics. |