30-Second Maths: The 50 Most Mind-Expanding Theories in by Richard J. Brown

By Richard J. Brown

From Rubik's cubes to Godel's incompleteness theorem, every thing mathematical defined, with color illustrations, in part a minute. Maths is having fun with a resurgence in reputation. So how are you going to stay away from being the one dinner visitor who has no concept who Fermat used to be, or what he proved? The extra you recognize approximately Maths, the fewer of a technology it turns into. 30 moment Maths takes the pinnacle 50 most tasty mathematical theories, and explains them to the overall reader in part a minute, utilizing not anything greater than pages, 2 hundred phrases and one photo. learn at your individual velocity, and become aware of that maths should be extra interesting than you ever imagined.

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'[30-Second Maths] unveils the beauty of arithmetic, concerning principles from the Mobius strip to infinity with transparent, enjoyable and delightfully concise explanations.' -- New Scientist

About the Author

Richard Brown is Director of Undergraduate experiences on the division of arithmetic, Johns Hopkins University. 

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Additional resources for 30-Second Maths: The 50 Most Mind-Expanding Theories in Mathematics, Each Explained in Half a Minute

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If the probability of an event happening is p, and its probability of not happening is 1 – p, then the ‘odds’ in favour of it happening are p/(1 – p). The ‘odds’ against it happening are (1 – p)/p. For example, the probability of rolling a 4 with a standard die is 1/6. The probability against rolling a 4 is 5/6. The ‘odds’ in favour of rolling a 4 are then (1/6)/(5/6), or 1/5. Expressed the usual way, we would say the odds of rolling a 4 are 1:5 in favour. The ‘odds’ against rolling a 4 are 5:1 (against).

Galileo constructed formulae that mapped one set of points to another, and Descartes introduced the concept of constructing a curve using an algebraic expression. The term ‘function’ was coined by Leibniz in the late 17th century. The set of all inputs of a function is called the domain, while the set of all outputs is called the image or range. Functions of a single variable (or argument) are often plotted using Cartesian coordinates, where x is the abscissa (horizontal axis), and f(x) is the ordinate (vertical axis).

Towards the end of his life, Pascal spent much of his time trying to reconcile faith and reason; his attempts are probably best exemplified by ‘Pascal’s Wager’, which appears in Pensées, a collection of philosophical considerations unfinished at the time of his death. The wager was concerned with the existence of God, and whether one should bet on it. Pascal set the odds in God’s favour, reasoning that if He does exist, your place in heaven is secure, and if He doesn’t, you have lost nothing. 19 June, 1623 Born in Clermont (now Clermont-Ferrand) 1631 Moved to Paris with his family 1639 Wrote Essay on Conics; family moved to Rouen 1642–1645 Constructed the Pascaline, a mechanical calculator 1647 Met Descartes and published New Experiments concerning Vacuums 1650 Converted to Jansenism 1653 Returned to scientific study 1653 Published Treatise on the Equilibrium of Liquids which explained his law of pressure 1654 Corresponded with Fermat 1655 Method for ‘Pascal’s Triangle’ printed; met Antoine Arthaud, leading Jansenist philosopher 1656–1657 Wrote Lettres Provinciales, in defence of Jansenism 1658 Wrote Essay on the Cycloids 1668 Began work on Pensées, a collection of philosophical and theological notes 19 August, 1662 Died in Paris 1670 Pensées published posthumously 1779 Essay on Conics published NUMBER THEORY the 30-second maths Number theory is the study of interesting properties that numbers possess.

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