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Tony Crilly is a Reader in Mathematical Sciences at Middlesex University, having previously taught at the University of Michigan, the City University in Hong Kong and the Open University. His principal research interest is the history of mathematics, and he has written and edited many works on fractals, chaos and computing. He is the author of the acclaimed biography of the English mathematician Arthur Cayley.
Who invented zero? Why 60 seconds in a minute? How big is infinity? Where do parallel lines meet? And can a butterfly's wings really cause a storm on the far side of the world? In 50 Maths Ideas You Really Need to Know, Professor Tony Crilly explains in 50 clear and concise essays the mathematical concepts - ancient and modern, theoretical and practical, everyday and esoteric - that allow us to understand and shape the world around us. Packed with diagrams, examples and anecdotes, this book is the perfect overview of this often daunting but always essential subject. For once, mathematics couldn't be simpler. Contents include: Origins of mathematics, from Egyptian fractions to Roman numerals; Pi and primes, Fibonacci numbers and the golden ratio; What calculus, statistics and algebra can actually do; The very real uses of imaginary numbers; The Big Ideas of relativity, Chaos theory, Fractals, Genetics and hyperspace; The reasoning behind Sudoku and code cracking, Lotteries and gambling, Money management and compound interest; Solving of Fermat's last theorem and the million-dollar question of the Riemann hypothesis.
What are the strangest numbers? Where do numbers come from? Can maths guarantee riches? Why are three dimensions not enough? Can a butterfly's wings really cause a hurricane? Can maths predict the future? In How Big is Infinity?, acclaimed writer Tony Crilly distills the wisdom of some of the greatest minds in history to help provide answers some of the most perplexing, stimulating and surprising questions in mathematics.
Arthur Cayley (1821-1895) was one of the most prolific and important mathematicians of the Victorian era. His influence still pervades modern mathematics, in group theory (Cayley's theorem), matrix algebra (the Cayley-Hamilton theorem), and invariant theory, where he made his most significant contributions. Yet Cayley's life has been overlooked by historians, who have lavished far more attention on lesser figures. Mathematician and biographer Tony Crilly, the world's leading authority on Cayley, rectifies this oversight with the first definitive account of his life. Born in England, Cayley spent his childhood in St. Petersburg, where his father was a commercial agent. After returning to England in 1828, Cayley received a first-rate education. As an undergraduate at Trinity College in Cambridge, he was named Senior Wrangler, the top mathematics student of his year. After graduating, he found himself at the vanguard of the revolution in British mathematics which included William Rowan Hamilton, George Boole, and James Joseph Sylvester. At the same time, needing a reliable income, he trained for the bar and became a barrister at Lincoln's Inn in 1849. Though a successful lawyer, Cayley devoted all his free time to mathematics and confirmed his reputation as one of the era's leading minds with a procession of brilliant articles on key aspects in pure mathematics. Only after 1863, when he was appointed to the Sadleirian Chair at Cambridge, could he fully pursue mathematical investigations, and he continued to publish influential papers until his death. Comprehensive and elegantly composed, this biography makes clear the scope of Arthur Cayley's prodigious achievements, firmly enshrining him as the Mathematician Laureate of the Victorian Age.
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