Zero -- Number systems -- Fractions -- Squares and square roots -- [Greek symbol for pi] -- e -- Infinity -- Imaginary numbers -- Primes -- Perfect numbers -- Fibonacci numbers -- Golden rectangles -- Pascal's triangle -- Algebra -- Euclid's algorithm -- Logic -- Proof -- Sets -- Calculus -- Constructions -- Triangles -- Curves -- Topology -- Dimension -- Fractals -- Chaos -- The parallel postulate -- Discrete geometry -- Graphs -- The four-colour problem -- Probability -- Baye's theory -- The birthday problem -- Distributions -- The normal curve -- Connecting data -- Genetics -- Groups -- Matrices -- Codes -- Advanced counting -- Magic squares -- Latin squares -- Money mathematics -- The diet problem -- The travelling salesperson -- Game theory -- Relativity -- Fermat's last theorem -- The Riemann hypothesis.

"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 Mathematical 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. Beginning with zero itself and concluding with the last great unsolved problem, 50 Mathematical Ideas introduces the origins of mathematics, from Egyptian fractions to Roman numerals; explains the near-mystical significance of pi and primes, Fibonacci numbers and the golden ratio; tells you the things they didn't at school - what calculus, statistics and algebra can actually do, and the very real uses of imaginary numbers; illuminates the big Ideas of relativity, chaos theory, fractals, genetics and hyperspace; reveals the unspoken reasoning behind Sudoku and code cracking, lotteries and gambling, money management and compound interest; explores the latest mind-shattering developments, including the solving of Fermat's last theorem and the million-dollar question of the Riemann hypothesis. Packed with diagrams, examples and anecdotes, 50 Mathematical Ideas is the perfect overview of this often daunting but always essential subject. For once, mathematics couldn't be simpler."--Publisher's description.