Introduction. Numbers: The Basics; Arithmetic; Number Systems; Rational Numbers; Factors and Multiples; Induction; Representation of Numbers; Transcendental Numbers; Ruler and Compass; Constructions; Diophantine Equations; Prime Numbers. Geometry: Euclidean Geometry; Triangles; Circles; Polygons and Polyhedra; Transformations; Tessellations; Curves and Surfaces; Polar Coordinates; Discrete Geometry; Differential Geometry; Topology; Knot Theory; Non-Euclidean Geometry; Algebraic Topology; Algebraic Geometry; Diophantine Geometry. Algebra: Letters for Numbers; Equations; Vectors and Matrices; Group Theory; Abstract Algebra. Discrete Mathematics: Combinations; Graph Theory; Ramsey Theory. Analysis: Sequences; Series; Continuity; Differential Calculus; Integral Calculus; Complex Analysis; Power Series; Exponentiation; Fractals; Dynamical Systems; Differential Equations; Fourier Analysis. Logic: Basic Logic; The Science of Deduction; Set Theory; Hilbert's program; Complexity theory; Computability theory; Model Theory; Uncertainty and Paradoxes. Metamathematics: What Mathematicians Do; Mathematics and Technology; Philosophies of Mathematics. Probability and Statistics: Statistics; Probability; Probability Distributions; Stochastic Processes; Cryptography. Mathematical Physics: Newtonian Mathematics; Waves; Fields and Flows; Special Relativity; Gravity; Quantum Mechanics; Quantum Field Theory. Games and Recreation: Game Theory; Fibonacci; Puzzles and Perplexities. Index.

The ultimate smart reference to the world of mathematics - from quadratic equations and Pythagoras' Theorem to chaos theory and quantum computing. Maths 1001 provides clear and concise explanations of the most fascinating and fundamental mathematical concepts. Distilled into 1001 bite-sized mini-essays arranged thematically, this unique reference book moves steadily from the basics through to the most advanced of ideas, making it the ideal guide for novices and mathematics enthusiasts. Whether used as a handy reference, an informal self-study course or simply as a gratifying dip-in, this book offers - in one volume - a world of mathematical knowledge for the general reader. Maths 1001 is an incredibly comprehensive guide, spanning all of the key mathematical fields including Numbers, Geometry, Algebra, Analysis, Discrete Mathematics, Logic and the Philosophy of Maths, Applied Mathematics, Statistics and Probability and Puzzles and Mathematical Games. From zero and infinity to relativity and Godel's proof that maths is incomplete, Dr Richard Elwes explains the key concepts of mathematics in the simplest language with a minimum of jargon. Along the way he reveals mathematical secrets such as how to count to 1023 using just 10 fingers and how to make an unbreakable code, as well as answering such questions as: Are imaginary numbers real? How can something be both true and false? Why is it impossible to draw an accurate map of the world? And how do you get your head round the mind-bending Monty Hall problem? Extensive, enlightening and entertaining, this really is the only maths book anyone would ever need to buy.