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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.
Dr Richard Okura Elwes is a writer, teacher, and researcher in mathematics and a Senior Teaching Fellow at University of Leeds, UK. He is the author of the books How to Build a Brain, The Maths Handbook, Maths in 100 Key Breakthroughs, and Chaotic Fishponds and Mirror Universes (all published by Quercus), and has written for New Scientist and Plus Magazine. His research interests include mathematical logic and random processes.