Maths 1001

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 Elwes is a writer, teacher and researcher in Mathematics and a Visiting Fellow at the University of Leeds. He contributes to New Scientist and Plus Magazine and publishes research on model theory. Dr Elwes is a committed populariser of mathematics which he regularly promotes at public lectures and on radio.