Provides a practical reference to all aspects of mathematics, using clear explanations of such key mathematical concepts as analysis, logic, metamathematics, and mathematical physics.

Includes index.

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 -- Combinatorics -- 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 & STATISTICS -- Statistics -- Probability -- Probability distributions -- Stochastic processes -- Cryptography -- MATHEMATICAL PHYSICS -- Newtonian mechanics -- Waves -- Fields and flows -- Special relativity -- Gravity -- Quantum mechanics -- Quantum field theory -- GAMES AND RECREATION -- Game theory -- Fibonacci -- Puzzles and perplexities.