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This gently guided, profusely illustrated Grand Tour of the world of mathematics takes the reader on a long and fascinating journey - from the dual invention of numbers and language, through the primary realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into symbolic logic, set theory, topology, fractals, probability, and assorted other mathematical byways. Mathematics: From the Birth of Numbers is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, and those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.
What does mathematics mean? Is it numbers or arithmetic, proofs or equations? Jan Gullberg starts his massive historical overview with some insight into why human beings find it necessary to "reckon," or count, and what math means to us. From there to the last chapter, on differential equations, is a very long, but surprisingly engrossing journey. Mathematics covers how symbolic logic fits into cultures around the world, and gives fascinating biographical tidbits on mathematicians from Archimedes to Wiles. It's a big book, copiously illustrated with goofy little line drawings and cartoon reprints. But the real appeal (at least for math buffs) lies in the scads of problems-with solutions-illustrating the concepts. It really invites readers to sit down with a cup of tea, pencil and paper, and (ahem) a calculator and start solving. Remember the first time you "got it" in math class? With Mathematics you can recapture that bliss, and maybe learn something new, too. Everyone from schoolkids to professors (and maybe even die-hard mathphobes) can find something useful, informative, or entertaining here.
Contents in Brief
Preface
Foreword. «Mathematics in Our Culture» by Peter Hilton
Information for the Reader
Numbers and Language
Systems of Numeration
Types of Numbers
Cornerstones of Mathematics
Combinatorics
Symbolic Logic
Set Theory
Introduction to Sequences and Series
Theory of Equations
Introduction to Functions
Overture to the Geometries
Elementary Geometry
Trigonometry
Hyperbolic Functions
Analytic Geometry
Vector Analysis
Fractals
Matrices and Determinants
Embarking on Calculus
Introduction to Differential Calculus
Introduction to Integral Calculus
Power Series
Indeterminate Limits
Complex Numbers Revisited
Extrema and Critical Points
Arc Length
Centroids
Area
Volume
Motion
Harmonic Analysis
Methods of Approximation
Probability Theory
Differential Equations
Bibliography
Name Index
Subject Index
Symbols in Common Use