Mathematics: From the Birth of NumbersThis extraordinary work takes the reader on a long and fascinating journeyfrom the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easytoread 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, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology. Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings. 
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Review: Mathematics: From the Birth of Numbers
User Review  William Schram  GoodreadsExcellent tome on general mathematics from counting all the way to differential equations. Contains examples galore. If you aren't satisfied after all of this, it contains an extensive bibliography ... Read full review
Review: Mathematics: From the Birth of Numbers
User Review  Kevin  GoodreadsExcellent for reference study or general rummaging. Not over laden with history, really the business if you need to know something useful that you don't and fast. Read full review
Contents
Numbers and Language  1 
Systems of Numeration  31 
Types of Numbers  69 
Cornerstones of Mathematics  97 
Combinatorics  183 
Symbolic Logic  215 
Set Theory  231 
Introduction to Sequences and Series  263 
Introduction to Integral Calculus  721 
Power Series  765 
Indeterminate Limits  779 
Complex Numbers Revisited  787 
Extrema and Critical Points  797 
Arc Length  827 
Centroids  837 
Area  851 
Theory of Equations  295 
Introduction to Functions  335 
Overture to the Geometries  363 
Elementary Geometry  385 
Trigonometry  457 
Hyperbolic Functions  533 
Analytic Geometry  547 
Vector Analysis  599 
Fractals  625 
Matrices and Determinants  637 
Embarking on Calculus  671 
Introduction to Differential Calculus  683 
Volume  871 
Motion  891 
Harmonic Analysis  907 
Methods of Approximation  923 
Probability Theory  961 
Differential Equations  989 
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Common terms and phrases
algebraic angle arcsin arctan arithmetic axis base calculation century circle coefficients complex numbers constant convergence cos2 cosh cosx cube cubic equation curve decimal denoted derivative determine diagonal differentiation digits distance elements ellipse equal equation Euler expressed factors finite formula fractions geometry graph Greek hyperbola hyperbolic imaginary unit infinite integer integral intersection interval inverse Latin law of sines Leibniz length Leonhard Euler logarithms magic square mathematician mathematics matrix method multiplication natural logarithm natural numbers negative notation origin orthogonal coordinate parabola parallel parametric equations permutations plane polynomial positive Pythagorean quartic equation radius ratio rational numbers real numbers roots sequence sides sin2 sine sinh solid of revolution solution solve spherical straight line subset subtraction symbols tangent theorem theory triangle trigonometric functions unit variable vector vertex vertices vigesimal xaxis yaxis zero