Calculus Gems: Brief Lives and Memorable Mathematics
Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices (Biographical Notes and Variety of Additional Topics) found in Simmons' 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The text is suitable as a supplement for a calculus course and/or a history of mathematics course, The overall aim is bound up in the question, What is mathematics for? and in Simmons' answer, To delight the mind and help us understand the world. The essays are independent of one another, allowing the instructor to pick and choose among them.
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Pythagoras ca 580500 B C
Democritus ca 460370 B C
Euclid ca 300 B C
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Abel algebra analysis angle Archimedes astronomy Bernoulli calculus called Cavalieri Cavalieri's Principle century circle complete complex numbers cone conic construction corresponding curve cycloid Democritus Descartes differential discovered discoveries ellipse equal equation Euclid Euler fact factor famous Fermat FIGURE follows formula function G. H. Hardy Galileo Gauss geometry given greatest Greek Huygens ideas infinite integer intellectual interesting irrational John Bernoulli Kepler known later Leibniz length mathematician mathematics Mersenne method modern Newton number theory orbit parabola parametric equations Pascal perfect numbers philosophy physics planets positive integers prime number prime number theorem problem proof properties prove published Pythagoras Pythagorean quaternions radius rational real numbers reasoning regular polygons remarkable Riemann scientific Section shown in Fig solid sphere square T. L. Heath tangent Thales theorem thought treatise triangle University Press vectors velocity volume Weierstrass write wrote