There he received a good understanding of basic mathematics, studying differential and integral calculus, analytic geometry, and the foundations of analysis. ... In the summer of 1854, Dedekind qualified as a university lecturer and began lecturing on the mathematics of probability as well as on geometry with parallel treatment of analytic and projective methods. ... Newton had discovered combined infinite sums (infinite series), the binomial theorem for fractional exponents, and the algebraic expression of the inverse relation between tangents and areas, methods we know today as calculus. ...

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• Approx Pages: 10
• Has Bibliography
• Grade Level: Undergraduate

Proclus, the last major Greek philosopher, who lived around 450 AD wrote: Not much younger than these [pupils of Plato] is Euclid, who put together the "Elements", arranging in order many of Eudoxus' theorems, perfecting many of Theaetetus's, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for Archimedes, who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry t...

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• Approx Pages: 8