History of Infinite series 
History of Infinite series
by UNSW / N.J. Wildberger
Video Lecture 16 of 32
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Date Added: January 19, 2015

Lecture Description

We discuss various uses of infinite series in the 17th and 18th centuries. In particular we look at the geometric series, power series of log, the Gregory-Newton interpolation formula, Taylor's formula, the Bernoulli's, Euler's summation of the reciprocals of the squares as pi squared over 6, the harmonic series, product expansion of sin(x), the zeta function and Euler's product expansion for it, the exponential function, complex values and finally the circular functions.

Course Index

Course Description

In this course, Prof. N.J. Wildberger from UNSW provides a great overview of the history of the development of mathematics. The course roughly follows John Stillwell's book 'Mathematics and its History' (Springer, 3rd ed)Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology and hyperbolic geometry.  This course is meant for a broad audience, not necessarily mathematics majors. All backgrounds are welcome to take the course and enjoy learning about the origins of mathematical ideas. Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. At UNSW, this is MATH3560 and GENS2005. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.

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