Fourier’s Series

Lecture by Professor Raymond Flood. Joseph Fourier was interested in the mathematical study of the diffusion of heat in solid bodies which he described using infinite trigonometric series which are now known as Fourier series. These series had major applications in many other types of physical problems and led to many of the most important mathematical discoveries of the nineteenth century. Fourier series are used not only in engineering, geology and astronomy but also in number theory, control theory and statistics. (from gresham.ac.uk)

Related Links
The Analytical Theory of Heat

Newton's Laws by Professor Raymond Flood

In his Principia Isaac Newton used his law of universal gravitation and three laws of motion to explain elliptical planetary motion, the orbits of comets, the variation of the tides and the flattening of the earth at its poles. Further important work on celestial mechanics was undertaken by Joseph-Louis Lagrange, Pierre-Simon Laplace and Henri Poincare. It was Poincare who discovered that even with Newton's deterministic laws the resulting motion may be irregular and unpredictable, the basis of modern day chaos theory. (from gresham.ac.uk)

Related Links
Books and Films - Isaac Newton

Fermat’s Theorems by Professor Raymond Flood

The seventeenth century mathematician Pierre de Fermat is mainly remembered for contributions to number theory even though he often stated his results without proof and published very little. He is particularly remembered for his 'last theorem' which was only proved in the mid-1990s by Andrew Wiles. He also stated other influential results, in particular Fermat's 'Little Theorem' about certain large numbers which can be divided by primes. His 'Little Theorem' is the basis of important recent work in cryptography and internet security. (from gresham.ac.uk)

Related Links
Fermat's Last Theorem

Butterflies, Chaos and Fractals by Professor Raymond Flood

In 1972 the meteorologist, Edward Lorenz, delivered a lecture with the title Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas? In this he showed that dynamical systems can exhibit chaotic, seemingly random, behaviour. Many scientists think that this ranks as one of the main scientific advances of the twentieth century together with relativity and quantum theory. I will also talk about how the butterfly effect links chaos and the beautiful geometric objects, fractals.

Related Links
Hunting the Hidden Dimension

From One to Many Geometries

For 100 years up to the end of the 19th century the study of geometry was completely changed with the development of non-Euclidean geometries and the use of techniques to think of geometries in higher dimensions - a development essential to Einstein in his development of the theory of General Relativity.

About the Lecturer
Raymond Flood is Professor of Geometry at Gresham College.

Ghosts of Departed Quantities: Calculus and its Limits

In 1734 Bishop Berkeley published a witty and effective attack on the foundations of the calculus as developed by Newton and Leibniz. But it took nearly 90 years for the calculus to be given a rigorous foundation through the work of the prolific mathematician, Augustin-Louis Cauchy, who formalised the concept of a limit and created the specialism now called analysis.

About the Lecturer
Raymond Flood is Professor of Geometry at Gresham College.

Related Links:
The Birth of the Calculus

James Clerk Maxwell: The Greatest Victorian Mathematical Physicists

James Clerk Maxwell (1831-1879) was one of the most important mathematical physicists of all time, after only Newton and Einstein. Within a relatively short lifetime he made enormous contributions to science which this lecture will survey. Foremost among these was the formulation of the theory of electromagnetism with light, electricity and magnetism all shown to be manifestations of the electromagnetic field. He also made major contributions to the theory of colour vision and optics, the kinetic theory of gases and thermodynamics, and the understanding of the dynamics and stability of Saturn's rings.

About the Lecturer
Raymond Flood is Professor of Geometry at Gresham College.

Related Links:
Books and Films - James Clerk Maxwell
Shock and Awe: The Story of Electricity