Shaping Modern Mathematics: The 19th Century

1
Ghosts of Departed Quantities: Calculus and its Limits  Professor Raymond Flood
by GreshamCollege 14,261 views
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, AugustinLouis Cauchy, who formalised the concept of a limit and created the specialism now called analysis.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lecturesandevents/ghostsofdepartedquantitiescalculusanditslimits
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There is currently over 1,300 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/GreshamCollege/14011689941 
2
Polynomials and their Roots  Professor Raymond Flood
by GreshamCollege 6,642 views
We are familiar with the formula for solving a quadratic equation where the highest power of the unknown is a square. The quest for a similar formula for equations where the highest power is three, four five or more led to dramatic changes in how this question was regarded. Powerful techniques in algebra were developed following work by Abel and Galois in the 19th century to show that there is no such formula when there are powers higher than four.
The transcript and downloadable versions of all of the lectures are available from the Gresham College website:
http://www.gresham.ac.uk/lecturesandevents/polynomialsandtheirroots
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There is currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/GreshamCollege/14011689941 
3
From One to Many Geometries  Professor Raymond Flood
by GreshamCollege 5,326 views
For 100 years up to the end of the 19th century the study of geometry was completely changed with the development of nonEuclidean 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.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lecturesandevents/fromonetomanygeometries
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/GreshamCollege/14011689941 
4
The Queen of Mathematics  Professor Raymond Flood
by GreshamCollege 25,186 views
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." The properties of primes play a crucial part in number theory. An intriguing question is how they are distributed among the other integers. The 19th century saw progress in answering this question with the proof of the Prime Number Theorem although it also saw Bernhard Riemann posing what many think to be the greatest unsolved problem in mathematics  the Rieman Hypothesis.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lecturesandevents/thequeenofmathematics
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/GreshamCollege/14011689941 
5
Are Averages Typical?  Professor Raymond Flood
by GreshamCollege 1,199 views
Not necessarily, for example the average person has fewer than two legs! This is because some people have fewer than two legs but nobody has more than two, so dividing the total number of legs by the total number of people to get the average gives a number less than two. Average does not mean typical! The lecture will examine how the work in the 19th century of such mathematicians as Florence Nightingale, Adolphe Queteller and Karl Pearson on describing and quantifying variation and uncertainty laid the foundations for the theory of statistics as a mathematical discipline.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lecturesandevents/areaveragestypical
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/GreshamCollege/14011689941 
6
Modelling the World  Professor Raymond Flood
by GreshamCollege 1,287 views
An area of which 19th century British mathematics could be uniformly proud was applied mathematics where new techniques were used on a wide range of problems. Figures such as William Thompson (later Lord Kelvin), Peter Guthrie Tait, George Stokes and James Clerk Maxwell succeeded in applying mathematics to understanding the physical world. They worked on many topics including mechanics, thermodynamics, electricity and magnetism, hydrodynamics and the theory of gases. This lecture will introduce and discuss some of their influential achievements.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lecturesandevents/modellingtheworld
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/GreshamCollege/14011689941