Project III (MATH3382) 2013-14


The Mathematics of Henri Poincare

Wilhelm Klingenberg

Description

As a mathematician and physicist, Poincare made fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincare conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002. In his research on the three-body problem, Poincare became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology. This project aims to explore some of the work of Poincare and place it into the context of his scientific biography and his time. Given the breadth of his work and its ubiquitious impact, there is a considerable scope of subjects to choose from, e.g. the three-body problem, relativity, differential equations.

Number of students

We have a limit of two students on this project.

Corequisite

Corequisite for this project is Analysis III.

Resources

Ferdinand Verhulst : Henri Poincare, Springer, 2012
Bell, Eric Temple, 1986. Men of Mathematics (reissue edition). Touchstone Books.
Miller, A.I. (1973), "A study of Henri Poincares "Sur la Dynamique de l'Electron", Arch. Hist. Exact. Scis. 10, 207 - 328
Jean Mawhin (October 2005), "Henri Poincare. A Life in the Service of Science" (PDF), Notices of the AMS 52 (9), 1036 - 1044
Folina, Janet, 1992. Poincare and the Philosophy of Mathematics. Macmillan, New York.
Bernstein, Peter L, 1996. "Against the Gods: A Remarkable Story of Risk". (p. 199 - 200). John Wiley & Sons
Diacu, F. (1996), "The solution of the n-body Problem", The Mathematical Intelligencer 18 (3), 66 - 70
Boyer, B. Carl, 1968. A History of Mathematics: Henri Poincaré, John Wiley & Sons
Grattan-Guinness, Ivor, 2000. The Search for Mathematical Roots 1870 - 1940. Princeton Uni. Press.
Gray, Jeremy, 1986. Linear differential equations and group theory from Riemann to Poincare, Birkhauser

email: W Klingenberg