What is striking when you talk with mathematicians is that sparkle in their eyes, and their sudden joyful voice trying to share with you a concept, a theory. They continuously use words such as invention, beauty, freedom. You then ask yourself : how such a rich language, this quasi-philosophical proposition about the world becomes rejected by a majority, 'the only discipline where one prides itself to be bad at it'! But for 40 years, mathematitians have become essential in sickness and in health!
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression.
Project-oriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social, and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results.
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods.
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology.
Astrophysicist Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond, all leading to the ultimate riddle: Is math an invention or a discovery? Humankind's clever trick, or the language of the universe? Join NOVA for a mathematical mystery tour–a provocative exploration of math's astonishing power across the centuries.