This is the most comprehensive survey of the mathematical life of the legendary Paul ErdÅ‘s (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of ErdÅ‘s' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two v…
To create the exotic materials and technologies needed to make stargates and warp drives is the holy grail of advanced propulsion. A less ambitious, but nonetheless revolutionary, goal is finding a way to accelerate a spaceship without having to lug along a gargantuan reservoir of fuel that you blow out a tailpipe. Tethers and solar sails are conventional realizations of the basic idea. Ther…
This is the most comprehensive survey of the mathematical life of the legendary Paul ErdÅ‘s (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of ErdÅ‘s' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two v…
Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of s…
No Inv.: 1271-1275/Perp/79/5c
No Inv.: 2714/Perp/85/1c
No Inv.: 583-585/Perp/84/3c~2727/Perp/86/1c
No Inv.: 1454-1455/Perp/85/2c~2761/Perp/86/1c
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent…
No Inv.: 1678-1679/BD/Perp/87/2c