Gauss

Aptech GAUSS Data Tool v8.0.0.910


GAUSS Data Tool is a stand-alone program for working with GAUSS data sets. GAUSS Data Tool loads the columns of the data sets into a workspace as vectors where they can be transformed or modified using simple intuitive statements. Data sets can also be created by simulation using a variety of models, e.g., probit, logit, GARCH, linear. A new version of a data set can be generated where missing data are replaced by single or multiple imputations from a maximum likelihood estimation using the EM algorithm.

Variables can be copied from one data set to another. Data sets can be merged on the basis of a keylist; i.e., one or more columns that uniquely define the observations. They can be concatenated, sorted, or added to. Variables can be dropped or kept, or modified in complex ways using any of the GAUSS operators or functions, including its powerful matrix operations.

GAUSS Data Tool is customizable by adding your own functions for modifying data. Hooks are described in the manual for adding your own procedures for simulating data or handling missing data. For the Windows version, a graphical user interface provides much of this capability in menus, toolbars, and dialogues, as well as a command line interface that turns data handling into a set of simple direct statements that make short work of complex data problems.

In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

This biography of Gauss, by far the most comprehensive in English, is the work of a professor of German, G. Waldo Dunnington, who devoted most of his scholarly career to studying the life of Germany's greatest mathematician.

CARL FRIEDRICH GAUSS nel corso della sua vita meritò l’appellativo di “Principe dei matematici” e nei due secoli trascorsi dalla sua morte nessuno ha mai messo in dubbio tale posizione di privilegio. La sua figura presenta interessanti parallelismi con quella di un altro genio a lui contemporaneo e suo compatriota: W. A. Mozart. Entrambi furono bambini prodigio le cui carriere vennero patrocinate da governanti ansiosi di legare le loro corti alle più grandi promesse delle arti e delle scienze. A differenza del compositore, però, Gauss ebbe la fortuna di godere di una vita lunga e serena e questo gli permise di contribuire allo sviluppo della geometria, della statistica,dell’astronomia e della fisica con apporti fondamentali. Tra le sue molte scoperte spiccano quelle relative alla teoria dei numeri, che Gauss coltivò con cura e che gli consentirono di raccogliere alcuni dei frutti più ricchi del pensiero umano.

Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet.