Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multi-facetted introduction to this emerging field.

This thesis focuses on the Army's infantry in Kansas during the development of the American frontier during the years from the Civil War until 1880. Infantry companies were the mainstay of the frontier Army during these years of westward expansion and development. Yet, twentieth century literature and Hollywood movies overlook the role of the infantry on the frontier. A small, fiscally constrained Army could not have safeguarded the nation's frontier without the employment of infantry alongside the cavalry. The central and western portions of the state of Kansas encapsulate the Army's role in the development of fly nation's frontier. Two overland trails the Smoky Hill and the Arkansas, passed through this area and were primary routes for westward expansion. The Kansas pacific railroad, one of two major westward lines, was built during these years. Settlement grew in this area under the Homestead Act of 1862. These elements brought conflict with the Indians; Kansas the scene of some of the most sustained and violent Indian attacks in the last half of the 1860s. To meet the tasks of frontier development the Army employed both cavalry and infantry.