This fall we will be offering a new course, Math 873 Differential and Geometric Topology. While waiting for the graduate catalog to catch up with the department, we will offer the course this fall as Math 856 (Differental Geometry). The prerequisites for 856 will be a course in point-set topology (Math 970 (or 871 as we will soon be calling it) is more than sufficient) plus undergraduate linear algebra and multivariable calculus. The goal of the course is to provide a survey of the concepts of differential topology. Essentially, differential topology adds the methods of calculus - differentiability, tangency, integration - to the study of topological spaces. The collection of spaces for which such an addition makes the most sense are called manifolds. Quoting the first words of the text: "Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for understanding `space' in all of its manifestations. Today, the tools of manifold theory are indispensible in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, computer graphics, biomedical imaging, and, of course, theoretical physics." The overall goal of the course is to provide an introduction to the objects, concepts and some of the techniques of this field. The specific topics covered will depend partly on the audience. The first several chapters of Lee's "Introduction to Smooth Manifolds" (which will serve as the primary text) will be our guide in the beginning. The table of contents of the text can be viewed at the amazon.com website; there is a link to it on the course website: www.math.unl.edu/~mbrittenham2/classwk/856f06/