For the last eighteen years, I have been teaching an introductory course in as­ trophysics. The course is intended for nonscience majors satisfying a general education requirement in natural science. It is a physics course with applications in astronomy. The only prerequisite is the high school mathematics required for ad­ mission to the university. For a number of years, I used an astronomy text, which I supplemented with lecture notes on physics. There are many good astronomy texts available, but this was not a satisfactory state of affairs, since the course is a physics course. The students needed a physics text that focused on astronomical applications. Over the last few years, I have developed a text which my students have been using in manuscript form in this course. This book is an outgrowth of that effort. The purpose of the book is to develop the physics that describes the behavior of matter here on the earth and use it to try to understand the things that are seen in the heavens. Following a brief discussion of the history of astronomy from the Greeks through the Copernican Revolution, we begin to develop the physics needed to understand three important problems at a level accessible to undergraduate nonscience majors: (1) the solar system, (2) the structure and evolution of stars, and (3) the early universe. All ofthese are related to the fundamental problem of how matter and energy behave in space and time.

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The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span­ ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon­ necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone.

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The present volume contains the proceedings of the workshop on "Minimax Theory and Applications" that was held during the week 30 September - 6 October 1996 at the "G. Stampacchia" International School of Mathematics of the "E. Majorana" Centre for Scientific Cul­ ture in Erice (Italy) . The main theme of the workshop was minimax theory in its most classical meaning. That is to say, given a real-valued function f on a product space X x Y , one tries to find conditions that ensure the validity of the equality sup inf f(x,y) = inf sup f(x, y). yEY xEX xEX yEY This is not an appropriate place to enter into the technical details of the proofs of minimax theorems, or into the history of the contribu­ tions to the solution of this basic problem in the last 7 decades. But we do want to stress its intrinsic interest and point out that, in spite of its extremely simple formulation, it conceals a great wealth of ideas. This is clearly shown by the large variety of methods and tools that have been used to study it. The applications of minimax theory are also extremely interesting. In fact, the need for the ability to "switch quantifiers" arises in a seemingly boundless range of different situations. So, the good quality of a minimax theorem can also be judged by its applicability. We hope that this volume will offer a rather complete account of the state of the art of the subject.

The history of triangular norms started with the paper "Statistical metrics" [Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de­ scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set­ ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in [Schweizer & Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in [Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph [Schweizer & Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.

Since the advent of the laser, coherent optics has developed at an ever increasing pace. There is no doubt about the reason. Coherent light, with its properties so different from the light we are surrounded by, lends itself to numerous applications in science, technology, and life. The bandwidth of coherent optics reaches from holography and interferometry, with its gravitational wave detectors, to the CD player for music, movies, and computers; from the laser scalpel, which allows surgical cutting in the interior of the eye without destruction of the layers penetrated in front of it, to optical information and data processing with its great impact on society. According to its importance, the foundations of coherent optics should be conveyed to students of natural sciences as early as possible to better prepare them for their future careers as physicists or engineers. The present book tries to serve this need: to promote the foundations of coherent optics. Special attention is paid to a thorough presentation of the fundamentals. This should enable the reader to follow the contemporary literature from a firm basis. The wealth of material, of course, makes necessary a restriction of the topics included. Therefore, from the main areas of optics, wave optics and the classical description oflight is given most ofthe space available. The book starts with a quick trip through the history of physics from the viewpoint of optics.

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