Bøger udgivet af Springer New York

Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can be used for a second year graduate course. My aim was to keep the second personality dominant, but the reference persona kept breaking out especially at the end of sections in the form of remarks that contain more advanced material. To satisfy this reference persona, I'll begin by telling you a little about the subject matter of the book, and then I'll talk about the textbook aspect. A flat riemannian manifold is a space in which you can talk about geometry (e. g. distance, angle, curvature, "e;straight lines,"e; etc. ) and, in addition, the geometry is locally the one we all know and love, namely euclidean geometry. This means that near any point of this space one can introduce coordinates so that with respect to these coordinates, the rules of euclidean geometry hold. These coordinates are not valid in the entire space, so you can't conclude the space is euclidean space itself. In this book we are mainly concerned with compact flat riemannian manifolds, and unless we say otherwise, we use the term "e;flat manifold"e; to mean "e;compact flat riemannian manifold. "e; It turns out that the most important invariant for flat manifolds is the fundamental group.

Nature is full of spidery patterns: lightning bolts, coastlines, nerve cells, termite tunnels, bacteria cultures, root systems, forest fires, soil cracking, river deltas, galactic distributions, mountain ranges, tidal patterns, cloud shapes, sequencing of nucleotides in DNA, cauliflower, broccoli, lungs, kidneys, the scraggly nerve cells that carry signals to and from your brain, the branching arteries and veins that make up your circulatory system. These and other similar patterns in nature are called natural fractals or random fractals. This chapter contains activities that describe random fractals. There are two kinds of fractals: mathematical fractals and natural (or random) fractals. A mathematical fractal can be described by a mathematical formula. Given this formula, the resulting structure is always identically the same (though it may be colored in different ways). In contrast, natural fractals never repeat themselves; each one is unique, different from all others. This is because these processes are frequently equivalent to coin-flipping, plus a few simple rules. Nature is full of random fractals. In this book you will explore a few of the many random fractals in Nature. Branching, scraggly nerve cells are important to life (one of the patterns on the preceding pages). We cannot live without them. How do we describe a nerve cell? How do we classify different nerve cells? Each individual nerve cell is special, unique, different from every other nerve cell. And yet our eye sees that nerve cells are similar to one another.

To the Instructor The purpose of this laboratory manual is not just to help students to set up electronic circuits that function as they should. The important thing is the electronic concepts that the student learns in the process of setting up and studying these circuits. Quite often a student learns more electronics when he has to trouble shoot a circuit than when the circuit performs as it should when first built. It is unlikely that any students would be able to complete all of these experiments in one semester. The author believes that all students should have laboratory experiences with power sup- plies, amplifiers, oscillators, and integrated circuits. Additionallabomtory experiments should be de- termined by the instructor. Therefore, you can choose those that you want done. Some students are more efficient in the labomtory than others. Therefore, some would be able to complete more exper- iments in a semester than others. Also many of these experiments cannot be completed in one two- hour laboratory period. If space is available, the circuits could be left intact from one period to the next. Or you might want to select steps in an experiment that you want to delete. Neither the val- ues of the components or the magnitudes of the power supplies, as given in the instructions, are critical. Therefore you could in most cases change them if the ones recommended are not available.

viii From discussions with our colleagues, we know that they recognize the problems and worry about them, but simply do not have the time to thoroughly study the highly specialized genetic literature available. This book is an attempt to fill this void. We have made an effort to keep it as short and clear as possible and to limit it to the important and most frequent genetic abnor- malities. In particular, we have tried to take into consid- eration the difficulties of the average student in under- standing genetic logic and to eliminate the most common errors. This guide is not designed to provide more than basic information. No reader will arise from the study of this volume as an expert genetic counselor. That requires, in this as in all other sciences, knowledge of the highly spe- cialized literature as well as extensive experience. Some geneticists therefore take the position that the general practitioner (or specialist in any other field of medicine) cannot possibly give proper genetic counsel to his patients. Because he is not a genetics expert, he should, without exception, refer all such cases to the geneticist. This point of view would condemn this guide as potentially more harmful than helpful in that it might increase the cases of well-meaning error as well as encouraging those who are not competent in this field to deal with problems which are beyond their capacity. We, obviously, do not share this pessimistic standpoint.

Science students have to spend much of their time learning how to do laboratory work, even if they intend to become theoretical, rather than experimental, scientists. It is important that they understand how experiments are performed and what the results mean. In science the validity of ideas is checked by experiments. If a new idea does not work in the laboratory, it must be discarded. If it does work, it is accepted, at least tentatively. In science, therefore, laboratory experiments are the touchstones for the acceptance or rejection of results. Mathematics is different. This is not to say that experiments are not part of the subject. Numerical calculations and the examina- tion of special and simplified cases are important in leading mathematicians to make conjectures, but the acceptance of a conjecture as a theorem only comes when a proof has been constructed. In other words, proofs are to mathematics as laboratory experiments are to science. Mathematics students must, therefore, learn to know what constitute valid proofs and how to construct them. How is this done? Like everything else, by doing. Mathematics students must try to prove results and then have their work criticized by experienced mathematicians. They must critically examine proofs, both correct and incorrect ones, and develop an appreciation of good style. They must, of course, start with easy proofs and build to more complicated ones.

Animal Physiologic Surgery presents an integrated approach to the study of surgery for first-year medical students and graduate students in physiology. The primary emphasis is on the interrela- tionships between surgical techniques and physiologic phenomena observed before, during, and after surgery. All procedures described in the book are designed so that the student with a limited knowledge of surgery can successfully assume responsibility for pre- and postoperative care, as well as for the operation. Therefore, the attitude reflected in this work shows the student his obligation, and his privilege, to find the best method of treatment for the patient and to work at his highest capacity. The text begins with an introduction to operating-room proce- dures, sutures and instruments, wound healing, anesthesia, and water and electrolyte balance. The second part deals with step-by- step surgical instructions and clinical consideration in techniques, such as laparotomy, splenectomy, nephrectomy, and laminectomy. This part is followed by a section on laboratory techniques neces- sary for following and evaluating the course of the patient and on postmortem techniques. The text strikes a balance between exacting detail and discussion of basic principles; it is easily adaptable to any curriculum. I am grateful to the contributors for their close cooperation, especially Dr. William J. White for sharing much of the responsi- bilities. I am also very appreciative to Catherine Jackson and Anne Kupstas for their valuable editorial assistance, and to Joyce Greene vii Preface and Becky Robertson for their assistance in preparing the manu- script.