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Elements of Large-Sample Theory provides a unified treatment of first- order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level and is suitable for students at the master's level in statistics and in aplied fields who have a background of two years of calculus.E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. Also available: Lehmann/Casella, Theory at Point Estimation, 2nd ed. Springer-Verlag New York, Inc., 1998, ISBN 0- 387-98502-6Lehmann, Testing Statistical Hypotheses, 2nd ed. Springer-Verlag New York, Inc., 1997, ISBN 0-387-94919-4

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom- mend to anyone to look through them. More recent texts have empha- sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal- ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.

We now apply the algorithm above to find the 121 orbits of norm -2 vectors from the (known) nann 0 vectors, and then apply it again to find the 665 orbits of nann -4 vectors from the vectors of nann 0 and -2. The neighbors of a strictly 24 dimensional odd unimodular lattice can be found as follows. If a norm -4 vector v E II . corresponds to the sum 25 1 of a strictly 24 dimensional odd unimodular lattice A and a !-dimensional lattice, then there are exactly two nonn-0 vectors of ll25,1 having inner product -2 with v, and these nann 0 vectors correspond to the two even neighbors of A. The enumeration of the odd 24-dimensional lattices. Figure 17.1 shows the neighborhood graph for the Niemeier lattices, which has a node for each Niemeier lattice. If A and B are neighboring Niemeier lattices, there are three integral lattices containing A n B, namely A, B, and an odd unimodular lattice C (cf. [Kne4]). An edge is drawn between nodes A and B in Fig. 17.1 for each strictly 24-dimensional unimodular lattice arising in this way. Thus there is a one-to-one correspondence between the strictly 24-dimensional odd unimodular lattices and the edges of our neighborhood graph. The 156 lattices are shown in Table 17 .I. Figure I 7. I also shows the corresponding graphs for dimensions 8 and 16.

This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners.

The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven- tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.

The initial ideas behind this edited volume started in spring of 1998 - some two years before the sixtieth birthday of Bernard P. Zeigler. The idea was to bring together distinguished researchers, colleagues, and former students of Professor Zeigler to present their latest findings at the AIS' 2000 conference. During the spring of 1999, the initial ideas evolved into creating a volume of articles surrounding seminal concepts pertaining to modeling and simulation as proposed, developed, and advocated by Professor Zeigler throughout his scientific career. Also included would be articles describing progress covering related aspects of software engineering and artificial intelligence. As this volume is emphasizing concepts and ideas spawned by the work of Bernard P. Zeigler, it is most appropriate to offer a biographical sketch of his scientific life, thus putting into a historical perspective the contributions presented in this volume as well as new research directions that may lie ahead! Bernard P. Zeigler was born March 5, 1940, in Montreal, Quebec, Canada, where he obtained his bachelor's degree in engineering physics in 1962 from McGill University. Two years later, having completed his MS degree in electrical engineering at the Massachusetts Institute of Technology, he spent a year at the National Research Council in Ottawa. Returning to academia, he became a Ph. D. student in computer and communication sciences at the University of Michigan, Ann Arbor.

[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "e;unnecessary"e; and "e;obvious"e; steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.

We will occasionally footnote a portion of text with a "e;**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "e;their own"e; by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per- sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative.

This text started out as a revised version of Buildings by the second-named author [53], but it has grown into a much more voluminous book. The earlier bookwasintendedtogiveashort,friendly,elementaryintroductiontothet- ory,accessibletoreaderswithaminimalbackground.Moreover,itapproached buildings from only one point of view, sometimes called the "e;old-fashioned"e; approach: A building is a simplicial complex with certain properties. The current book includes all the material of the earlier one, but we have added a lot. In particular, we have included the "e;modern"e; (or "e;W-metric"e;) approach to buildings, which looks quite di?erent from the old-fashioned - proach but is equivalent to it. This has become increasingly important in the theory and applications of buildings. We have also added a thorough tre- ment of the Moufang property, which occupies two chapters. And we have added many new exercises and illustrations. Some of the exercises have hints or solutions in the back of the book. A more extensive set of solutions is ava- able in a separate solutions manual, which may be obtained from Springer's Mathematics Editorial Department. We have tried to add the new material in such a way that readers who are content with the old-fashioned approach can still get an elementary treatment of it by reading selected chapters or sections. In particular, many readers will want to omit the optional sections (marked with a star). The introduction below provides more detailed guidance to the reader.

Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms.This volume reflects the workshop "e;Software for Algebraic Geometry"e; held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.

The rapid and impressive results obtained through the application of numerical methods of analysis to electrodynamics created the rather false impression (es- cially to inexperienced engineers) that all problems were solved long ago or that some of them were not solved because one lacked suf?cient time. However, it is suf?cient to formulate these problems clearly, to give the task to a programmer to create the corresponding program, and to let a computer "e;think. "e; It is only left for an engineer to make the corresponding plots and to explain calculation results if the latter do not agree with existing physical notions. However, de?nite conf- mity to natural laws starts inevitably to appear while realizing this sequence of steps: the problem is prepared for calculations more thoroughly-the probability to obtain the correct answer is higher, and the obtained information is richer and more interesting-the calculated algorithm is simpler; and as expenditure of calculation time is less, correspondingly, the problems to solve effectively are more complex. Theproblemformulationisnotonlycompilationofinitialequationsandanumerical algorithm. It is necessary to foresee a qualitative character of the obtained results and expected order of values, to reveal the peculiarities of the searched solution, complicating its numerical realization and, as a result, choosing the known solution algorithm or working out a new one. If this work has not been done properly, then unexpected anomalies may appear during the numerical calculation process, and the results can be the basis for the most sensational "e;discoveries.

The Paris Meridian is the name of the line running north-south through the astronomical observatory in Paris. One of the original intentions behind the founding of the Paris Observatory was to determine and measure this line. The French government financed the Paris Academy of Sciences to do so in the seventeenth to nineteenth centuries. It employed both astronomers - people who study and measure the stars - and geodesists - people who study and measure the Earth. This book is about what they did and why.This is the first English language presentation of this historical material. It is attractively written and it features the story of the community of scientists who created the Paris Meridian. They knew each other well - some were members of the same families, in one case of four generations. Like scientists everywhere they collaborated and formed alliances; they also split into warring factions and squabbled. They travelled to foreign countries, somehow transcending the national and political disputes, as scientists do now, their eyes fixed on ideas of accuracy, truth and objective, all enduring values - yet when the reception given to their own work was concerned some became blind to high ideals and descended into petty politics.To establish the Paris Meridian, the scientists endured hardship, survived danger, and gloried in amazing adventures during a time of turmoil in Europe consisting of the French Revolution and the Napoleonic War between France and Spain. Some were accused of witchcraft. Some of their associates lost their heads on the guillotine. Some died of disease. Some won honor and fame. One became the Head of State in France. Some found dangerous love in foreign countries. One scientist was killed in self defence when attacked by a jealous lover, another was himself killed by a jealous lover, a third brought back a woman to France and then jilted her, whereupon she joined a convent... The scientists worked on practical problems of interest to the government and to the people. They also worked on one of the most important intellectual problems of the time, a problem of great interest to their fellow scientists all over the world- the theory of universal gravitation. They succeeded in their intellectual work while affecting politics and the affairs of state; their endeavours have left marks on the landscape, in art, and in literature still visible today.

This book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the linear algebra from the other basic algebraic structures fits all existing tendencies affecting undergraduate teaching, and I agree with these tendencies. I have made the present book self contained logically, but it is probably better if students take the linear algebra course before being introduced to the more abstract notions of groups, rings, and fields, and the systematic development of their basic abstract properties. There is of course a little overlap with the book Lin- ear Algebra, since I wanted to make the present book self contained. I define vector spaces, matrices, and linear maps and prove their basic properties. The present book could be used for a one-term course, or a year's course, possibly combining it with Linear Algebra. I think it is important to do the field theory and the Galois theory, more important, say, than to do much more group theory than we have done here. There is a chapter on finite fields, which exhibit both features from general field theory, and special features due to characteristic p. Such fields have become important in coding theory.

The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book is Modern in that is contains more recent topics such as function spaces, atomic decompositions, singular integrals of nonconvolution type, and weighted inequalities. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables, and knowledge of classical Fourier analysis topics. This book is intended to present the selected topics in depth and stimulate further study. This third edition includes a new chapter entitled "e;Multilinear Harmonic Analysis"e;, which includes sections on multilinear operators, multilinear interpolation, multilinear multiplier operators, Calderon-Zygmund operators of several functions, and multiple weights and weighted norm inequalities. The new chapter will tie nicely with the material in chapters 8, 9, and 10, and the author may add a new section in this chapter applying the techniques of chapter 11 in the context of multilinear harmonic analysis. In addition to a new chapter, the third edition contains 1000 different corrections and improvements in the existing text, more examples and applications, new and more relevant hints for the existing exercises, about 20-30 new exercises in the existing chapters, and improved references.

The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book contains the classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood-Paley theory. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables. This book is intended to present the selected topics in depth and stimulate further study. This third edition includes a new chapter entitled "e;Topics on Fourier series,"e; which includes sections on Gibbs phenomenon, summability methods and Jackson's theorem, Tauberian theorems, spherical Fourier inversion, and Fourier transforms on the line. The new chapter ties really well with the material in the existing chapter 3 "e;Fourier Analysis on the Torus"e; and will prepare the students for (the existing) chapter 4. In addition to a new chapter, the third edition contains 1000 different corrections and improvements in the existing text, more examples and applications, new and more relevant hints for the existing exercises, about 20-30 new exercises in the existing chapters, and improved references.