丛书名：
AMS short course lecture notes;proceedings of symposia in appliedmathematics,,proceedings of symposia in appliedmathematics;proceedings of symposia in appliedmathematics.
Computational complexity theory is the study of the quantitative laws that govern computing. During the last 25 years, this field has grown into a rich mathematical theory. Currently one of the most active research ar...
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ISBN:
(纸本)9780821801314
Computational complexity theory is the study of the quantitative laws that govern computing. During the last 25 years, this field has grown into a rich mathematical theory. Currently one of the most active research areas in computer science, complexity theory is of considerable interest to mathematicians as well, since some of the key open problems in this field raise basic questions about the nature of mathematics. Many experts in complexity theory believe that, in coming decades, the strongest influence on the development of mathematics will come from the extended use of computing and from concepts and problems arising in computer science. This volume contains the proceedings of the AMS Short Course on Computational Complexity Theory, held at the Joint mathematics Meetings in Atlanta in January 1988. The purpose of the short course was to provide an overview of complexity theory and to describe some of the current developments in the field. The papers presented here represent contributions by some of the top experts in this burgeoning area of research.
These introductory survey lectures, the result of a 1984 AMS Short Course, focus on the algorithmic problems arising in the construction and utilization of large-scale information systems. Addressed to both mathematic...
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ISBN:
(纸本)9780821800867
These introductory survey lectures, the result of a 1984 AMS Short Course, focus on the algorithmic problems arising in the construction and utilization of large-scale information systems. Addressed to both mathematicians and computer scientists, the lectures require a background in the methodologies of discrete mathematics, in particular the elements of algebra, combinatorics and graph theory, discrete probability, logic and the theory of computation. All of the articles either are of high research value or survey profound themes in current research. They cover the two fundamental aspects of the field, i.e., database systems and communication networks. An overview of database architectures, the theory of data dependencies, and transaction management are provided, respectively, by the articles of Jacobs, Fagin and Vardi, and Garcia-Molina. Chung evaluates problems in the design of communication networks. Miller's discussion of data compression algorithms links current research to classical information theory. Finally, Tuzhilin describes a general framework evolved in the Soviet Union for modelling problems of information processing.
The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture ...
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ISBN:
(纸本)9780821800980
The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture describes and illustrates the basic concerns of the field. Topics highlighted in the other lectures include the following: approximation in the complex domain, \(N\)-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate setting for the last three topics. The book is aimed at mathematicians interested in an introduction to areas of current research and to engineers and scientists interested in exploring the field for possible applications to their own fields. The book is best understood by those with a standard first graduate course in real and complex analysis, but some of the presentations are accessible with the minimal requirements of advanced calculus and linear algebra.
These lecture notes from the 1985 AMS Short Course examine a variety of topics from the contemporary theory of actuarial mathematics. Recent clarification in the concepts of probability and statistics has laid a much ...
ISBN:
(纸本)0821800965;9780821800966;3619844895
These lecture notes from the 1985 AMS Short Course examine a variety of topics from the contemporary theory of actuarial mathematics. Recent clarification in the concepts of probability and statistics has laid a much richer foundation for this theory. Other factors that have shaped the theory include the continuing advances in computer science, the flourishing mathematical theory of risk, developments in stochastic processes, and recent growth in the theory of finance. In turn, actuarial concepts have been applied to other areas such as biostatistics, demography, economic, and reliability engineering.
The lecture notes contained in this volume were presented at the AMS Short Course on Population Biology, held August 6–7, 1983, in Albany, New York in conjunction with the summer meeting of the American Mathematical ...
ISBN:
(纸本)9780821800836
The lecture notes contained in this volume were presented at the AMS Short Course on Population Biology, held August 6–7, 1983, in Albany, New York in conjunction with the summer meeting of the American Mathematical Society. These notes will acquaint the reader with the mathematical ideas that pervade almost every level of thinking in population biology and provide an introduction to the many applications of mathematics in the field. Research mathematicians, college teachers of mathematics, and graduate students all should find this book of interest. Population biology is probably the oldest area in mathematical biology, but remains a constant source of new mathematical problems and the area of biology best integrated with mathematical theory. The need for mathematical approaches has never been greater, as evolutionary theory is challenged by new interpretations of the paleontological record and new discoveries at the molecular level, as world resources for feeding populations become limiting, as the problems of pollution increase, and as both animal and plant epidemiological problems receive closer scrutiny. A background of advanced calculus, introduction to ordinary and partial differential equations, and linear algebra will make the book accessible. All of the papers included have high research value. A list of the contents follows.
This collection of six papers provides a valuable source of material on the real-world problem of allocating objects among competing claimants. The examples given show how mathematics, particularly the axiomatic metho...
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ISBN:
(纸本)0821800949;9780821800942;1519741952
This collection of six papers provides a valuable source of material on the real-world problem of allocating objects among competing claimants. The examples given show how mathematics, particularly the axiomatic method, can be applied to give insight into complex social problems. Originally presented as an AMS Short Course, these papers could serve as a suitable text for courses touching on game theory, decision sciences, economics, or quantitative political science. Most of the material is accessible to the mathematically mature undergraduate with a background in advanced calculus and algebra. Each article surveys the recent literature and includes statements and sketches of proofs, as well as unsolved problems which should excite student curiosity. The articles analyze the question of fair allocation via six examples: the apportionment of political representation, the measurement of income inequality, the allocation of joint costs, the levying of taxes, the design of voting laws, and the framing of auction procedures. In each of these examples fairness has a somewhat different significance, but common axiomatic threads reveal broad underlying principles. Each of the topics is concerned with norms of comparative equity for evaluating allocations or with standards of procedures for effecting them; it is this focus on normative properties which suggests that a mathematical analysis is appropriate. Though game theory provides a useful tool in many of these allocation problems, the emphasis here is on standards rather than strategy and equity rather than rationality, an approach which more accurately mirrors real-world social problems.
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