Many well-known models in the natural sciences and engineering, and today even in economics, depend on partial di?erential equations. Thus the e?cient numerical solution of such equations plays an ever-increasing role in state-- the-art technology. This demand and the computational power available from current computer hardware have together stimulated the rapid development of numerical methods for partial di?erential equations--a development that encompasses convergence analyses and implementational aspects of software packages. In 1988 we started work on the ?rst German edition of our book,...
Many well-known models in the natural sciences and engineering, and today even in economics, depend on partial di?erential equations. Thus the e?cient...
Error-correcting codes have been incorporated in numerous working communication and memory systems. This book covers the mathematical aspects of the theory of block error-correcting codes together, in mutual reinforcement, with computational discussions, implementations and examples of all relevant concepts, functions and algorithms. This combined approach facilitates the reading and understanding of the subject.
The digital companion of the book is a non-printable .pdf document with hyperlinks. The examples included in the book can be run with just a mouse click and modified and...
Error-correcting codes have been incorporated in numerous working communication and memory systems. This book covers the mathematical aspects of th...
The two-volume textbook Comprehensive Mathematics for the Working Computer Scientist, of which this is the second volume, is a self-contained comprehensive presentation of mathematics including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. The concept framework is streamlined but defining and proving virtually everything. The style implicitly follows the spirit of recent topos-oriented theoretical computer science....
The two-volume textbook Comprehensive Mathematics for the Working Computer Scientist, of which this is the second volume, is a self-contained compr...
An entire generation of mathematicians has grown up during the time - tween the appearance of the ?rst edition of this textbook and the publication of the fourth edition, a translation of which is before you. The book is fam- iar to many people, who either attended the lectures on which it is based or studied out of it, and who now teach others in universities all over the world. I am glad that it has become accessible to English-speaking readers. This textbook consists of two parts. It is aimed primarily at university students and teachers specializing in mathematics and natural sciences,...
An entire generation of mathematicians has grown up during the time - tween the appearance of the ?rst edition of this textbook and the publication of...
This book is addressed to all those - logicians, computer scientists, mathe- maticians, philosophers of science as well as the students in all these disci- plines - who may be interested in the development and current status of one of the major themes of mathematical logic in the twentieth century, namely the classical decision problem known also as Hilbert's Entscheidungsproblem. The text provides a comprehensive modern treatment of the subject, includ- ing complexity theoretic analysis. We have made an effort to combine the features of a research monograph and a textbook. Only the basic...
This book is addressed to all those - logicians, computer scientists, mathe- maticians, philosophers of science as well as the students in all these d...
This unusual book, richly illustrated with 19 colour platesand about 250 line drawings, explores the relationshipbetween classical tessellations and3-manifolds. In hisoriginal entertaining style with numerous exercises andproblems, the author provides graduate students with asource of geomerical insight to low-dimensional topology, while researchers in this field will find here an account ofa theory that is on the one hand known tothem but here ispresented in a very different framework.
This unusual book, richly illustrated with 19 colour platesand about 250 line drawings, explores the relationshipbetween classical tessellations and3-...
The notion of an order plays an important role DEGREES not only throughout mat- maticsbutalsoinadjacentdisciplinessuchaslogicandcomputerscience. The purpose of the present text is to provide a basic introduction to the theory of ordered structures. Taken as a whole, the material is mainly designed for a postgraduate course. However, since prerequisites are minimal, selected parts of it may easily be considered suitable to broaden the horizon of the advanced undergraduate. Indeed, this has been the author's practice over many years. A basic tool in analysis is the notion of a continuous...
The notion of an order plays an important role DEGREES not only throughout mat- maticsbutalsoinadjacentdisciplinessuchaslogicandcomputerscience. The p...
Hypothesis formation is known as one of the branches of Artificial Intelligence, The general question of Artificial IntelligencE' ,"Can computers think?" is specified to the question ,"Can computers formulate and justify hypotheses?" Various attempts have been made to answer the latter question positively. The present book is one such attempt. Our aim is not to formalize and mechanize the whole domain of inductive reasoning. Our ultimate question is: Can computers formulate and justify scientific hypotheses? Can they comprehend empirical data and process them rationally, using the apparatus...
Hypothesis formation is known as one of the branches of Artificial Intelligence, The general question of Artificial IntelligencE' ,"Can computers thin...
The text of this book is derived from courses taught by the author in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook. The audience for these courses was composed almost entirely of fourth year undergraduate students majoring in the mathematical sciences. The students had ordinarily completed four semesters of calculus and one of probability. Few had any prior experience with differential equations, stochastic processes, or epidemiology. It also seems prudent to mention that the author's background is in engineering and applied...
The text of this book is derived from courses taught by the author in the Department of Applied Mathematics and Statistics at the State University of ...
During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This book deals with one part of this development, and has two aims. The first is to give a comprehensive account of the close connection between analytic and probabilistic potential theory with the notion of a balayage space appearing as a natural link. The second aim is to demonstrate the fundamental importance of this concept by using it to give a straight presentation of balayage theory which in turn is then applied to the Dirichlet problem. We...
During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This bo...
