The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas...
The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the ...
This text is based on a course given at the Mathematical Institute in Oxford over many years to final-year mathematics students. Chapters include: 'Newtonian Gravity', 'Curved Space-Time', 'Tensor Calculus', 'Spherical Symmetry', 'Black Holes', 'Rotating Bodies' and 'Gravitational Waves'.
This text is based on a course given at the Mathematical Institute in Oxford over many years to final-year mathematics students. Chapters include: 'Ne...
This book has been primarily written for the student of mathematics who is in the second year or the early part of the third year of an undergraduate course. It will also be very useful for students of engineering and the physical sciences for whom Laplace Transforms continue to be an extremely useful tool. The book demands no more than an elementary knowledge of calculus and linear algebra of the type found in many first year mathematics modules for applied subjects. For mathematics majors and specialists, it is not the mathematics that will be challenging but the applications to the real...
This book has been primarily written for the student of mathematics who is in the second year or the early part of the third year of an undergraduate ...
Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as...
Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph ...
As this Preface is being written, the twentieth century is coming to an end. Historians may perhaps come to refer to it as the century of information, just as its predecessor is associated with the process of industrialisation. Successive technological developments such as the telephone, radio, television, computers and the Internet have had profound effects on the way we live. We can see pic tures of the surface of Mars or the early shape of the Universe. The contents of a whole shelf-load of library books can be compressed onto an almost weight less piece of plastic. Billions of people can...
As this Preface is being written, the twentieth century is coming to an end. Historians may perhaps come to refer to it as the century of information,...
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the...
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More e...
The development of the di?erential calculus was one of the major achievements of seventeenth century European mathematics, originating in the work of N- ton, Leibniz and others. Integral calculus can be traced back to the work of Archimedes in the third century B. C. Since its inception, calculus has dev- oped in two main directions. One is the growth of applications and associated techniques, indiverse?eldssuchasphysics, engineering, economics, probability and biology. The other direction is that of analytical foundations, where the intuitive and largely geometrical approach is replaced by...
The development of the di?erential calculus was one of the major achievements of seventeenth century European mathematics, originating in the work of ...
This book is an introduction to game theory from a mathematical perspective. It is intended to be a ?rst course for undergraduate students of mathematics, but I also hope that it will contain something of interest to advanced students or researchers in biology and economics who often encounter the basics of game theory informally via relevant applications. In view of the intended audience, the examples used in this book are generally abstract problems so that the reader is not forced to learn a great deal of a subject either biology or e- nomics that may be unfamiliar. Where a context is...
This book is an introduction to game theory from a mathematical perspective. It is intended to be a ?rst course for undergraduate students of mathemat...
Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential.
"Regression: Linear Models in Statistics" fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions.
The book begins with simple linear...
Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor varia...
