Discrete mathematics is a compulsory subject for undergraduate computer scientists. This new edition includes new chapters on statements and proof, logical framework, natural numbers and the integers and updated exercises from the previous edition.

Mathematics did not spring spontaneously into life, with rules set in stone for all time. Its story is closely linked with the problems of measurement and money that have often driven its progress. Quite Right explains how mathematical ideas have gradually emerged since prehistoric times, so that they pervade almost every aspect of life in the twenty-first century. Many histories of mathematics focus on the activities of those for whom mathematics itself was the motivation. Professor Biggs adopts a wider viewpoint. Making use of new discoveries of artefacts and documents, he explains the part that mathematics has played in the human story, and what that tells us about the nature of mathematics. The story reveals the power and beauty of mathematical concepts, which often belie their utilitarian origins. The twin paradigms of logical justification and algorithmic calculation recur throughout the book. No other book tells the story of mathematics, measurement, and money in this way. Includes secontions on: -- The origins of calculation in ancient and medieval times -- How mathematics provides answers that are right, and what that means -- The impact of trade and the use of money on the development of mathematical algorithms -- The use of mathematics for secure communications -- How money and information are linked in our electronic world Quite Right is a fascinating story, suitable for anyone interested in the mathematical foundations of the world we live in. Norman Biggs is Professor (Emeritus) of Mathematics at the London School of Economics. He is the author of 12 books, including a perennial best-selling book Discrete Mathematics (Oxford University Press). He has a special interest in measurement and was Chair of the International Society of Weights and Scales Collectors from 2009-14. He served as a Vice President of the British Society for the History of Mathematics in 2014 and is an active member of the British Numismatic Society. 'This is a history of mathematics book with a difference. Instead of the usual chronological sequence of events, presented with mathematical hindsight (interpreting mathematical achievements from a modern point of view), this book tries to see things more from the context of the time - presenting the topics thematically rather than strictly chronologically, and including results and problems only when they fit into the themes ... the level of exposition is first-rate, with a far greater fluency than most mathematical writers can attain ... I am very happy to recommend it wholeheartedly.' Professor Robin Wilson, University of Oxford

First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historical development of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students. From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics, when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Biggs, Lloyd and Wilson's unusual and remarkable book traces the evolution and development of graph theory...Conceived in a very original manner and obviously written with devotion and a very great amount of painstaking historical research, it contains an exceptionally fine collection of source material, and to a graph theorist it is a treasure chest of fascinating historical information and curiosities with rich food for thought.' (Gabriel Dirac in Centaurus) 'The lucidity, grace and wit of the writing makes this book a pleasure to read and re-read.' (S. H. Hollingdale in Bulletin of the Institute of Mathematics and its Applications)

This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.

Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.

The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.

This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.