Norman Linstead Biggs (born 2 January 1941) is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics. [1]
Biggs was educated at Harrow County Grammar School and then studied mathematics at Selwyn College, Cambridge. In 1962, Biggs gained first-class honours in his third year of the university's undergraduate degree in mathematics. [2]
He was a lecturer at University of Southampton, lecturer then reader at Royal Holloway, University of London, and Professor of Mathematics at the London School of Economics. He has been on the editorial board of a number of journals, including the Journal of Algebraic Combinatorics . He has been a member of the Council of the London Mathematical Society.
He has written 12 books and over 100 papers on mathematical topics, many of them in algebraic combinatorics and its applications. He became Emeritus Professor in 2006 and continues to teach History of Mathematics in Finance and Economics for undergraduates. He is also vice-president of the British Society for the History of Mathematics.
Biggs married Christine Mary Farmer in 1975 and has one daughter Clare Juliet born in 1980.
Biggs' interests include computational learning theory, the history of mathematics and historical metrology. Since 2006, he has been an emeritus professor at the London School of Economics.
Biggs hobbies consist of writing about the history of weights and scales. He currently holds the position of Chair of the International Society of Antique Scale Collectors (Europe), and a member of the British Numismatic Society.
In 2002, Biggs wrote the second edition of Discrete Mathematics breaking down a wide range of topics into a clear and organised style. Biggs organised the book into four major sections; The Language of Mathematics, Techniques, Algorithms and Graphs, and Algebraic Methods. This book was an accumulation of Discrete Mathematics, first edition, textbook published in 1985 which dealt with calculations involving a finite number of steps rather than limiting processes. The second edition added nine new introductory chapters; Fundamental language of mathematicians, statements and proofs, the logical framework, sets and functions, and number system. This book stresses the significance of simple logical reasoning, shown by the exercises and examples given in the book. Each chapter contains modelled solutions, examples, exercises including hints and answers. [3]
In 1974, Biggs published Algebraic Graph Theory which articulates properties of graphs in algebraic terms, then works out theorems regarding them. In the first section, he tackles the applications of linear algebra and matrix theory; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. Next, there is and wide-ranging description of the theory of chromatic polynomials. The last section discusses symmetry and regularity properties. Biggs makes important connections with other branches of algebraic combinatorics and group theory. [4]
In 1997, N. Biggs and M. Anthony wrote a book titled Computational Learning Theory: an Introduction. Both Biggs and Anthony focused on the necessary background material from logic, probability, and complex theory. This book is an introduction to computational learning.
Biggs contributed to thirteen journals and books developing topics such as the four-colour conjecture, the roots/history of combinatorics, calculus, Topology on the 19th century, and mathematicians. [5] In addition, Biggs examined the ideas of William Ludlam, Thomas Harriot, John Arbuthnot, and Leonhard Euler. [6]
The chip-firing game has been around for less than 20 years. It has become an important part of the study of structural combinatorics. The set of configurations that are stable and recurrent for this game can be given the structure of an abelian group. In addition, the order of the group is equal to the tree number of the graph. [7] [8]
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For other published work on the history of mathematics, please see. [11]
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
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Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
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The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to study the four color problem. It was generalised to the Tutte polynomial by Hassler Whitney and W. T. Tutte, linking it to the Potts model of statistical physics.
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants.
Herbert Saul Wilf was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania. He wrote numerous books and research papers. Together with Neil Calkin he founded The Electronic Journal of Combinatorics in 1994 and was its editor-in-chief until 2001.
The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role in graph theory. It is defined for every undirected graph and contains information about how the graph is connected. It is denoted by .
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and D. H. Smith.
Jacobus Hendricus ("Jack") van Lint was a Dutch mathematician, professor at the Eindhoven University of Technology, of which he was rector magnificus from 1991 till 1996.
Ronald Cedric Read was a British mathematician, latterly a professor emeritus of mathematics at the University of Waterloo, Canada. He published many books and papers, primarily on enumeration of graphs, graph isomorphism, chromatic polynomials, and particularly, the use of computers in graph-theoretical research. A majority of his later work was done in Waterloo. Read received his Ph.D. (1959) in graph theory from the University of London.
Herbert John Ryser was a professor of mathematics, widely regarded as one of the major figures in combinatorics in the 20th century. He is the namesake of the Bruck–Ryser–Chowla theorem, Ryser's formula for the computation of the permanent of a matrix, and Ryser's conjecture.
Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West.
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David Ronald Wood is a Professor in the School of Mathematics at Monash University in Melbourne, Australia. His research area is discrete mathematics and theoretical computer science, especially structural graph theory, extremal graph theory, geometric graph theory, graph colouring, graph drawing, and combinatorial geometry.
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