Norman Linstead Biggs (born 2 January 1941) is a leading British mathematician focusing on

discrete mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...

and in particular

algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algeb ...

Education

Biggs was educated at

Harrow County Grammar School Harrow County Grammar School may refer to one of two schools closed in 1975: *Harrow County School for Boys, a grammar school now an academy called Harrow High School *Harrow County School for Girls, a grammar school no longer in existence {{set ...

and then studied mathematics at

Selwyn College, Cambridge Selwyn College, Cambridge is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. The college was founded in 1882 by the Selwyn Memorial Committee in memory of George Selwyn (bishop of Lichfield), Georg ...

. In 1962, Biggs gained first-class honours in his third year of the university's undergraduate degree in mathematics. *1946–1952: Uxendon Manor Primary School, Kenton, Middlesex *1952–1959:

*1959–1963:

(Entrance Exhibition 1959, Scholarship 1961) *1960: First Class, Mathematical Tripos Pt. I *1962: Wrangler, Mathematical Tripos Pt. II; B.A. (Cantab.) *1963: Distinction, Mathematical Tripos Pt. III *1988: D.Sc. (London); M.A. (Cantab.)

Career

He was a lecturer at

University of Southampton The University of Southampton (abbreviated as ''Soton'' in post-nominal letters) is a public university, public research university in Southampton, England. Southampton is a founding member of the Russell Group of research-intensive universit ...

, lecturer then reader at

Royal Holloway, University of London Royal Holloway, University of London (RH), formally incorporated as Royal Holloway and Bedford New College, is a public university, public research university and a constituent college, member institution of the federal University of London. It ...

, and Professor of Mathematics at the

London School of Economics The London School of Economics and Political Science (LSE), established in 1895, is a public research university in London, England, and a member institution of the University of London. The school specialises in the social sciences. Founded ...

. He has been on the

editorial board The editorial board is a group of editors, writers, and other people who are charged with implementing a publication's approach to editorials and other opinion pieces. The editorials published normally represent the views or goals of the publicat ...

of a number of journals, including the ''

Journal of Algebraic Combinatorics ''Journal of Algebraic Combinatorics'' is a peer-reviewed scientific journal covering algebraic combinatorics. It was established in 1992 and is published by Springer Science+Business Media. The editor-in-chief is Ilias S. Kotsireas (Wilfrid Lauri ...

''. He has been a member of the Council of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

. He has written 12 books and over 100 papers on mathematical topics, many of them in

and its applications. He became

Emeritus Professor ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

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.

Family

Biggs married Christine Mary Farmer in 1975 and has one daughter Clare Juliet born in 1980.

Interests and Hobbies

Biggs' interests include

computational learning theory In computer science, computational learning theory (or just learning theory) is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms. Overview Theoretical results in machine learning m ...

, the

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the History of mathematical notation, mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples ...

and historical

metrology Metrology is the scientific study of measurement. It establishes a common understanding of Unit of measurement, units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to stan ...

. Since 2006, he has been an

emeritus professor ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

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 The British Numismatic Society exists to promote the study and understanding of British numismatics. The Society was founded in 1903, focusing on all forms of coinage, tokens, banknotes and medals relating to the British Isles and former parts ...

Work

Mathematics

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 In mathematics and computer science, an algorithm () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for per ...

and

Graphs Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties * Graph (topology), a topological space resembling a graph in the sense of discre ...

, 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 Finite number may refer to: * Natural number, a countable number less than infinity, being the cardinality of a finite set * Real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional qua ...

of steps rather than limiting processes. The second edition added nine new introductory chapters; Fundamental language of mathematicians,

statements Statement or statements may refer to: Common uses *Statement (computer science), the smallest standalone element of an imperative programming language * Statement (logic and semantics), declarative sentence that is either true or false *Statement, ...

and proofs, the logical framework, sets and functions, and

number system A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...

. This book stresses the significance of simple

logical reasoning Logical reasoning is a mind, mental Action (philosophy), activity that aims to arrive at a Logical consequence, conclusion in a Rigour, rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reason ...

, shown by the exercises and examples given in the book. Each chapter contains modelled solutions, examples, exercises including hints and answers.

Algebraic Graph Theory

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 Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

and

matrix theory In mathematics, a matrix (: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. ...

; algebraic constructions such as

adjacency matrix In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph (discrete mathematics), graph. The elements of the matrix (mathematics), matrix indicate whether pairs of Vertex (graph theory), vertices ...

and the

incidence matrix In mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation. If the first class is ''X'' and the second is ''Y'', the matrix has one row for each element o ...

and their applications are discussed in depth. Next, there is a wide-ranging description of the theory of chromatic

polynomials In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative int ...

. The last section discusses

symmetry Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant und ...

and regularity properties. Biggs makes important connections with other branches of

and

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

Computational Learning Theory

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 Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

, and complex theory. This book is an introduction to computational learning.

History of Mathematics

Biggs contributed to thirteen journals and books developing topics such as the four-colour conjecture, the roots/history of

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

, Topology on the 19th century, and mathematicians. In addition, Biggs examined the ideas of

William Ludlam William Ludlam (1717–1788) was an English clergyman and mathematician. Life Born at Leicester, he was elder son of the physician Richard Ludlam (1680–1728), who practised there; Thomas Ludlam, the clergyman, was his youngest brother. (His so ...

Thomas Harriot Thomas Harriot (; – 2 July 1621), also spelled Harriott, Hariot or Heriot, was an English astronomer, mathematician, ethnographer and translator to whom the theory of refraction is attributed. Thomas Harriot was also recognized for his con ...

John Arbuthnot John Arbuthnot FRS (''baptised'' 29 April 1667 – 27 February 1735), often known simply as Dr Arbuthnot, was a Scottish physician, satirist and polymath in London. He is best remembered for his contributions to mathematics, his membership ...

, and

Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

Chip-Firing Game

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 mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commu ...

. In addition, the order of the

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ...

is equal to the

tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only ...

number of the

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discret ...

Publications

Summary of Biggs' published Books on Mathematics

*''Finite Groups of Automorphisms'', Cambridge University Press (1971) *''Algebraic Graph Theory'', Cambridge University Press (1974) *''

Graph Theory, 1736–1936 ''Graph Theory, 1736–1936'' is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the ...

'' (with E.K. Lloyd and R.J. Wilson), Oxford University Press (1976) (Japanese edition 1986) *''Interaction Models'', Cambridge University Press (1977) *''Permutation Groups and Combinatorial Structures'' (with A.T. White), Cambridge University Press, (1979), (Chinese edition 1988) *''Discrete Mathematics'', Oxford University Press (1989) (Spanish edition 1994) *''Introduction to Computing with Pascal'', Oxford University Press (1989) *''Computational Learning Theory: an Introduction'' (with M. Anthony) (1997)
''Algebraic Graph Theory''
(Second Edition), Cambridge University Press (1993) *''Mathematics for Economics and Finance'' (with M. Anthony), Cambridge University Press (1996) (Chinese edition 1998; Japanese edition 2000) *''Discrete Mathematics'', (Second Edition), Oxford University Press (2002) *''Codes: An Introduction to Information Communication and Cryptography'', Springer Verlag (2008)

Summary of Biggs' latest published Papers on Mathematics

2000 *'A matrix method for chromatic polynomials – II', ''CDAM Research Report Series'', LSE-CDAM 2000–04, April 2000. *(with P.Reinfeld), 'The chromatic roots of generalised dodecahedra', ''CDAM Research Report Series'', LSE-CDAM 2000–07, June 2000. 2001 *'Equimodular curves for reducible matrices', ''CDAM Research Report Series'', LSE-CDAM 2001–01, January 2001. *'A matrix method for chromatic polynomials', ''Journal of Combinatorial Theory, Series B'', 82 (2001) 19–29. 2002 *'Chromatic polynomials for twisted bracelets', ''Bull. London Math. Soc.'' 34 (2002) 129–139. *'Chromatic polynomials and representations of the symmetric group', ''Linear Algebra and its Applications'' 356 (2002) 3–26. *'Equimodular curves', ''Discrete Mathematics'' 259 (2002) 37–57. 2004 *'Algebraic methods for chromatic polynomials' (with M H Klin and P Reinfeld), ''Europ. J. Combinatorics'' 25 (2004) 147–160. *'Specht modules and chromatic polynomials', ''Journal of Combinatorial Theory, Series B'' 92 (2004) 359 – 377. 2005 *'Chromatic polynomials of some families of graphs I: Theorems and Conjectures', ''CDAM Research Report Series'', LSE-CDAM 2005–09, May 2005. 2007 *'The critical group from a cryptographic perspective', ''Bull. London Math. Soc.'', 39 (2007) 829–836. 2008 *'Chromatic Roots of the Quartic Mobius Ladders', ''CDAM Research Report'' LSE-CDAM 2008–05, May 2008. *'A Matrix Method for Flow Polynomials', ''CDAM Research Report'' LSE-CDAM 2008–08, June 2008. 2009 *'Tutte Polynomials of Bracelets', ''CDAM Research Report'' LSE-CDAM-2009-01, January 2009. *'Strongly Regular Graphs with No Triangles', ''Research Report'', September 2009. arXiv:0911.2160v1 *'Families of Parameters for SRNT Graphs', ''Research Report'', October 2009. arXiv:0911.2455v1 2010 *'Tutte Polynomials of Bracelets', ''J. Algebraic Combinatorics'' 32 (2010) 389–398. *'The Second Subconstituent of some Strongly Regular Graphs', ''Research Report'', February 2010. arXiv:1003.0175v1 2011 *'Some Properties of Strongly Regular Graphs', ''Research Report'', May 2011. arXiv:1106.0889v1 For other published work on the history of mathematics, please see.

References

External links

*Norman Biggs personal web page at LSE *
Cambridge University Press: Norman L Biggs
{{DEFAULTSORT:Biggs, Norman L. 1941 births Living people People educated at Harrow High School Alumni of Selwyn College, Cambridge 20th-century English mathematicians 21st-century English mathematicians Algebraists British historians of mathematics British theoretical computer scientists Academics of the University of Southampton Academics of Royal Holloway, University of London Academics of the London School of Economics Alumni of the University of London