School of Mathematics, University of Manchester
Encyclopedia
University of Manchester
The University of Manchester is a public research university located in Manchester, United Kingdom. It is a "red brick" university and a member of the Russell Group of research-intensive British universities and the N8 Group...
is one of the largest
mathematics departments in the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
, with around 80 academic staff and an undergraduate intake of roughly 400 a year (including students studying mathematics with a minor in another subject) and another 200 postgraduate students. The school was formed in 2004 by the merger of the mathematics departments of University of Manchester Institute of Science and Technology (UMIST) and the Victoria University of Manchester
Victoria University of Manchester
The Victoria University of Manchester was a university in Manchester, England. On 1 October 2004 it merged with the University of Manchester Institute of Science and Technology to form a new entity, "The University of Manchester".-1851 - 1951:The University was founded in 1851 as Owens College,...
(VUM). In July 2007 the school moved into a purpose-designed building – the first three floors of the Alan Turing Building
Alan Turing Building
The Alan Turing Building, named after the mathematician and founder of computer science Alan Turing, is a building at the University of Manchester, in Manchester, England. It houses the School of Mathematics, the Photon Science Institute and the Jodrell Bank Centre for Astrophysics...
– on Upper Brook Street.
Organization
Nicholas Higham
Nicholas John Higham FRS is a numerical analyst and Richardson Professor of Applied Mathematics at the School of Mathematics, University of Manchester....
FRS, who is also Director of Research. Other high profile mathematicians at Manchester include Sir Martin Taylor
Martin J. Taylor
Sir Martin John Taylor FRS was professor of pure mathematics at the School of Mathematics, University of Manchester and, prior to its formation and merger, UMIST where he was appointed to a chair after moving from Trinity College, Cambridge in 1986...
FRS and Jeff Paris
Jeff Paris
Jeffrey Bruce Paris is a British mathematician known for his work on mathematical logic, in particular provability in arithmetic, uncertain reasoning and inductive logic with an emphasis on rationality and common sense principles....
(Fellow of the British Academy
British Academy
The British Academy is the United Kingdom's national body for the humanities and the social sciences. Its purpose is to inspire, recognise and support excellence in the humanities and social sciences, throughout the UK and internationally, and to champion their role and value.It receives an annual...
)
Since its formation, the school has made some influential appointments including the topologist
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
Viktor Buchstaber
Viktor Buchstaber
Viktor Matveyevich Buchstaber is a Soviet and Russian mathematician known for his work on algebraic topology, homotopy and mathematical physics.-Work:Buchstaber's first research work was in cobordism theory...
(a member of the Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
) and model theorist
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
Alex Wilkie
Alex Wilkie
Alex Wilkie FRS is a British mathematician known for his contributions to Model theory and logic. Previously Reader in Mathematical Logic at the University of Oxford, he was appointed to the Fielden Chair of Pure Mathematics at the University of Manchester in 2007.Wilkie attended Aylesbury...
FRS. Numerical analyst Jack Dongarra
Jack Dongarra
Jack J. Dongarra is a University Distinguished Professor of Computer Sciencein the Electrical Engineering and Computer Science Department at the University of Tennessee...
, famous as one of the authors of LINPACK
LINPACK
LINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Gilbert Stewart, and was intended for use on supercomputers in the 1970s and early 1980s...
, was appointed in 2007 as Turing Fellow. In the autumn of 2007 another corresponding member of the Russian Academy of Sciences Albert Shiryaev
Albert Shiryaev
Al'bert Nikolayevich Shiryaev is a Soviet and Russian mathematician. He is known for his work in probability theory, statistics and financial mathematics....
was appointed to a 20% chair. Shiryaev is famous for his work on probability theory (he was a student of Kolmogorov
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
) and for his work on financial mathematics.
As might be expected from its size, the school has a wide range of research interests, including the traditionally pure areas of Algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, Analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, Noncommutative geometry
Noncommutative geometry
Noncommutative geometry is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative algebras of functions...
, Ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, Mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
, Number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, Geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and Topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
; and the more applied Dynamical system
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
, Fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
, Solid mechanics
Solid mechanics
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation...
, Inverse problem
Inverse problem
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in...
s, Mathematical finance
Mathematical finance
Mathematical finance is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive and extend the mathematical...
, Wave propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
and Scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
. The school also has a strong tradition in Numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
and well established groups in Probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, and Mathematical statistics
Mathematical statistics
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis...
.
Manchester mathematicians have a long tradition of applying mathematics to industrial problems. Nowadays this involves not only the traditional applications in engineering and the physical sciences, but also in the life sciences and the financial sector. Some of the recent industrial partners include Qinetiq
QinetiQ
Qinetiq is a British global defence technology company, formed from the greater part of the former UK government agency, Defence Evaluation and Research Agency , when it was split up in June 2001...
, Hewlett Packard, NAg
Numerical Algorithms Group
The Numerical Algorithms Group is a software company which provides methods for the solution of mathematical and statistical problems, and offers services to users of HPC systems. Its products and services are employed by tens of thousands of users from Global 500 companies, universities,...
, MathWorks, Comsol, Philips
Philips
Koninklijke Philips Electronics N.V. , more commonly known as Philips, is a multinational Dutch electronics company....
Labs, Thales Underwater Systems
Thales Underwater Systems
Thales Underwater Systems , formerly known as Thomson Marconi Sonar, is an international defence manufacturer specialising in sonar systems for submarines, surface warships, and aircraft as well as communications masts and systems for submarines. TUS is a subsidiary of Thales Naval, part of the...
, Rapiscan Systems
Rapiscan Systems
Rapiscan Systems is a global privately held company that specializes in walk-through metal detectors, and x-ray machines for airport luggage and cargo screening...
and Schlumberger
Schlumberger
Schlumberger Limited is the world's largest oilfield services company. Schlumberger employs over 110,000 people of more than 140 nationalities working in approximately 80 countries...
.
History
At the time of merger the two departments that came together to form the school were of roughly equal sizes and academic strengths, and already had a substantial record of collaboration including shared research seminar programmes and fourth year undergraduate and MSc programmes.Many famous mathematicians have worked at the precursor departments to the school.
In 1885 Horace Lamb
Horace Lamb
Sir Horace Lamb FRS was a British applied mathematician and author of several influential texts on classical physics, among them Hydrodynamics and Dynamical Theory of Sound...
, famous for his contribution to fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
accepted a chair at the VUM and under his leadership the department grew rapidly. Newman wrote:
- 'His lecture courses were numerous, and his books provide a record of his methods. Many of his students were engineers, and they found in him a sympathetic guide, one who understood their difficulties and shared their interest in applications of mathematics to mechanics.'
In 1907 famous analyst and number theorist J.E. Littlewood
John Edensor Littlewood
John Edensor Littlewood was a British mathematician, best known for the results achieved in collaboration with G. H. Hardy.-Life:...
was appointed to the Richardson Lectureship
Richardson Chair of Applied Mathematics
The Richardson Chair of Applied Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England. The chair was founded by an endowment of £3,600 from one John Richardson, in 1890. The endowment was originally used to support the Richardson...
which he held for three years.
During 1912–1913 the pioneer of weather forecasting and numerical analysis Lewis Fry Richardson
Lewis Fry Richardson
Lewis Fry Richardson, FRS was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them...
worked at Manchester College of Science and Technology
UMIST
The University of Manchester Institute of Science and Technology was a university based in the centre of the city of Manchester in England. It specialised in technical and scientific subjects and was a major centre for research...
(later to become UMIST). Number theorist Louis Mordell
Louis Mordell
Louis Joel Mordell was a British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian extraction...
joined the College in 1920. During this time he discovered the result for which he is best known, namely the finite basis theorem (or Mordell–Weil theorem
Mordell–Weil theorem
In mathematics, the Mordell–Weil theorem states that for an abelian variety A over a number field K, the group A of K-rational points of A is a finitely-generated abelian group, called the Mordell-Weil group...
), which proved a conjecture of Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
. Mordell then went on to become Fielden Reader in Pure Mathematics at VUM in 1922 and then held the Fielden Chair in 1923. Mordell built up the department, offering posts to a number of outstanding mathematicians who had been forced from posts on the continent of Europe. He brought in Reinhold Baer
Reinhold Baer
Reinhold Baer was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings....
, G. Billing, Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, Chao Ko
Chao Ko
Ke Zhao or Chao Ko was a Chinese mathematician born in Wenling, Taizhou, Zhejiang, People's Republic of China.Zhao graduated from Tsinghua University in 1933 and obtained his doctorate from the University of Manchester under Louis Mordell in 1937. His main fields of study were algebra, number...
, Kurt Mahler
Kurt Mahler
Kurt Mahler was a mathematician and Fellow of the Royal Society.He was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D...
, and Beniamino Segre
Beniamino Segre
Beniamino Segre was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry....
. He also recruited J. A. Todd
J. A. Todd
John Arthur Todd FRS was a British geometer. He was born in Liverpool, and went to Trinity College of the University of Cambridge in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester. He became a lecturer at Cambridge in 1937...
, Patrick du Val
Patrick du Val
Patrick du Val was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him....
, Harold Davenport
Harold Davenport
Harold Davenport FRS was an English mathematician, known for his extensive work in number theory.-Early life:...
, L. C. Young, and invited distinguished visitors.
Although Manchester was later to be known as the birthplace of the electronic computer, Douglas Hartree
Douglas Hartree
Douglas Rayner Hartree PhD, FRS was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser.-Early life:Douglas Hartree was born in...
made an earlier contribution building a differential analyser
Differential analyser
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration...
in 1933. The machine was used for ballistics
Ballistics
Ballistics is the science of mechanics that deals with the flight, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.A ballistic body is a body which is...
calculations as well calculating railway timetables.
Mordell was succeeded by the famous topologist and cryptanalyst
Cryptanalysis
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...
Max Newman
Max Newman
Maxwell Herman Alexander "Max" Newman, FRS was a British mathematician and codebreaker.-Pre–World War II:Max Newman was born Maxwell Neumann in Chelsea, London, England, on 7 February 1897...
in 1945 who, as head of department, transformed it into a centre of international renown. Undergraduate numbers increased from eight per year to 40 and then 60. In 1948 Newman recruited Alan Turing
Alan Turing
Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...
as Reader in the department, and he worked there until his death in 1954, completing some of his profound work on the foundations of computer science including Computing Machinery and Intelligence
Computing machinery and intelligence
Computing Machinery and Intelligence, written by Alan Turing and published in 1950 in Mind, is a seminal paper on the topic of artificial intelligence in which the concept of what is now known as the Turing test was introduced to a wide audience....
. Newnam retired in 1964. From 1949 to 1960 M.S. Bartlett held the first chair in mathematical statistics
Mathematical statistics
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis...
at VUM, he is known for his contribution to the analysis of data with spatial and temporal patterns, the theory of statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
and in multivariate analysis
Multivariate analysis
Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time...
. At Manchester he developed an interest in epidemiology
Epidemiology
Epidemiology is the study of health-event, health-characteristic, or health-determinant patterns in a population. It is the cornerstone method of public health research, and helps inform policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive...
, building a strong group in mathematical statistics and strengthening the department.
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
Sydney Goldstein
Sydney Goldstein
Sydney Goldstein FRS was a British mathematician noted for his contribution to fluid dynamics. He is described as:...
held the Beyer Chair of Applied Mathematics
Beyer Chair of Applied Mathematics
The Beyer Chair of Applied Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England. The endowment came from the engineer Charles Frederick Beyer, a generous supporter of the University....
from 1945 to 1950, and was succeeded from 1950 to 1959 by James Lighthill
James Lighthill
Sir Michael James Lighthill, FRS was a British applied mathematician, known for his pioneering work in the field of aeroacoustics.-Biography:...
, also a fluid dynamicist. In pure mathematics, Bernhard Neumann
Bernhard Neumann
Bernhard Hermann Neumann AC FRS was a German-born British mathematician who was one of the leading figures in group theory, greatly influencing the direction of the subject....
, an influential group theorist
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
, joined the department at VUM in 1948, leaving as a Reader in 1961 to take a chair in Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
. In 1964, VUM's Mathematics Tower, an 18 storey skyscraper
Skyscraper
A skyscraper is a tall, continuously habitable building of many stories, often designed for office and commercial use. There is no official definition or height above which a building may be classified as a skyscraper...
on Oxford Road, was completed.
Hanna Neumann
Johanna Neumann was a German-born mathematician who worked on group theory.Johanna was born in Lankwitz, Steglitz-Zehlendorf, Germany. She attended Auguste-Viktoria-Schule and the University of Berlin and completed her studies in 1936 with distinctions in mathematics and physics. She began...
, did not have a strong focus on research. Neumann was later to be the first woman appointed to a Professorial Chair of Mathematics in Australia.
Maths and Social Sciences Building
The Maths and Social Sciences Building is a highrise tower in Manchester. It was part of the University of Manchester Institute of Science and Technology until that university merged with the Victoria University of Manchester, to form the University of Manchester, in 2004.The MSS Building was...
(MSS) was completed on UMIST campus to house the growing department. In 1960 Robin Bullough
Robin Bullough
Robin K. Bullough was a British Mathematical Physicist famous for his contributions to the theory of solitons, in particular for his role in the development of the theory of the optical soliton, now commonly used, for example, in the theory of trans-oceanic optical fibre communication theory, but...
joined the UMIST department initiating four decades of mathematical physics focusing especially on solitons. The statistics group also grew in strength with an emphasis on time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
, led by Maurice Priestley
Maurice Priestley
Maurice Bertram Priestley is emeritus professor of statistics in the School of Mathematics, University of Manchester. He gained his first degree at the University of Cambridge and went on to gain a Ph.D. from the University of Manchester....
and also Tata Subba Rao
Tata Subba Rao
Tata Subba Rao is emeritus professor of statistics in the School of Mathematics, University of Manchester. He gained his MA at Karnatak, his PhD from...
. In 1986 pure mathematics at UMIST was strengthened by the appointment of Martin Taylor
Martin J. Taylor
Sir Martin John Taylor FRS was professor of pure mathematics at the School of Mathematics, University of Manchester and, prior to its formation and merger, UMIST where he was appointed to a chair after moving from Trinity College, Cambridge in 1986...
FRS, famous for his work on properties and structures of algebraic numbers.
Another renowned topologist, Frank Adams
Frank Adams
John Frank Adams FRS was a British mathematician, one of the founders of homotopy theory.-Life:He was born in Woolwich, a suburb in south-east London. He began research as a student of Abram Besicovitch, but soon switched to algebraic topology. He received his Ph.D. from the University of...
, succeeded Newman in the Fielden Chair, which he held from 1964 to 1970.
The VUM Mathematics tower was demolished in 2005, with most of the staff moving to temporary buildings, the pure mathematicians to one named after Newman and the applied to one named after Lamb. The history of the School entered a new phase in July 2007 with the move to the Alan Turing Building
See also
- Mathematics section in People Associated with the University of Manchester
- Richardson Chair of Applied MathematicsRichardson Chair of Applied MathematicsThe Richardson Chair of Applied Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England. The chair was founded by an endowment of £3,600 from one John Richardson, in 1890. The endowment was originally used to support the Richardson...
- Fielden Chair of Pure MathematicsFielden Chair of Pure MathematicsThe Fielden Chair of Pure Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England.In 1870 Samuel Fielden, a wealthy mill owner from Todmorden, donated £150 to Owens College for the teaching of evening classes and a further £3000 for the...
- Beyer Chair of Applied MathematicsBeyer Chair of Applied MathematicsThe Beyer Chair of Applied Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England. The endowment came from the engineer Charles Frederick Beyer, a generous supporter of the University....