field_of_work richard a. parker
West Sussex is a county in the south of England , bordering East Sussex ( with Brighton and Hove ) to the east , Hampshire to the west and Surrey to the north , and to the south the ___MASK18___ Channel . Chichester in the southwest is the county town and only city in West Sussex , with the largest towns being Crawley , Worthing and Horsham . West Sussex has a range of scenery , including wealden , downland and coastal . The highest point of the county is Blackdown , at 280 metres ( 919 ft ). It has a number of stately homes including Goodwood , Petworth House and Uppark and also castles such as Arundel Castle and Bramber Castle . Over half the county is protected countryside , offering walking , ___MASK32___ and other recreational opportunities . In ___MASK45___ and abstract ___MASK92___ , ___MASK85___ studies the algebraic structures known as groups . The concept of a group is central to abstract ___MASK92___ : other well - known algebraic structures , such as rings , fields , and vector spaces , can all be seen as groups endowed with additional operations and axioms . Groups recur throughout ___MASK45___ , and the methods of ___MASK85___ have influenced many parts of ___MASK92___ . Linear algebraic groups and Lie groups are two branches of ___MASK85___ that have experienced advances and have become subject areas in their own right . John Horton Conway FRS ( born 26 December 1937 ) is an ___MASK18___ mathematician active in the theory of finite groups , knot theory , ___MASK62___ , combinatorial ___MASK44___ and coding theory . He has also contributed to many branches of recreational mathematics , notably the invention of the cellular automaton called the Game of Life . Conway is currently Professor Emeritus of Mathematics at Princeton University in New Jersey . In abstract ___MASK92___ , a finite group is a mathematical group with a finite number of elements . A group is a set of elements together with an operation which associates , to each ordered pair of elements , an element of the set . With a finite group , the set is finite . A ___MASK14___ is someone who uses an extensive knowledge of mathematics in his / her work , typically to solve mathematical problems . East Sussex is a county in South East England . It is bordered by the counties of Kent to the north and east , Surrey to the north west and West Sussex to the west , and to the south by the ___MASK18___ Channel . In the area of modern ___MASK92___ known as ___MASK85___ , the Monster group " M " ( also known as the Fischer  Griess Monster , or the Friendly Giant ) is the largest sporadic simple group , having order In ___MASK45___ , a Moufang loop is a special kind of algebraic structure . It is similar to a group in many ways but need not be associative . Moufang loops were introduced by . Smooth Moufang loops have an associated ___MASK92___ , the Malcev ___MASK92___ , similar in some ways to how a Lie group has an associated Lie ___MASK92___ . ___MASK45___ ( from Greek  " máthma ",  knowledge , study , learning ) is the study of topics such as quantity ( numbers ), structure , space , and change . There is a range of views among mathematicians and philosophers as to the exact scope and definition of ___MASK45___ . England is a country that is part of the United Kingdom . It shares land borders with Scotland to the north and Wales to the west . The Irish Sea lies northwest of England and the Celtic Sea lies to the southwest . England is separated from continental Europe by the North Sea to the east and the ___MASK18___ Channel to the south . The country covers five - eighths of the island of Great Britain ( which lies in the North Atlantic ) in its centre and south ; and includes over 100 smaller islands such as the Isles of Scilly , and the Isle of Wight . Princeton University is a private Ivy League ___MASK67___ university in Princeton , New Jersey , United States . Cambridge is a university city and the county town of Cambridgeshire , England , on the ___MASK22___ Cam about north of London . At the United Kingdom Census 2011 , its population was 123 , 867 , including 24 , 488 students . The North Sea is a marginal sea of the Atlantic Ocean located between Great Britain , Scandinavia , Germany , the Netherlands , Belgium , and France . An epeiric ( or " shelf ") sea on the European continental shelf , it connects to the ocean through the ___MASK18___ Channel in the south and the Norwegian Sea in the north . It is more than long and wide , with an area of around . The United Kingdom of Great Britain and Northern Ireland , commonly known as the United Kingdom ( UK ) or Britain , is a sovereign country in western Europe . Lying off the north - western coast of the European mainland , it includes the island of Great Britain ( the name of which is also loosely applied to the whole country ), the north - eastern part of the island of Ireland , and many smaller islands . Northern Ireland is the only part of the UK that shares a land border with another sovereign statethe Republic of Ireland . Apart from this land border , the UK is surrounded by the Atlantic Ocean , with the North Sea to its east , the ___MASK18___ Channel to its south and the Celtic Sea to its south - south - west , giving it the 12th - longest coastline in the world . The Irish Sea lies between Great Britain and Ireland . With an area of , the UK is the 78th - largest sovereign state in the world and the 11th - largest in Europe . It is also the 21st - most populous country , with an estimated 65 . 1 million inhabitants . Together , this makes it the fourth most densely populated country in the European Union . Ernst Witt ( June 26 , 1911  July 3 , 1991 ) was a German ___MASK14___ , one of the leading algebraists of his time . He was born on the island of Als ( German : " Alsen "). Shortly after his birth , he and his parents moved to China , and he did not return to Europe until he was nine . ___MASK62___ or , in older usage , arithmetic is a branch of pure mathematics devoted primarily to the study of the integers . It is sometimes called " The Queen of Mathematics " because of its foundational place in the discipline . Number theorists study prime numbers as well as the properties of objects made out of integers ( e . g ., rational numbers ) or defined as generalizations of the integers ( e . g ., algebraic integers ). For the Egyptologist Richard A . Parker , see Richard Anthony Parker . Richard A . Parker ( b . 29 January 1953 , in Surrey ) is a ___MASK14___ and freelance computer programmer in Cambridge , England . He invented many of the algorithms for computing the modular character tables of finite simple groups . He discovered the relation between Niemeier lattices and deep holes of the Leech lattice , and constructed Parker ' s Moufang loop of order 213 ( which was used by John Horton Conway in his construction of the monster group ) . A shire is a traditional term for a division of land , found in the United Kingdom and ___MASK27___ . It was first used in Wessex from the beginning of Anglo - Saxon settlement , and spread to most of the rest of England in the tenth century . In ___MASK45___ , a Malcev ___MASK92___ ( or Maltsev ___MASK92___ or Moufang  Lie ___MASK92___ ) over a field is a nonassociative ___MASK92___ that is antisymmetric , so that Combinatorial ___MASK44___ ( CGT ) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information . Study has been largely confined to two - player games that have a " position " in which the players take turns changing in defined ways or " moves " to achieve a defined winning condition . CGT has not traditionally studied games of chance or those that use imperfect or incomplete information , favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players . However , as mathematical techniques advance , the types of game that can be mathematically analyzed expands , thus the boundaries of the field are ever changing . Scholars will generally define what they mean by a " game " at the beginning of a paper , and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field . The home counties are the counties of England that surround London ( although several of them do not border it ). The counties generally included in the list are Berkshire , Buckinghamshire , Essex , Hertfordshire , Kent , Surrey , and Sussex . Other counties more distant from London  such as Bedfordshire , Cambridgeshire , Hampshire and Oxfordshire  are also sometimes regarded as home counties due to their proximity to London and their connection to the London regional ___MASK8___ . A cellular automaton ( pl . cellular automata , abbrev . CA ) is a discrete model studied in computability theory , ___MASK45___ , ___MASK35___ , complexity ___MASK47___ , theoretical biology and microstructure modeling . Cellular automata are also called cellular spaces , tessellation automata , homogeneous structures , cellular structures , tessellation structures , and iterative arrays . In ___MASK45___ , a Lie group is a group that is also a differentiable manifold , with the property that the group operations are compatible with the smooth structure . Lie groups are named after Sophus Lie , who laid the foundations of the theory of continuous transformation groups . The term " groupes de Lie " first appeared in ___MASK65___ in 1893 in the thesis of Lie  s student Arthur Tresse . In ___MASK30___ , Euclidean space encompasses the two - dimensional Euclidean plane , the three - dimensional space of Euclidean ___MASK30___ , and certain other spaces . It is named after the Ancient Greek ___MASK14___ Euclid of Alexandria . The term " Euclidean " distinguishes these spaces from other types of spaces considered in modern ___MASK30___ . Euclidean spaces also generalize to higher dimensions . In ___MASK45___ , and more specifically in abstract ___MASK92___ , an algebraic structure is a set ( called carrier set or underlying set ) with one or more finitary operations defined on it that satisfies a list of axioms . The ___MASK22___ Cam is the main ___MASK22___ flowing through Cambridge in eastern England . After leaving Cambridge , it flows north and east into the Great Ouse to the south of Ely at Pope ' s Corner . The Great Ouse connects the Cam to the North Sea at King ' s Lynn : The total distance from Cambridge to the sea is about and is navigable for punts , small boats , and rowing craft . The Great Ouse also connects to England ' s canal system via the Middle Level Navigations and the ___MASK22___ Nene . In total , the Cam runs for around from its furthest source ( near Debden in Essex ) to its confluence with the Great Ouse . The Celtic Sea (; ) is the area of the Atlantic Ocean off the south coast of Ireland bounded to the east by Saint George ' s Channel ; other limits include the Bristol Channel , the ___MASK18___ Channel , and the Bay of Biscay , as well as adjacent portions of Wales , Cornwall , Devon , and Brittany . The southern and western boundaries are delimited by the continental shelf , which drops away sharply . The Isles of Scilly are an archipelago of small islands in the sea . The ___MASK18___ Channel (" the Sleeve " [ hence ] " Sea of Brittany " " British Sea "), also called simply the Channel , is the body of water that separates southern England from northern France , and joins the southern part of the North Sea to the rest of the Atlantic Ocean . Surrey is a county in the south east of England and also one of the home counties bordering Greater London . Surrey shares borders with Kent to the east , East Sussex to the south - east , West Sussex to the south , Hampshire to the west and south - west and Berkshire to the north - west . The county town is Guildford . Surrey County Council sits extraterritorially at Kingston upon Thames , administered as part of Greater London since 1965 . With a resident population of 1 . 1 million , Surrey is the most densely populated and third most populated county in the South East region , after Kent and Hampshire . In ___MASK30___ and mathematical ___MASK85___ , a unimodular ___MASK87___ is an integral ___MASK87___ of determinant 1 or  1 . For a ___MASK87___ in " n "- dimensional Euclidean space , this is equivalent to requiring that the volume of any fundamental domain for the ___MASK87___ be 1 . Hampshire (; abbreviated Hants , archaically known as the County of Southampton ) is a county on the southern coast of England in the United Kingdom . The county town of Hampshire is Winchester , the former capital city of England . Hampshire is the most populous ceremonial county in the United Kingdom ( excluding the metropolitan counties ) with almost half of the county ' s population living within the South Hampshire conurbation which includes the cities of Southampton and Portsmouth . The larger South Hampshire metropolitan area has a population of 1 , 547 , 000 . Hampshire is notable for housing the birthplaces of the Royal ___MASK13___ , British Army , and Royal Air Force . It is bordered by Dorset to the west , Wiltshire to the north - west , Berkshire to the north , Surrey to the north - east , and West Sussex to the east . The southern boundary is the coastline of the ___MASK18___ Channel and the Solent , facing the Isle of Wight . In ___MASK39___ , knot theory is the study of mathematical knots . While inspired by knots which appear in daily life in shoelaces and rope , a mathematician ' s knot differs in that the ends are joined together so that it cannot be undone . In mathematical language , a knot is an embedding of a circle in 3 - dimensional Euclidean space , R ( in ___MASK39___ , a circle isn ' t bound to the classical geometric concept , but to all of its homeomorphisms ). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R upon itself ( known as an ambient isotopy ); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself . In ___MASK30___ , a kissing number is defined as the number of non - overlapping unit spheres that can be arranged such that they each touch another given unit sphere . For a ___MASK87___ packing the kissing number is the same for every sphere , but for an arbitrary sphere packing the kissing number may vary from one sphere to another . Other names for kissing number that have been used are Newton number ( after the originator of the problem ), and contact number . Coding theory is the study of the properties of codes and their respective fitness for specific applications . Codes are used for ___MASK10___ , cryptography , error - correction , and networking . Codes are studied by various scientific disciplines  such as ___MASK69___ , electrical engineering , mathematics , linguistics , and computer science  for the purpose of designing efficient and reliable data transmission methods . This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data . Recreational ___MASK45___ is a term for ___MASK45___ carried out for recreation ( ___MASK46___ ) rather than as a strictly research and application - based professional activity . Although it is not necessarily limited to being an endeavor for amateurs , it often involves mathematical puzzles and games . In ___MASK45___ , the Leech ___MASK87___ is an even unimodular ___MASK87___  in 24 - dimensional Euclidean space , which is one of the best models for the kissing number problem . It was discovered by . It may also have been discovered ( but unpublished ) by Ernst Witt in 1940 . A country is a region that is identified as a distinct national entity in political ___MASK57___ . A country may be an independent sovereign state or one that is occupied by another state , as a non - sovereign or formerly sovereign political division , or a geographic region associated with sets of previously independent or differently associated people with distinct political characteristics . Regardless of the physical ___MASK57___ , in the modern internationally accepted legal definition as defined by the League of Nations in 1937 and reaffirmed by the United Nations in 1945 , a resident of a country is subject to the independent exercise of legal jurisdiction . In ___MASK45___ , a Lie ___MASK92___ ( not ) is a vector space together with a non - associative multiplication called " Lie bracket " formula_1 . When an algebraic product is defined on the space , the Lie bracket is the commutator formula_2 . A census of the population of the United Kingdom is taken every ten years . The 2011 census was held in all countries of the UK on 27 March 2011 . It was the first UK census which could be completed online via the Internet . The Office for National ___MASK53___ ( ONS ) is responsible for the census in England and Wales , the General Register Office for Scotland ( GROS ) is responsible for the census in Scotland , and the Northern Ireland ___MASK53___ and Research Agency ( NISRA ) is responsible for the census in Northern Ireland . The Isle of Wight is a county and the largest and second - most populous island in England . It is located in the ___MASK18___ Channel , about 4 miles ( 6 km ) off the coast of Hampshire , separated by the Solent . The island has resorts that have been holiday destinations since Victorian times , and is known for its mild climate , coastal scenery , and verdant landscape of fields , downland and chines .