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Ralph Duncan James (8 February 1909,
Liverpool Liverpool is a City status in the United Kingdom, city and metropolitan borough in Merseyside, England. With a population of in 2019, it is the List of English districts by population, 10th largest English district by population and its E ...
, England – 19 May 1979,
Salt Spring Island Salt Spring Island or Saltspring Island is one of the Gulf Islands in the Strait of Georgia between mainland British Columbia, Canada, and Vancouver Island. The island was initially inhabited by various Salishan peoples before being settle ...
,
British Columbia British Columbia (commonly abbreviated as BC) is the westernmost Provinces and territories of Canada, province of Canada, situated between the Pacific Ocean and the Rocky Mountains. It has a diverse geography, with rugged landscapes that include ...
, Canada) was a Canadian
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
working on
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
and
mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
. Born in Liverpool, Ralph moved with his parents to
Vancouver Vancouver ( ) is a major city in western Canada, located in the Lower Mainland region of British Columbia. As the most populous city in the province, the 2021 Canadian census recorded 662,248 people in the city, up from 631,486 in 2016. Th ...
,
British Columbia British Columbia (commonly abbreviated as BC) is the westernmost Provinces and territories of Canada, province of Canada, situated between the Pacific Ocean and the Rocky Mountains. It has a diverse geography, with rugged landscapes that include ...
when he was 10 years old. After graduating from
high school A secondary school describes an institution that provides secondary education and also usually includes the building where this takes place. Some secondary schools provide both '' lower secondary education'' (ages 11 to 14) and ''upper seconda ...
, Ralph attended
University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...
. After graduating, he continued in mathematics, writing a master’s thesis on ''Tangential Coordinates''. Proceeding to
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
, he studied
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
and
Waring's problem In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural numb ...
under
L. E. Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remem ...
. In 1932 he was a awarded a Ph.D. on the strength of his dissertation ''Analytical Investigations of Waring's Theorem''. He continued post-graduate study, first with
E. T. Bell Eric Temple Bell (7 February 1883 – 21 December 1960) was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction as John Tain ...
at
California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
, then in 1934 with G. H. Hardy at
Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
. He published in the
Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 ...
and extended some work of Viggo Brun in 1938. Ralph James was a
professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professor ...
of mathematics at
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
from 1934 to 1939. He was then called to
University of Saskatchewan A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which ...
where he became Head of the mathematics department.Prominent people
from
University of Saskatchewan A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which ...
In 1943 he began his long tenure at
University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...
, becoming Head of the department in 1948. James made contributions to the theory of the Perron integral and to solution of Goldbach's conjecture. Since 1978, the
Canadian Mathematical Society The Canadian Mathematical Society (CMS) (french: Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. It serves the ...
have awarded the Coxeter–James Prize in his honor.


Papers

Ralph Duncan James published the following papers in the course of his career: * 1934:
Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...
"On the representation of integers as sums of pyramidal numbers" * 1934:
Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 ...
36(2):395–444 "The value of the number g(k) in Waring's problem" * 1938: ''Transactions of the American Mathematical Society'' 43(2):296–302 "A problem in additive number theory" * 1939: Duke Mathematical Journal 5:948–62 "Integers which are not represented by certain ternary quadratic forms" * 1942: (with
Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is ass ...
)
American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United ...
64:539–52 "Elementary note on prime number problems of Vinogradoff’s type" * 1943:
Bulletin of the American Mathematical Society The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. ...
49:422–32 "On the sieve method of Viggo Brun" * 1946: (with Walter Gage ) ''Transactions of the Royal Society of Canada'' Section III(3) 40:25–35 "A generalized integral" * 1949: Bulletin of the AMS 55:246–60 "Recent progress on the Goldbach problem" * 1950:
Canadian Journal of Mathematics The ''Canadian Journal of Mathematics'' (french: Journal canadien de mathématiques) is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The ...
2:297–306 "A generalized integral II" * 1954: (with Ivan Niven)
Proceedings of the American Mathematical Society ''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ...
5:834–8 "Unique factorization in multiplicative systems" * 1955: Bulletin of the AMS 61:1–15 "Integrals and summable trigonometric series" * 1956:
Pacific Journal of Mathematics The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisati ...
6:99–110 "Summable trigonometric series" * 1968:
Canadian Mathematical Bulletin The ''Canadian Mathematical Bulletin'' (french: Bulletin Canadien de Mathématiques) is a mathematics journal, established in 1958 and published quarterly by the Canadian Mathematical Society. The current editors-in-chief of the journal are Anto ...
11:733–5 "The factors of a square-free integer" * 1970:
American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an ...
77(1):94 "Review: ''Studies in Number Theory''"


References


Ralph James dies suddenly at Salt Spring Island home
from ''Gulf Islands Driftwood'', May 23, 1979, page 3. * * {{DEFAULTSORT:James, Ralph Duncan 1909 births 1979 deaths Number theorists 20th-century Canadian mathematicians British emigrants to Canada Presidents of the Canadian Mathematical Society The American Mathematical Monthly editors