Ottawa
Ottawa (, ; Canadian French: ) is the capital city of Canada. It is located at the confluence of the Ottawa River and the Rideau River in the southern portion of the province of Ontario. Ottawa borders Gatineau, Quebec, and forms the core ...
,
Ontario
Ontario ( ; ) is one of the thirteen provinces and territories of Canada.Ontario is located in the geographic eastern half of Canada, but it has historically and politically been considered to be part of Central Canada. Located in Central Ca ...
, 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, structure, space, models, and change.
History
On ...
and
computer scientist
A computer scientist is a person who is trained in the academic study of computer science.
Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...
, a professor of mathematics at the
University of Calgary
The University of Calgary (U of C or UCalgary) is a public research university located in Calgary, Alberta, Canada. The University of Calgary started in 1944 as the Calgary branch of the University of Alberta, founded in 1908, prior to being ins ...
and of computer science at the
University of Ottawa
The University of Ottawa (french: Université d'Ottawa), often referred to as uOttawa or U of O, is a bilingual public research university in Ottawa, Ontario, Canada. The main campus is located on directly to the northeast of Downtown Ottawa ...
....
Rival's Ph.D. thesis concerned
lattice theory
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper boun ...
. After moving to Calgary he began to work more generally with
partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a Set (mathematics), set. A poset consists of a set toget ...
s, and to study
fixed point theorem
In mathematics, a fixed-point theorem is a result saying that a function ''F'' will have at least one fixed point (a point ''x'' for which ''F''(''x'') = ''x''), under some conditions on ''F'' that can be stated in general terms. Some authors clai ...
s for partially ordered structures. He was a frequent organizer of conferences in
order theory
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article intr ...
, and in 1984 he founded the journal ''
Order
Order, ORDER or Orders may refer to:
* Categorization, the process in which ideas and objects are recognized, differentiated, and understood
* Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of d ...
''. As a computer scientist at Ottawa, he shifted research topics, applying his expertise in order theory to the study of
data structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, a ...
s,
computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems ar ...
, and
graph drawing
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graph (discrete mathematics), graphs arising from applications such a ...
.
Rival grew up in
Hamilton, Ontario
Hamilton is a port city in the Canadian province of Ontario. Hamilton has a population of 569,353, and its census metropolitan area, which includes Burlington and Grimsby, has a population of 785,184. The city is approximately southwest of T ...
. He earned a bachelor's degree at
McMaster University
McMaster University (McMaster or Mac) is a public research university in Hamilton, Ontario, Canada. The main McMaster campus is on of land near the residential neighbourhoods of Ainslie Wood and Westdale, adjacent to the Royal Botanical Ga ...
in 1969, and received his Ph.D. from the
University of Manitoba
The University of Manitoba (U of M, UManitoba, or UM) is a Canadian public research university in the province of Manitoba.. After postdoctoral stints visiting
Robert Dilworth
Robert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician. His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say ...
at
Caltech
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 ...
and
Rudolf Wille
Rudolf Wille (2 November 1937 – 22 January 2017) was a German mathematician and was professor of General Algebra from 1970 to 2003 at Technische Universität Darmstadt (TU Darmstadt). His most celebrated work is the invention of formal concep ...
at the Technische Hochschule Darmstadt, he took a faculty position at Calgary in 1975, and was promoted to full professor in 1981. In 1986, he moved to the University of Ottawa, where he became chair of the computer science department.
Rival's doctoral students included Dwight Duffus, the Goodrich C. White Professor of Mathematics & Computer Science at
Emory University
Emory University is a private research university in Atlanta, Georgia. Founded in 1836 as "Emory College" by the Methodist Episcopal Church and named in honor of Methodist bishop John Emory, Emory is the second-oldest private institution of ...