Cecilia Krieger
Encyclopedia
Austria-Hungary
Austria-Hungary , more formally known as the Kingdoms and Lands Represented in the Imperial Council and the Lands of the Holy Hungarian Crown of Saint Stephen, was a constitutional monarchic union between the crowns of the Austrian Empire and the Kingdom of Hungary in...
(more specifically, Galician)-born mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
of Jewish ancestry who lived and worked in Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
.
Krieger was the third person (and first woman) to earn a Ph.D in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from a university in Canada, in 1930as well as the third woman to have been awarded a doctorate in any discipline in Canada.
Krieger is well-known for having translated two works of Sierpinski in general topology
General topology
In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...
.
The Krieger-Nelson Prize
Krieger-Nelson Prize
The Krieger–Nelson Prize is presented by the Canadian Mathematical Societyin recognition of an outstanding woman in mathematics. It was firstawarded in 1995.The award is named after Cecilia Krieger andEvelyn Nelson, both known for their...
, awarded annually by the Canadian Mathematical Society
Canadian Mathematical Society
The Canadian Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and education in Canada.It was originally conceived in June 1945 as the Canadian Mathematical Congress...
since 1995 for outstanding research by a female mathematician, is named in honour of Krieger and Evelyn Nelson
Evelyn Nelson (mathematician)
Evelyn Merle Nelson , born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science...
.
Early life and education
Krieger was born on April 9, 1894, in Jasło in Galicia.The town was then part of Austria-Hungary, but is in modern-day Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
.
Her parents, Moses and Sarah Krieger, had two sons and two daughters besides Cecilia.
Krieger began studying mathematics and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
at the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
in 1919, but moved with her family to Toronto
Toronto
Toronto is the provincial capital of Ontario and the largest city in Canada. It is located in Southern Ontario on the northwestern shore of Lake Ontario. A relatively modern city, Toronto's history dates back to the late-18th century, when its land was first purchased by the British monarchy from...
, Ontario
Ontario
Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa....
, Canada in 1920.
Krieger earned a B.A
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in 1924 and a M.A
Master of Arts (postgraduate)
A Master of Arts from the Latin Magister Artium, is a type of Master's degree awarded by universities in many countries. The M.A. is usually contrasted with the M.S. or M.Sc. degrees...
in 1925 from the University of Toronto
University of Toronto
The University of Toronto is a public research university in Toronto, Ontario, Canada, situated on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in Upper Canada...
.
She obtained her Ph.D from the same university in 1930.
Her thesis, under the supervision of W.J. Webber, was entitled
"On the summability of trigonometric series with localized parameters--on Fourier constants and convergence factors of double Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
".
At the University of Toronto
While pursuing her Ph.D, Krieger was appointed as an instructor in 1928 and promoted to LecturerLecturer
Lecturer is an academic rank. In the United Kingdom, lecturer is a position at a university or similar institution, often held by academics in their early career stages, who lead research groups and supervise research students, as well as teach...
in 1930 when she completed her Ph.D.
Krieger continued working at the rank of Lecturer until she was promoted to Assistant Professor at the University of Toronto in 1942.
She taught in both the Department of Engineering and the Department of Mathematics.
Krieger married Dr. Zygmund Dunaij in 1953.
Retirement
Krieger continued at the rank of Assistant Professor until her retirement in 1962.However, she continued teaching after her retirement: for five years at the University of Toronto, leaving in 1968 upon the death of her husband and for six more years at Upper Canada College
Upper Canada College
Upper Canada College , located in midtown Toronto, Ontario, Canada, is an independent elementary and secondary school for boys between Senior Kindergarten and Grade Twelve, operating under the International Baccalaureate program. The secondary school segment is divided into ten houses; eight are...
, a private school
Private school
Private schools, also known as independent schools or nonstate schools, are not administered by local, state or national governments; thus, they retain the right to select their students and are funded in whole or in part by charging their students' tuition, rather than relying on mandatory...
in Toronto, until her own death in 1974.
Publications
In 1934, Krieger published an English translation of Sierpinski's book Introduction to General Topology. She also translated General Topology by Sierpinski in 1952, adding a 30-page appendix on infinite cardinalsCardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...
and ordinals
Ordinal number
In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...
.
Recognition
Krieger was a strong supporter of women in mathematics.In honour of the contributions of Krieger and Evelyn Nelson
Evelyn Nelson (mathematician)
Evelyn Merle Nelson , born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science...
, the Canadian Mathematical Society
Canadian Mathematical Society
The Canadian Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and education in Canada.It was originally conceived in June 1945 as the Canadian Mathematical Congress...
created the Krieger-Nelson Prize
Krieger-Nelson Prize
The Krieger–Nelson Prize is presented by the Canadian Mathematical Societyin recognition of an outstanding woman in mathematics. It was firstawarded in 1995.The award is named after Cecilia Krieger andEvelyn Nelson, both known for their...
in 1995. It is awarded to an outstanding woman in mathematics.