Mildred Sanderson
Encyclopedia
Mildred Sanderson was an American mathematician, best known for her mathematical theorem concerning modular invariants.
, in 1889 and was the valedictorian of her class at the Waltham High School. She graduated from Mount Holyoke College in 1910, winning Senior Honors in Mathematics. She obtained her PhD from the University of Chicago
in 1913, publishing the thesis in which she set forth her mathematical theorem. She was Leonard Eugene Dickson's first female doctoral student. Dickson later wrote of her thesis, "This paper is a highly important contribution to this field of work; its importance lies partly in the fact that it establishes a correspondence between modular
and formal invariants
. Her main theorem has already been frequently quoted on account of its fundamental character. Her proof is a remarkable piece of mathematics." E.T. Bell later wrote that, "Miss Sanderson's single contribution (1913) to modular invariant
s has been rated by competent judges as one of the classics of the subject." After completing her Ph.D., Sanderson briefly taught at the University of Wisconsin before her untimely death in 1914 due to tuberculosis. She is mentioned in the book Pioneering women in American mathematics: the pre-1940 PhD's, by Judy Green and Jeanne LaDuke. A Mildred L. Sanderson prize for excellence in mathematics was established in her honor in 1939 at Mount Holyoke College.
"To any modular invariant i of a system of forms under any group G of linear transformations with coefficients in the GF[pn], there corresponds a formal invariant I under G such that I = i for all sets of values in the field of the coefficients of the system of forms."
Life
Sanderson was born in Waltham, MassachusettsWaltham, Massachusetts
Waltham is a city in Middlesex County, Massachusetts, United States, was an early center for the labor movement, and major contributor to the American Industrial Revolution. The original home of the Boston Manufacturing Company, the city was a prototype for 19th century industrial city planning,...
, in 1889 and was the valedictorian of her class at the Waltham High School. She graduated from Mount Holyoke College in 1910, winning Senior Honors in Mathematics. She obtained her PhD from the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
in 1913, publishing the thesis in which she set forth her mathematical theorem. She was Leonard Eugene Dickson's first female doctoral student. Dickson later wrote of her thesis, "This paper is a highly important contribution to this field of work; its importance lies partly in the fact that it establishes a correspondence between modular
Modular invariant of a group
In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic...
and formal invariants
Invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties from the point of view of their effect on functions...
. Her main theorem has already been frequently quoted on account of its fundamental character. Her proof is a remarkable piece of mathematics." E.T. Bell later wrote that, "Miss Sanderson's single contribution (1913) to modular invariant
Modular invariant of a group
In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic...
s has been rated by competent judges as one of the classics of the subject." After completing her Ph.D., Sanderson briefly taught at the University of Wisconsin before her untimely death in 1914 due to tuberculosis. She is mentioned in the book Pioneering women in American mathematics: the pre-1940 PhD's, by Judy Green and Jeanne LaDuke. A Mildred L. Sanderson prize for excellence in mathematics was established in her honor in 1939 at Mount Holyoke College.
Sanderson's theorem
Sanderson's theorem states:"To any modular invariant i of a system of forms under any group G of linear transformations with coefficients in the GF[pn], there corresponds a formal invariant I under G such that I = i for all sets of values in the field of the coefficients of the system of forms."