Mildred Sanderson

Mildred Sanderson was an American mathematician, best known for her mathematical theorem concerning modular invariants.^[1][2]

Life

Sanderson was born in Waltham, Massachusetts, in 1889 and was the valedictorian of her class at the Waltham High School.^[1] She graduated from Mount Holyoke College in 1910, winning Senior Honors in Mathematics.^[1] She obtained her PhD from the University of Chicago in 1913,^[3] publishing the thesis (Sanderson 1913) in which she set forth her mathematical theorem. She was Leonard Eugene Dickson's first female doctoral student.^[1][3] 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."^[1] E.T. Bell later wrote that, "Miss Sanderson's single contribution (1913) to modular invariants has been rated by competent judges as one of the classics of the subject."^[1] After completing her Ph.D., Sanderson briefly taught at the University of Wisconsin before her untimely death in 1914 due to tuberculosis.^[1][4] She is mentioned in the book Pioneering women in American mathematics: the pre-1940 PhD's, by Judy Green and Jeanne LaDuke.^[5] A Mildred L. Sanderson prize for excellence in mathematics was established in her honor in 1939 at Mount Holyoke College.^[5]

Sanderson's theorem

Sanderson's theorem (Sanderson 1913, p.490) 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."

References

1. ^ ^{a b c d e f g} Mildred Leonora Sanderson
2. ^ Rutherford (2007, p.39)
3. ^ ^{a b} The Mathematics Genealogy Project - Mildred Sanderson
4. ^ Pioneering women in American ... - Google Books
5. ^ ^{a b} Pioneering women in American ... - Google Books

• Rutherford, Daniel Edwin (2007) [1932], Modular invariants, Cambridge Tracts in Mathematics and Mathematical Physics, No. 27, Ramsay Press, ISBN 978-1-4067-3850-6, MR0186665, http://www.archive.org/details/modularinvariant033204mbp 
• Sanderson, Mildred (1913), "Formal Modular Invariants with Application to Binary Modular Covariants", Transactions of the American Mathematical Society (Providence, R.I.: American Mathematical Society) 14 (4): 489–500, ISSN 0002-9947, JSTOR 1988702 

Persondata
Name	Sanderson, Mildred
Alternative names
Short description
Date of birth	1889
Place of birth	Waltham, Massachusetts
Date of death	1914
Place of death