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Margaret Willerding

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Margaret Frances Willerding (1919–2003)[1] was an American mathematician known for her combinatorial enumeration of quadratic forms, for her mathematics textbooks, and for her editorship of the problems department of the mathematics journal School Science and Mathematics.[2]

Early life and education

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Willerding was born on April 26, 1919, in St. Louis, Missouri.[1] After graduating from high school in 1936, she went to a local school, Harris Teachers College, despite being highly ambitious academically, because it was free; her parents were not especially supportive and could not afford a more expensive school. She majored in education there, with a minor in mathematics,[3] and graduated in 1940.[1]

After a year working as a schoolteacher,[3] she went to Saint Louis University for graduate study in mathematics,[2] choosing it as the best of the two universities local enough to allow her to continue living with her parents,[3] and despite her mother's dismissal of her academic ambitions.[4] During this time she continued working as a schoolteacher to support herself, before obtaining a fellowship in the final year of her program, the first woman to do so.[3] She earned a master's degree in 1943 and completed her Ph.D. in 1947.[1][3]

Her dissertation, Determination of All Classes of Positive Quaternary Quadratic Forms Which Represent All (Positive) Integers, was supervised by Arnold Ross,[2][5]. A short summary of it was later published in the Bulletin of the American Mathematical Society,[6] the main result of which being that "there are exactly 178 classes of universal classic positive quaternary quadratic forms". This was later found to be incorrect. Based on the use of the 15 theorem, Manjul Bhargava determined the correct number to be 204.[7][8] As noted by John H. Conway,[7] "Willerding’s work had been unusually defective. [...] she missed 36 forms, listed 1 form twice, and listed 9 non-universal forms!"

While she was still working on her doctorate, Ross moved to the University of Notre Dame to become department chair, and she commuted there by train to visit him. She became engaged to an older physicist at Notre Dame, Eugene Guth, but did not end up marrying him, and Ross's plans to hire her at Notre Dame also did not work out.[2][4]

Career and later life

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After completing her doctorate, Willerding became a mathematics instructor at Washington University in St. Louis, beginning in 1947.[2] However, after being told that she would be passed over for promotions in favor of male faculty members, and being asked to pour tea for faculty wives at a mathematics meeting held at the university, she left after a single semester. Instead, she returned to Harris Teachers College and began focusing on mathematics education instead of mathematical research.[2][4] During this time she also became active in the Missouri Section of the Mathematical Association of America.[2]

In 1954 she started her work as mathematical problems editor for School Science and Mathematics, a position she held until 1976 despite a colleague undercutting her in the early 1960s by suggesting to the journal's editor-in-chief that she was too old for the position.[2][9]

She moved in 1956 to San Diego State University,[2][1] and retired as a professor emeritus in 1976.[1] She died on December 29, 2003.[2][1]

Books

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Willerding wrote over 30 mathematical textbooks.[2] They include:

  • The Business of Mathematics (Prindle, Weber & Schmidt, 1977)[10]
  • College Algebra and Trigonometry (with Stephen Hoffman, Wiley, 1971; 2nd ed., 1975)[11]
  • Elementary Mathematics: Its Structure and Concepts (Wiley, 1966)[12]
  • A First Course in College Mathematics: Module 4—The Integers and Their Operations; Equations and Inequalities; Squares, Square Roots, and Similar Triangles (Prindle, Weber & Schmidt, 1975)[13]
  • Mathematics: The Alphabet of Science (with Ruth A. Hayward, 2nd ed., Wiley, 1972)[14]
  • Modern Intermediate Algebra (2nd ed., Wiley, 1975)[15]
  • The Numbers Game (Prindle, Weber & Schmidt, 1977)[16]
  • A Probability Primer (Prindle, Weber & Schmidt, 1968)[17]

References

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  1. ^ a b c d e f g "Margaret Frances Willerding", San Diego Union-Tribune, December 31, 2003, retrieved 2022-04-10 – via Legacy.com
  2. ^ a b c d e f g h i j k Hall, Leon (2017), "Founders, feminists, and a fascist – some notable women in the Missouri Section of the MAA", in Beery, Janet L.; Greenwald, Sarah J.; Jensen-Vallin, Jacqueline A.; Mast, Maura B. (eds.), Women in Mathematics: Celebrating the Centennial of the Mathematical Association of America, Association for Women in Mathematics Series, vol. 10, Springer International Publishing, pp. 121–140, doi:10.1007/978-3-319-66694-5_7, S2CID 188856599; see Section 7.5, "Margaret Willerding", pp. 128–131.
  3. ^ a b c d e Bart, Jody (2000), Women Succeeding in the Sciences: Theories and Practices Across Disciplines, Purdue University Press, pp. 62–63, ISBN 9781557531223
  4. ^ a b c Murray, Margaret A. M. (2001), Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America, MIT Press, pp. 40, 57, 193–195, ISBN 9780262632461
  5. ^ Margaret Willerding at the Mathematics Genealogy Project
  6. ^ Willerding, Margaret (1948). "Determination of all classes of positive quaternary quadratic forms which represent all (positive) integers" (PDF). Bull. Amer. Math. Soc. 54 (4): 334–337. doi:10.1090/S0002-9904-1948-08998-4. MR 0024939. Zbl 0032.26603.
  7. ^ a b Conway, J.H. (2000). "Universal quadratic forms and the fifteen theorem". Quadratic forms and their applications (Dublin, 1999) (PDF). Contemp. Math. Vol. 272. Providence, RI: Amer. Math. Soc. pp. 23–26. ISBN 0-8218-2779-0. Zbl 0987.11026.
  8. ^ Bhargava, Manjul (2000). "On the Conway–Schneeberger fifteen theorem". Quadratic forms and their applications (Dublin, 1999) (PDF). Contemp. Math. Vol. 272. Providence, RI: Amer. Math. Soc. pp. 27–37. ISBN 0-8218-2779-0. MR 1803359. Zbl 0987.11027.
  9. ^ Mallinson, George G. (May 1976), "To Dr. Margaret F. Willerding: So That's What in H-a Dean Looks Like!", School Science and Mathematics, 76 (5), Wiley: 363–364, doi:10.1111/j.1949-8594.1976.tb09306.x
  10. ^ Review of The Business of Mathematics:
    • Spangler, Richard C. (October 1977), The Mathematics Teacher, 70 (7): 624, JSTOR 27961000{{citation}}: CS1 maint: untitled periodical (link)
  11. ^ Reviews of College Algebra and Trigonometry:
  12. ^ Reviews of Elementary Mathematics: Its Structure and Concepts:
  13. ^ Review of A First Course in College Mathematics: Module 4:
    • Spangler, Richard C. (February 1976), The Mathematics Teacher, 69 (2): 167, JSTOR 27960414{{citation}}: CS1 maint: untitled periodical (link)
  14. ^ Reviews of Mathematics: The Alphabet of Science:
  15. ^ Review of Modern Intermediate Algebra:
    • Skeen, Kenneth C. (December 1975), The Mathematics Teacher, 68 (8): 698, JSTOR 27960341{{citation}}: CS1 maint: untitled periodical (link)
  16. ^ Review of The Numbers Game:
    • Johnston, Hiram D. (December 1977), The Mathematics Teacher, 70 (9): 790, JSTOR 27961113{{citation}}: CS1 maint: untitled periodical (link)
  17. ^ Review of A Probability Primer:
    • Miller, David W. (February 1969), Management Science, 15 (6): B345, JSTOR 2628949{{citation}}: CS1 maint: untitled periodical (link)
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