Adolph Winkler Goodman

Adolph Winkler Goodman (July 20, 1915 – July 30, 2004) was an American mathematician who contributed to number theory, graph theory and to the theory of univalent functions:[2] The conjecture on the coefficients of multivalent functions named after him is considered the most interesting challenge in the area after the Bieberbach conjecture, proved by Louis de Branges in 1985.[3]

Adolph Winkler Goodman
Born(1915-07-20)July 20, 1915
DiedJuly 30, 2004(2004-07-30) (aged 89)
NationalityAmerican
Known forAnalytic geometry, graph theory, number theory
Scientific career
FieldsMathematics
ThesisOn some determinants related to ρ-Valent functions (1947)
Doctoral advisorOtto Szász, Edgar Raymond Lorch[1]

Life and workEdit

In 1948, he made a mathematical conjecture on coefficients of ρ-valent functions, first published in his Columbia University dissertation thesis[4] and then in a closely following paper.[5] After the proof of the Bieberbach conjecture by Louis de Branges, this conjecture is considered the most interesting challenge in the field,[3] and he himself and coauthors answered affirmatively to the conjecture for some classes of ρ-valent functions.[6] His researches in the field continued in the paper Univalent functions and nonanalytic curves, published in 1957:[7] in 1968, he published the survey Open problems on univalent and multivalent functions,[8] which eventually led him to write the two-volume book Univalent Functions.[9][10]

Apart from his research activity, He was actively involved in teaching: he wrote several college and high school textbooks including Analytic Geometry and the Calculus, and the five-volume set Algebra from A to Z.[2]

He retired in 1993, became a Distinguished Professor Emeritus in 1995, and died in 2004.[2]

Selected worksEdit

NotesEdit

  1. ^ Adolph Winkler Goodman at the Mathematics Genealogy Project
  2. ^ a b c See the brief obituary on him published on the newsletter of the department of Mathematics of the University of South Florida.
  3. ^ a b According to Hayman (1994, p. xi and p. 163).
  4. ^ Goodman, A W (1948). On some determinants related to ρ-valent formulas. Columbia University. OCLC 36602209..
  5. ^ Goodman, A. W. (1948). "On some determinants related to ρ-valent formulas". Transactions of the American Mathematical Society. 63 (1): 175–92. doi:10.1090/S0002-9947-1948-0023910-X.
  6. ^ His contributions are described in the brief survey on Goodman's conjecture found in (Hayman 1994, pp. 162–163).
  7. ^ Goodman, A. W. (1957). "Univalent functions and nonanalytic curves". Proceedings of the American Mathematical Society. 8 (3): 598–601. doi:10.1090/S0002-9939-1957-0086879-9.
  8. ^ Goodman, A. W. (1968). "Open problems on Univalent and multivalent functions". Bulletin of the American Mathematical Society. 74 (6): 1035–1051. doi:10.1090/S0002-9904-1968-12045-2.
  9. ^ Goodman, A. W. (1983). Univalent functions. Univalent Functions. Vol. 1. Mariner Pub. Co. ISBN 9780936166100. LCCN 83007930.
  10. ^ Goodman, A.W. (1983). Univalent functions. Univalent Functions. Vol. 2. Mariner Pub. Co. ISBN 9780936166117. LCCN 83007930.

Biographical referencesEdit

  • Grinshpan, Arcadii Z. (1997), "A. W. Goodman: research mathematician and educator", Complex Variables, Theory and Application, 33 (1–4): 1–28, doi:10.1080/17476939708815008
  • The Editorial Staff (2004). "In Memoriam: Al Goodman". The Quaternion - the Newsletter of the Department of Mathematics. University of South Florida. 19 (1).

ReferencesEdit

Additional sourcesEdit