James Donaldson

### Personal

 First Name: James
 Last Name: Donaldson

### Education

 College: University of Illinois-Urbanna
 Degree: Ph.D.

 College: Lincoln University
 Degree: B.A.
 Major: Mathematics

 College: University of Illinios
 Degree: M.S.
 Birthplace: Madison County Florida   RESEARCH NOTES Dr. James A. Donaldson's interests in differential equations (especially boundary value problems for partial differential equations) have continued and his research publications include numerous papers in analysis, differential equations and applied mathematics. He has lectured widely on his research in North America, Africa, Asia, and Europe. Under consideration presently are questions arising in the theory of shallow water. You may obtain information about, view, and download some of his 18 publications at Dr. Donaldson's personal web page. Donaldson interests also include History of Mathematics and Mathematics Accessibilty Issues, and he has published in these areas as well. SELECTED PUBLICATIONS Integral representations of the extended Airy integral type for the modified Bessel function, J. Math. and Phys. 46 (1967), 111--114. 33.25 Expansions for $K\sb{\nu }\,(\xi )$ involving Airy's function, Proc. Cambridge Philos. Soc. 66 (1969), 91--94. 33.25 A singular abstract Cauchy problem, Proc. Nat. Acad. Sci. U.S.A. 66 (1970), 269--274. 35.97 (34.00) (with R. Hersh) A perturbation series for Cauchy's problem for higher-order abstract parabolic equations, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 41--44. 47.65 (35.00) New integral representations for solutions of Cauchy's problem for abstract parabolic equations, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 2025--2027. 35.95 (47.00) An operational calculus for a class of abstract operator equations, J. Math. Anal. Appl. 37 (1972), 167--184. 35R20 (47D05) (with A. G. Gibson and R. Hersh) On the invariance principle of scattering theory, J. Functional Analysis 14 (1973), 131--145. 47A40 (with G. H. Butcher) Regular and singular perturbation problems for a singular abstract Cauchy problem, Duke Math. J. 42 (1975), 435--445. 47D05 (35R20) The abstract Cauchy problem, J. Differential Equations 25 (1977), 400--409. 34G05 (with Jerome A. Goldstein) Some remarks on uniqueness for a class of singular abstract Cauchy problems, Proc. Amer. Math. Soc. 54 (1976), 149--153. 34G05 (47A50) The Cauchy problem for a first order system of abstract operator equations, Bull. Amer. Math. Soc. 81 (1975), 576--578. 34G05 (47A50) (with Daniel A. Williams) The linear shallow water theory: a mathematical justification, SIAM J. Math. Anal. 24 (1993), 892--910. 35Q35 (76B15) (with Daniel A. Williams) An abstract two-point boundary value problem, Mathematical analysis, wavelets, and signal processing (Cairo, 1994), Contemp. Math., 190 (1995), Amer. Math. Soc., Providence, RI, 107--116. 34G10 (47N20) History of Mathematics Black Americans in mathematics, A century of mathematics in America, Part III, 449--469, Hist. Math., 3, Amer. Math. Soc., Providence, RI, 1989. 01A80 (01A60)   from two rooms to the university James Ashley Donaldson was born on a farm in rural Madison County, Florida, in 1941. His parents, Audrey Brown and Oliver Donaldson, had three daughters and eight sons. His uncle Enoch Donaldson, a largely self-taught man, taught little James how to read, write, and calculate long before he entered elementary school. The first eight grades of his education were provided in a two-room rural school house--grades one through four taught in one room by Ms. Lennie L. Collins and grades five through eight taught in the other room by Mrs. Alma Jean McKinney. Along with his Uncle Enoch, these two teachers and later his high school mathematics teacher Mrs. Juanita Miller were great influences on his early life. When the Supreme Court decision striking down segregated public schools was issued in 1954, Donaldson was in the tenth grade. Donaldson's questions concerning the continuation of the dual segregated educational system after this landmark decision caused some concern for his safety and his education. "During my unior and senior year in high school, my mathematics teacher [Ms. Juanita Miller] who had gone to Hampton, suggested that I take some scholarship examinations, then provided by the United Negro College Fund" It was Mrs. Miller who encouraged Donaldson to go north for his college education. "She thought Lincoln University would be a good place for me to go." As a result of Miller's recommendation and assistance, Donaldson entered Lincoln University near Oxford, Pennsylvania in 1957. Initially, Donaldson was unsure of the course of study he would pursue in college. His interest in studying biology ended quickly after being presented a pickled frog and being told by the biology instructor that each successful student would be expected to dissect this unfortunate frog and learn each of its muscles and bones. Interest in pursuing studies leading to an engineering degree ceased when he learned that opportunities for minority engineers were very limited. Although chemistry and physics interested him as well, he discovered that the mathematics co-requisite for these disciplines were more interesting. The energetic and clear mathematics teaching of Professor James Frankowsky [an African American mathematician] was also a great contributing factor in his decision to major in Mathematics. So in 1961 he graduated from Lincoln University with an AB degree in Mathematics. After the Bachelor's degree, Donalson decided to join the military. So he went to Chicago to be in the Navy. "I learned that I was about one and half inch higher than the height restriction." Professor Frankowsky encouraged him to pursue a graduate degree in Mathematics. In the six months between college and graduate school "The people of the Alumni Association of Lincoln University in Chicago more or less supported me. They thought they were giving me the money, but I kept accurate records of what I received from each person. On of the first things I did after getting my Ph.D. was to pay each person back with interest." He enrolled in the graduate program at the University of Illinois in Urbana-Champaign. Donaldson liked the Mathematics Department at the University of Illinois. He found constraining, character building and inconvenient, however, the elements of racism and racial tensions that existed on the campus-- mainly in housing and some on-campus employment-- and in the wider community. All during his graduate days at the University of Illinois he was part of the unending campaign to rid that community of all vestiges of both subtle and overt racism. He recalls vividly one incident that occurred during his first year at the University. He was given a summer position as a computer operator. The Director of the Computer Center told Donaldson that he needed to go to the university's employment center to complete an application. A few weeks later he was informed by the employment service that he had received a score of 71 on his employment entrance examination. This information was a puzzle since Donaldson had completed only an application form. A co-worker told Donaldson of his good fortune to have been given the position before completing the application because the employment service's practice was to send for interviews for the position the three applicants receiving the highest scores. Upon questioning how the examination was scored, Donaldson was told 70 points was given for completing high school, and five additional points were given for every additional year of post-secondary education. The employment service was unable to explain how Donaldson, a first year graduate student, had received a score of only 71.