Hans Adolph Rademacher(German:[ˈʁaːdəmaxɐ];3 April 1892 – 7 February 1969) was aGerman-born Americanmathematician,known for work inmathematical analysisandnumber theory.
Hans Adolph Rademacher | |
|---|---|
| Born | 3 April 1892 |
| Died | 7 February 1969(aged 76) |
| Education | University of Göttingen |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Berlin University of Hamburg University of Pennsylvania |
| Doctoral advisor | Constantin Carathéodory |
| Notable students | George Andrews Paul T. Bateman Leila Bram Theodor Estermann Emil Grosswald |
Biography
editRademacher received his Ph.D. in 1916 fromGeorg-August-Universität Göttingen;Constantin Carathéodorysupervised his dissertation.[1]In 1919, he becameprivatdozentunderConstantin CarathéodoryatUniversity of Berlin.In 1922, he became an assistant professor at theUniversity of Hamburg,where he supervised budding mathematicians likeTheodor Estermann.[2]He was dismissed from his position at theUniversity of Breslauby theNazisin 1933 due to his public support of theWeimar Republic,[3]and emigrated from Europe in 1934.
After leaving Germany, he moved toPhiladelphiaand worked at theUniversity of Pennsylvaniauntil his retirement in 1962; he held theThomas A. Scott Professorship of Mathematicsat Pennsylvania from 1956 to 1962. Rademacher had a number of well-known students, includingGeorge Andrews,Paul T. Bateman,Theodor EstermannandEmil Grosswald.
Research
editRademacher performed research inanalytic number theory,mathematicalgenetics,thetheory of functions of a real variable,andquantum theory.Most notably, he developed the theory ofDedekind sums.In 1937 Rademacher discovered an exact convergent series for thepartition functionP(n), the number of integer partitions of a number, improving uponRamanujan's asymptotic non-convergent series and validating Ramanujan's supposition that an exact series representation existed.
Awards and honors
editWith his retirement from theUniversity of Pennsylvania,a group of mathematicians provided the seed funding for The Hans A. Rademacher Instructorships, and honored him with an honorary degree as Doctor of Science.
Rademacher is the co-author (withOtto Toeplitz) of the popular mathematics bookThe Enjoyment of Mathematics,published in German in 1930 and still in print.[4][5]
Works
edit- withOtto Toeplitz:Von Zahlen und Figuren.1930. 2nd edn. 1933. Springer 2001,ISBN3-540-63303-0.[6]
- The Enjoyment of Mathematics.Von Zahlen und Figurentranslated into English by Herbert Zuckerman, Princeton University Press, 1957[7]
- withErnst SteinitzVorlesungen über die Theorie der Polyeder- unter Einschluss der Elemente der Topologie.Springer 1932, 1976.
- Generalization of the Reciprocity Formula for Dedekind Sums.In:Duke Math. Journal.Vol. 21, 1954, pp. 391–397.
- Lectures on analytic number theory.1955.
- Lectures on elementary number theory.Blaisdell, New York 1964, Krieger 1977.
- with Grosswald:Dedekind sums.Carus Mathematical Monographs 1972.
- Topics in analytic number theory.[8]ed. Grosswald. Springer Verlag, 1973 (Grundlehren der mathematischen Wissenschaften).
- Collected papers.2 vols. ed. Grosswald. MIT press, 1974.
- Higher mathematics from an elementary point of view.Birkhäuser 1983.
Further reading
edit- George E. Andrews, David M. Bressoud, L. Alayne Parson (eds.)The Rademacher legacy to mathematics.American Mathematical Society, 1994.
- Lexikon bedeutender Mathematiker.Deutsch, Thun, Frankfurt am Main,ISBN3-8171-1164-9.
- Tom Apostol:Introduction to Analytical number theory.Springer
- Tom Apostol:Modular functions and Dirichlet Series in Number Theory.Springer
- Berndt, Bruce C.(1992)."Hans Rademacher (1892–1969)"(PDF).Acta Arithmetica.61(3): 209–231.doi:10.4064/aa-61-3-209-225.Retrieved2009-02-07.Obituary and list of publications.
See also
editReferences
edit- ^Hans Rademacherat theMathematics Genealogy Project.
- ^"Theodor Estermann - Biography".Maths History.Retrieved2022-08-24.
- ^Siegmund-Schultze, Reinhard (2009).Mathematicians fleeing from Nazi Germany: individual fates and global impact.Princeton University Press. p.69.ISBN978-0-691-14041-4..
- ^The Enjoyment of MathReview by Allen Stenger,Mathematical Association of America
- ^Oakley, C. O. (October 1957). "Recent publications:The Enjoyment of Mathematics".The American Mathematical Monthly.64(8): 603.doi:10.2307/2308857.JSTOR2308857.
- ^Wrinch, D. M. "Review: Von Zahlen und Figuren: Proven mathematischen Denkens für Liebhaber der Mathematik by Hans Rademacher, Otto Toeplitz"The Mathematical Gazette,vol. 16, no. 217, 1932, pp. 63–63. JSTOR,https://doi.org/10.2307/3608155.Accessed 11 Aug. 2022.
- ^Benz, Harry E. "Review: The Enjoyment of Mathematics by Hans Rademacher, Otto Toeplitz"The Mathematics Teacher,vol. 50, no. 6, 1957, pp. 454–455. JSTOR,http://www.jstor.org/stable/27955473.Accessed 11 Aug. 2022.
- ^Stark, H. M.(1975)."Review: Hans Rademacher,Topics in analytic number theory".Bull. Amer. Math. Soc.81(4): 663–672.doi:10.1090/s0002-9904-1975-13815-8.