Robert Hermann Breusch (April 2, 1907 – March 29, 1995) was a German-American number theorist, the William J. Walker Professor of Mathematics at Amherst College.[1][2]
Breusch was born in Freiburg, Germany, and studied mathematics both at the University of Freiburg and the University of Berlin.[1][3] Unable to secure a university position after receiving his doctorate, Breusch became a schoolteacher near Freiburg, where he met his future wife, Kate Dreyfuss; Breusch was Protestant, but Dreyfuss was Jewish, and the two of them left Nazi Germany for Chile in the mid-1930s.[1][4] They married there, and Breusch found a faculty position at Federico Santa María Technical University in Valparaiso.[1] In 1939, they left Chile for the United States, inviting Robert Frucht to take Breusch's place at Santa María;[5] after some years working again as a schoolteacher, Breusch found a position at Amherst College in 1943. He became the Walker professor in 1970, and retired to become an emeritus professor in 1973.[1][2] The Robert H. Breusch Prize in Mathematics, for the best senior thesis from an Amherst student, was endowed in his memory.[1]
As a mathematician, Breusch was known for his new proof of the prime number theorem[1][6] and for the many solutions he provided to problems posed in the American Mathematical Monthly.[1] His thesis work combined Bertrand's postulate with Dirichlet's theorem on arithmetic progressions by showing that each of the progressions 3i + 1, 3i + 2, 4i + 1, and 4i + 3 (for i = 0, 1, 2, ...) contains a prime number between x and 2x for every x ≥ 7.[3][7][8] For instance, he proved that for n > 47 there is at least one prime between n and (9/8)n. He also wrote a calculus textbook, Calculus and Analytic Geometry with Applications (Prindle, Weber & Schmidt, 1969) with C. Stanley Ogilvy.
^ abBrief biography (in German), German Mathematical Society, retrieved 2010-04-24.
^ abRobert Breusch at the Mathematics Genealogy Project.
^Siegmund-Schultze, Reinhard (2009), Mathematicians fleeing from Nazi Germany: individual fates and global impact, Princeton University Press, p. 131, ISBN 978-0-691-14041-4.
^Biography of Frucht (in Spanish), Walter Gaete and Raúl González, retrieved 2010-04-22.
^Breusch, R. (1954), "Another proof of the prime number theorem", Duke Mathematical Journal, 21 (1): 49–53, doi:10.1215/S0012-7094-54-02106-7, MR 0068567.
^Breusch, R. (1932), "Zur Verallgemeinerung des Bertrandschen Postulates, daß zwischenx und 2x stets Primzahlen liegen", Mathematische Zeitschrift (in German), 34 (1): 505–526, doi:10.1007/BF01180606, S2CID 121351858.
^Shorey, T. N.; Tijdeman, R. (1990), "On the greatest prime factor of an arithmetical progression", in Baker, Alan; Bollobás, Béla; Hajnal, A. (eds.), A Tribute to Paul Erdős, Cambridge University Press, pp. 385–390, ISBN 978-0-521-38101-7.
Robert Hermann Breusch (April 2, 1907 – March 29, 1995) was a German-American number theorist, the William J. Walker Professor of Mathematics at Amherst...
Breusch is a surname. Notable people with the surname include: RobertBreusch (1907–1995), German-American number theorist Trevor S. Breusch (born c. 1953)...
academia prevented him from obtaining the necessary visa. At the same time RobertBreusch, another German mathematician who had been working in Chile for three...
Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test...
function theory".) About the same time, similar results were published by RobertBreusch (1960) and Enrico Bombieri (1962). Elementary proofs of the prime number...
that has become more commonly used, particularly in econometrics, since Breusch and Pagan's much-cited 1980 paper. The main advantage of the score test...
Canada: Collector's Guide Publishing. p. 497. ISBN 978-1-894959-62-9. Breusch, Matthias (1992). "Review Album des Monats: W.A.S.P. - The Crimson Idol"...
night together ("Not What You See"). In a contemporary review, Matthias Breusch of Rock Hard magazine remarked how the album is the band's "most significant...
and Words". Metal Storm. January 9, 2004. Retrieved January 26, 2017. Breusch, Matthias (1992). "Review Album des Monats: Dream Theater – Images and...
the northern Vosges and the whole of the Wasgau, which lie north of the Breusch valley, fall within the Germanic-speaking area because, from Schirmeck...
2022 at the Wayback Machine, Hire: Journal of the Hire Industry, Keith Breusch Publishing Pty. Ltd., Sydney, Australia, volume 8, number 2, August/September...
only every life is precious but also every hour of that life. Matthias Breusch of Rock Hard praised the album for being "a super-melodic, varied, one...
and Time Series. Academic Press. ISBN 978-0-12-564922-3. (p. 375). Kass, Robert E.; Raftery, Adrian E. (1995), "Bayes Factors", Journal of the American...
Journal of Official Statistics. 9: 407–426. 1993. Jackson, Charles; Murphy, Robert F.; Kovačević, Jelena (September 2009). "Intelligent Acquisition and Learning...
Jeff. "Earliest Known Uses of Some of the Words of Mathematics". Harr, Robert R. (2012). Medical laboratory science review. Philadelphia: F. A. Davis...
article – see documents link at left Good and Hardin, chapter 8. Harris, Robert L. (1999). Information graphics : a comprehensive illustrated reference...
Autocorrelation Plot". www.itl.nist.gov. Retrieved 2022-07-14. Shumway, Robert H.; Stoffer, David S. (2017). Time Series Analysis and Its Applications:...
loss Hinge loss Scoring rule Statistical risk Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome H. (2001). The Elements of Statistical Learning. Springer...
of Economics, UCSD. 2003 (15). Retrieved 2007-05-30. Cited in Varian. Breusch, Trevor; Edith Gray (2004-09-17). "Does marriage improve the wages of men...
Applications, Vol I. Wiley. p. 221. ISBN 0471257087. Elementary Statistics by Robert R. Johnson and Patricia J. Kuby, p. 279 Weisstein, Eric W. "Population Mean"...
103–123. doi:10.3758/s13423-015-0947-8. PMC 4742505. PMID 26450628. Matthews, Robert (2021). "The p-value statement, five years on". Significance. 18 (2): 16–19...
PMID 24361065. S2CID 7799662. Roche, Dominique G.; Kruuk, Loeske E. B.; Lanfear, Robert; Binning, Sandra A. (2015). "Public Data Archiving in Ecology and Evolution:...
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