Thomas Craig Brown (born 1938) is an American-Canadian mathematician, Ramsey Theorist, and Professor Emeritus at Simon Fraser University.[1]
Tom Brown | |
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| Born | Thomas Craig Brown 1938 (age 85–86) Portland, Oregon, U.S. |
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| Institutions | Simon Fraser University |
| Thesis | On Semigroups which are Unions of Periodic Groups (1964) |
| Doctoral advisor | Earl Edwin Lazerson |
Collaborations edit
As a mathematician, Brown’s primary focus in his research is in the field of Ramsey Theory. When completing his Ph.D., his thesis was 'On Semigroups which are Unions of Periodic Groups'[2] In 1963 as a graduate student, he showed that if the positive integers are finitely colored, then some color class is piece-wise syndetic.[3]
In A Density Version of a Geometric Ramsey Theorem.[4] he and Joe P. Buhler show that “for every there is an such that if then any subset of with more than elements must contain 3 collinear points” where is an -dimensional affine space over the field with elements, and ".
In Descriptions of the characteristic sequence of an irrational,[5] Brown discusses the following idea: Let be a positive irrational real number. The characteristic sequence of is ; where .” From here he discusses “the various descriptions of the characteristic sequence of α which have appeared in the literature” and refines this description to “obtain a very simple derivation of an arithmetic expression for .” He then gives some conclusions regarding the conditions for which are equivalent to .
![{\displaystyle f_{n}=[(n+1)\alpha ][\alpha ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/967b9889bac3577a53866c5fd3c88ede0f311662)
![{\displaystyle [n\alpha ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52a2a404aa178e221c4b6e91cc8d4d300c70ebda)
He has collaborated with Paul Erdős, including Quasi-Progressions and Descending Waves[6] and Quantitative Forms of a Theorem of Hilbert.[7]
References edit
- ^ "Tom Brown Professor Emeritus at SFU". Retrieved 10 November 2020.
- ^ Jensen, Gary R.; Krantz, Steven G. (2006). 150 Years of Mathematics at Washington University in St. Louis. American Mathematical Society. p. 15. ISBN 978-0-8218-3603-3.
- ^ Brown, T. C. (1971). "An interesting combinatorial method in the theory of locally finite semigroups" (PDF). Pacific Journal of Mathematics. 36 (2): 285–289. doi:10.2140/pjm.1971.36.285.
- ^ Brown, T. C.; Buhler, J. P. (1982). "A Density version of a Geometric Ramsey Theorem" (PDF). Journal of Combinatorial Theory. Series A. 32: 20–34. doi:10.1016/0097-3165(82)90062-0.
- ^ Brown, T. C. (1993). "Descriptions of the Characteristic Sequence of an Irrational" (PDF). Canadian Mathematical Bulletin. 36: 15–21. doi:10.4153/CMB-1993-003-6.
- ^ Brown, T. C.; Erdős, P.; Freedman, A. R. (1990). "Quasi-Progressions and Descending Waves". Journal of Combinatorial Theory. Series A. 53: 81–95. doi:10.1016/0097-3165(90)90021-N.
- ^ Brown, T. C.; Chung, F. R. K.; Erdős, P. (1985). "Quantitative Forms of a Theorem of Hilbert" (PDF). Journal of Combinatorial Theory. Series A. 38 (2): 210–216. doi:10.1016/0097-3165(85)90071-8.