Tom Brown (mathematician)

Tom Brown
Tom Brown
Born	Thomas Craig Brown; 1938 (age 85–86); Portland, Oregon, U.S.
Alma mater	Reed College (BS); Washington University in St. Louis (Ph.D.);
Known for	Brown's Lemma;
	Scientific career
Fields	Mathematics; Ramsey Theory;
Institutions	Simon Fraser University
Thesis	On Semigroups which are Unions of Periodic Groups (1964)
Doctoral advisor	Earl Edwin Lazerson

Thomas Craig Brown (born 1938) is an American-Canadian mathematician, Ramsey Theorist, and Professor Emeritus at Simon Fraser University.^[1]

Collaborations

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 showed that “for every $\varepsilon >0$ there is an $n(\varepsilon )$ such that if $n=dim(V)\geq n(\varepsilon )$ then any subset of $V$ with more than $\varepsilon |V|$ elements must contain 3 collinear points” where $V$ is an $n$ -dimensional affine space over the field with $p^{d}$ elements, and $p\neq 2$ ".

In Descriptions of the characteristic sequence of an irrational,^[5] Brown discusses the following idea: Let $\alpha$ be a positive irrational real number. The characteristic sequence of $\alpha$ is $f(\alpha )=f_{1}f_{2}\ldots$ ; where $f_{n}=[(n+1)\alpha ][\alpha ]$ .” 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 $[n\alpha ]$ .” He then gives some conclusions regarding the conditions for $[n\alpha ]$ which are equivalent to $f_{n}=1$ .

He has collaborated with Paul Erdős, including Quasi-Progressions and Descending Waves^[6] and Quantitative Forms of a Theorem of Hilbert.^[7]

References

^ "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.

External links

[1] "Tom Brown Professor Emeritus at SFU". Retrieved 10 November 2020.

[2] 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.

[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.

[4] 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.

[5] 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.

[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.

[7] 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.

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