Tom Brown (mathematician)

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

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' In 1963 as a graduate student, he showed that if the positive integers are finitely colored, then some color class is piece-wise syndetic.

In A Density Version of a Geometric Ramsey Theorem. he and Joe P. Buhler show 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, 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 and Quantitative Forms of a Theorem of Hilbert.