Thomas Craig Brown (born 1938) is an American-Canadian mathematician, Ramsey Theorist, and Professor Emeritus at Simon Fraser University.
As a mathematician, BrownâÂÂs 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 showed that âÂÂfor every there is an such that if then any subset of with more than elements must contain 3 collinear pointsâ where is an -dimensional affine space over the field with elements, and ".
In Descriptions of the characteristic sequence of an irrational, Brown discusses the following idea: Let be a positive irrational real number. The characteristic sequence of is ; where .â From here he discusses âÂÂthe various descriptions of the characteristic sequence of ñ which have appeared in the literatureâ and refines this description to âÂÂobtain a very simple derivation of an arithmetic expression for .â He then gives some conclusions regarding the conditions for which are equivalent to .
He has collaborated with Paul Erdà Âs, including Quasi-Progressions and Descending Waves and Quantitative Forms of a Theorem of Hilbert.