No description available.

No description available.

There is no abstract available for this dissertation.

The central result presented in this thesis is van der Waerden's theorem on arithmetic progressions. Van der Waerden's theorem guarantees that for any integers k and r, there is an n so that however the set {1, 2, ... , n} is split into r disjoint partition classes, at least one partition class will contain a k-term arithmetic progression. Presented here are a number of variations and generalizations of van der Waerden's theorem that utilize a wide range of techniques from areas of mathematics including combinatorics, number theory, algebra, and topology.

No description available.

The central result presented in this thesis is van der Waerden's theorem on arithmetic progressions. Van der Waerden's theorem guarantees that for any integers k and r, there is an n so that however the set {1, 2, ... , n} is split into r disjoint partition classes, at least one partition class will contain a k-term arithmetic progression. Presented here are a number of variations and generalizations of van der Waerden's theorem that utilize a wide range of techniques from areas of mathematics including combinatorics, number theory, algebra, and topology.

No description available.

Bibliography: leaves 121-123 / viii, 123 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1985

Thesis (Ph. D.)--University of Missouri, 1929. / Vita. Bibliography: p. 52. Also issued in print.

Thesis (Ph. D.)--Catholic University of America, 1926. / Published also as Catholic University of America. Educational research bulletins ... vol. I, nos. 4-5. Bibliography: p. 71-74.