Past junior combinatorics seminars

Summer 2007

Week 1 (17 July): Robert Berke. Transversals in multipartite graphs.

Trinity 2007

Week 2 (1 May): Louigi Addario-Berry. Acyclic dominating partitions.

Week 3 (8 May): Luis Cereceda (LSE). Finding paths between graph colourings.

Week 5 (22 May): Nicolas Broutin (McGill). About weighted heights of trees.

Hilary 2007

Week 4 (6 Feb): Bilyana Shoilekova. Unlabelled enumeration of treelike graphs using cycle indices.

Bean-Shaped Bodies

Mathematics is not usually considered an experimental science. However, there are many analogies between the approach to mathematical research and the more familiar experimental scientific process. While mathematicians do not usually go out and directly observe and experiment with real-world phenomena, research is by no means entirely deductive. Attempting to solve a problem can entail much trial and error, guesswork, and experimentation. When trying to prove or disprove a theorem, a good starting point is looking for counter-examples.

Ruled Surfaces

A ruled surface is defined by the property that through every point in the surface, there is at least one straight line which also lies in the surface. A ruled surface may be thought of as one "swept out" by a straight line moving in space. To describe how such a line moves, first recall that any line is uniquely determined by two distinct points which lie on it. Then by choosing two curves, and a suitable map between their points, we can join up points with lines in order to define a ruled surface.


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