Thesis (M.A.)--Brigham Young University. Dept. of Mathematics Education, 2007. / Includes bibliographical references (p. 80-82).

Thesis (M. Ed)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 79-82).

Thesis (M.Ed)--University of Hong Kong, 1998. / Includes bibliographical references (leaves 79-82). Also available in print.

No description available.

Thesis (M.A.)--Victoria University of Wellington, 2008. / Includes bibliographical references.

Thesis (Ph. D.)--Illinois State University, 2004. / Title from title page screen, viewed Jan. 11, 2005. Dissertation Committee: Jeffrey Barrett, Sharon McCrone (co-chairs), Saad El-Zanati. Includes bibliographical references (leaves 192-204) and abstract. Also available in print.

Thesis (M.Ed.) -- Memorial University of Newfoundland. / Bibliography : leaves 77-82. Also available online.

The construction introduced by Gross, Hacking and Keel in [28] allows one to construct a mirror family to (S, D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti-ample class. To do so one constructs a formal smoothing of a singular variety they call the n-vertex. By arguments of Gross, Hacking and Keel one knows that this construction can be lifted to an algebraic family if the intersection matrix for D is not negative semi-definite. In the case where the intersection matrix is negative definite the smoothing exists in a formal neighbourhood of a union of analytic strata. A proof of both of these is found in [GHK]. In our first project we use these ideas to find explicit formulae for the mirror families to low degree del Pezzo surfaces. In the second project we treat the remaining case of a negative semi-definite intersection matrix, corresponding to S being a rational elliptic surface and D a rational fibre. Using intuition from the first project we prove in the second project that in this case the formal family of their construction lifts to an analytic family.

Thesis (M.Ed. (Education)) - Rhodes University, 2009. / Submitted in partial fulfilment of the requirements for the degree of Master in Education (Mathematics Education)

This thesis contains two main results. The first is a comparison formula for the Donaldson-Thomas invariants of two (complex, smooth and projective) Calabi-Yau threefolds related by a flop; the second is a proof of the projective case of the Crepant Resolution Conjecture for Donaldson-Thomas invariants, as stated by Bryan, Cadman and Young. Both results rely on Bridgeland’s category of perverse coherent sheaves, which is the heart of a t-structure in the derived category of the given Calabi-Yau variety. The first formula is a consequence of various identities in an appropriate motivic Hall algebra followed by an implementation of the integration morphism (using the technology of Joyce and Song). Our proof of the crepant resolution conjecture is a quick and elegant application of the first formula in the context of the derived McKay correspondence of Bridgeland, King and Reid. The first chapter is introductory and is followed by two chapters of background material. The last two chapters are devoted to the proofs of the main results.