Development of a Game-Based Mathematics Curriculum for Preschool

America’s deficiency in mathematics can be benefitted by an emphasis in mathematics from an early age. An effective math curriculum for preschool should consist of the most important aspects of early childhood mathematics, including number writing and identification, one-to-one correspondence, cardinality, number comparison, ordinality, number sequence, and number bonds.

Combining Leaf Shape and Texture for Costa Rican Plant Species Identification

In the last decade, research in Computer Vision has developed several algorithms to help botanists and non-experts to classify plants based on images of their leaves. LeafSnap is a mobile application that uses a multiscale curvature model of the leaf margin to classify leaf images into species. It has achieved high levels of accuracy on 184 tree species from Northeast US. We extend the research that led to the development of LeafSnap along two lines. First, LeafSnap’s underlying algorithms are applied to a set of 66 tree species from Costa Rica. Then, texture is used as an additional criterion to measure the level of improvement achieved in the automatic identification of Costa Rica tree species. A 25.6% improvement was achieved for a Costa Rican clean image dataset and 42.5% for a Costa Rican noisy image dataset. In both cases, our results show this increment as statistically significant. Further statistical analysis of visual noise impact, best algorithm combinations per species, and best value of , the minimal cardinality of the set of candidate species that the tested algorithms render as best matches is also presented in this research

Almost Disjoint Families of Representing Sets

The thesis is concerned with a number of problems in Combinatorial Set Theory. The Generalized Continuum Hypothesis is assumed. Suppose X and K are non-zero cardinals. By successively identifying K with airwise disjoint sets of power K, a function/: X-*•K can be viewed as a transversal of a pairwise disjoint (X, K)family A . Questions about families of functions in K can thus bethought of as referring to families of transversals of A. We wish to consider generalizations of such questions to almost disjoint families; in particular we are interested in extensions of the following two problems: (i) What is the 'maximum' cardinality of an almost disjoint family of functions each mapping X into K? (ii) Describe the cardinalities of maximal almost disjoint families of functions each mapping X into K. Article in Bulletin of the Australian Mathematical Society 27(03):477 - 479 · June 1983  

Automorphisms of irreducible holomorphic symplectic manifolds and related problems

We study automorphisms and the mapping class group of irreducible holomorphic symplectic (IHS) manifolds. We produce two examples of manifolds of K3[2] type with a symplectic action of the alternating group A7. Our examples are realized as double EPW-sextics, the large cardinality of the group allows us to prove the irrationality of the associated families of Gushel-Mukai threefolds. We describe the group of automorphisms of double EPW-cubes. We give an answer to the Nielsen realization problem for IHS manifolds in analogy to the case of K3 surfaces, determining when a finite group of mapping classes fixes an Einstein (or Kähler-Einstein) metric. We describe, for some deformation classes, the mapping class group and its representation in second cohomology. We classify non-symplectic involutions of manifolds of OG10 type determining the possible invariant and coinvariant lattices. We study non-symplectic involutions on LSV manifolds that are geometrically induced from non-symplectic involutions on cubic fourfolds.