Mathematics Abstracts of Presentations

Some open problems in Domain Theory

Ho Weng Kin

Domain theory, roughly speaking, is topology done on partially ordered sets, and is hence a meeting place of Topology and Order. Being a successful theory in explaining the phenomenon of approximation in many contexts ranging from Computer Science to even linguistics, Domain Theory is very rich in itself as a field of mathematical study. In this talk, we shall look at some open problems in Domain Theory which are both interesting in their own right and important in the mainstream theoretical development.

Independence polynomials and independence equivalence classes

Ng Boon Leong

The independence polynomial of a graph $G$ is the polynomial where the coefficient of $x^k$ is the number of independent sets in $G$ of cardinality $k$. Graphs with the same independence polynomial are called independence equivalent graphs. In this presentation, some properties of the independence polynomial will be discussed, with an emphasis on independence equivalence of trees and cyclic graphs.

Baire One Functions

Vera Lee Man Er

We are all familiar with the epsilon-delta definition of continuity at a point. Given an equivalent definition of continuity, we would like to study the type of functions that can be obtained when a simple modification to this definition is made.

l,+m systems for positive integer pairs

Janice Lim Hong Min

Given the numbers 1,1,2,2,3,3,4,4, how can we arrange them in a row such that there are exactly r-1 numbers between a pair of `r' where r=1,2,3,4? And is there always a way to arrange 2n numbers, 1,1,2,2,3,3,…,n,n in this way for different values of n where n∈N?
Thoralf Skolem explored this problem in his paper. My project involves rewriting his paper in a more detailed and comprehensive manner with additional theorems as extensions and addressing certain errors made in the paper. In this presentation, I will prove some of the main results and include a few computer programming codes created using Visual Basic for Applications (VBA) on Excel to demonstrate the l,+m systems for different values.

Combinatorial Identities

Dong Fengming

An interpretation to an identity is very helpful for understanding the identity. Finding an interpretation to an identity may be quite challenging for students. This talk will introduce some well-known combinatorial identities and their interpretations.