Mathematics Abstracts of Presentations

Reflection on my research done at NIE

Teo Beng Chong

In this talk, I would like to share some of things I did for the various research projects undertaken over the years at NIE. Since I joined NIE in 1992, there have been many opportunities to participate in various projects and initiative programs such as the IT Master Plans (various phases), CITE, SMAPP, TDU, edulab, MDA Testbed, Maker Space and CRPP/OER with over a few millions of funding involved. I will be talking about some of these work, their outcomes and some lessons I have learned through them.

Proofs of Eta Quotients Identities and its Applications to Ramanujan’s Congruences

Chun Guan Yang

Abstract: The Jacobi Triple Product Identity and Quintuple Product Identity are two well-known identities, as we can represent an infinite product as an infinite sum of a closed form expression. By using the Triple and Quintuple Product Identity, we can derive other identities called the eta quotient identities, where we can express products or quotients of Dedekind eta functions as a single variate theta function. Oliver proved that there are only twenty eta quotient identities which can be expressed as a single variate theta function but did not prove these identities. We aim to cover the gap by including all twenty proofs of the eta quotient identities. Some of these eta quotient identities can be used to prove two of Ramanujan’s partition congruences for the partition function, which is considered as an uncommon approach. Other than proving Ramanujan’s partition congruence, we aim to introduce two other expressions conjectured by Lin which has some fascinating partition congruences and prove the partition congruences using the eta quotient identities.

Hamilton Decompositions of Graphs

Hang Hao Chuien

The talk will introduce and define relevant concepts, and survey the topic of Hamilton decompositions of graphs. Some new results that we have recently obtained in this area will then be presented

Statistics on Ascent Sequences

Soh Chin Gi

High-dimensional spectroscopic data is informative, and has applications in many fields such as biomedical sciences and food science. The fitting of regression models for the purposes of prediction is known to be a challenging task due to the high-dimension of the datasets, as well as high correlation between wavenumbers in the data. One method that has gained interest in recent years is the use of regularization to overcome these challenges. In this talk, we present a regularized model for spectroscopic data. Depending on the penalty functions used in the regularized model, different computational challenges may arise. We will discuss some algorithms that are of interest in solving for such regularized model coefficients, as well as the advantages and disadvantages of these algorithms.

A Haskell Implementation of the Lyness-Moler's Numerical Differentiation Algorithm

Ho Weng Kin

This paper describes a computational problem encountered in numerical differentiation. By restricting the problem to a proper subclass of differentiable functions, a numerical solution first proposed by Lyness and Moler is considered and implemented in the functional programming language Haskell. The accuracy of the calculation of the numerical derivative using the Lyness-Moler's method crucially lies in our recursive algorithm for computing contour integrals.