## Profiles

# Kumudini Dharmadasa

# Kumudini Dharmadasa

## Lecturer

Room 459, Maths-Physics Building, Sandy Bay Campus

Dr. Kumudini Dharmadasa is a lecturer at the Discipline of Mathematics, School of Physical Science. Her broad area of interest is Pure Mathematics in which she teaches from year 1 to year 4 levels. Her main field of research is the Theory of Representations. She is also committed to many community engagement activities which involves the mathematics education at school level: (i) catering for the Gifted; (ii) Pre-tertiary maths education; (iii) Nurturing maths talent of the educators responsible for the Gifted.

### Biography

Kumudini obtained her Masters Degree in Mathematics at the University of Ottawa, Canada and the PhD at the University of Adelaide, South Australia. She was a lecturer at the University of Kelaniya prior to this. She joined the University of Tasmania as a tutor, and is now a lecturer in Mathematics.

### Career summary

#### Qualifications

Degree | Thesis Title | University | Country | Date of Award |
---|---|---|---|---|

PhD | The Theory of A^{p}_{q } Spaces | University of Adelaide | Australia | 1996 |

M.Sc (Course work and Thesis) | Random Walks on Groups | University of Ottawa | Canada | 1984 |

BSc (1^{st} Class Hons) | Galois Theory | University of Kelaniya | Sri Lanka | 1979 |

#### Languages (other than English)

Sinhalese

### Memberships

#### Professional practice

- Australian Mathematics Trust
- Australian Maths Teachers Association

### Administrative expertise

Kumudini is regularly involved in organising community engagement projects and schemes which enhances maths education of pre-tertiary students and teachers in Tasmania.

### Teaching

Real and Complex Analysis, Calculus, Abstract Algebra, Theory of Integration, Functional Analysis

#### Teaching responsibility

- KMA152 - Calculus and Applications 1A
- KMA251 - Algebra and Applications 2
- KMA352 - Analysis 3
- KMA427 Functional Analysis (Honours)
- KMA444 The Theory of Measure and Integration (Honours)

### Research Invitations

2015: Towards Educating Mathematics Professionals Encompassing Science and Technology (TEMPEST)

View more on Dr Kumudini Dharmadasa in WARP

### Expertise

- Harmonic Analysis
- Theory of Topological groups
- Theory of Group Representations
- Theory of Integration

Kumudini is also interested in research which aims at seeking strategies which enhance teaching methods for (i) gifted students in mathematics, (ii) pre-tertiary - tertiary transition, (iii) educating teachers responsible for the gifted students in mathematics.

### Research Themes

Kumudini's research aligns with the University's research theme of Data, Knowledge and Decisions. One fo the aims of her research is to use MODIS satellite data to obtain 'Change Detection Algorithms' which can predict whether a change is occurring, for instance, in vegetation in a particular part of the world. This involves (mainly) using analytical methods in Stochastic Processes and Fourier Analysis. Her main research theme is The Theory of Representations, which is a Pure Mathematics area.

### Collaboration

*Assessment Standards In Undergraduate Mathematics – Part 2:* Kumudini has joined the Monash University team working on the project 'Assessment
Standards In Undergraduate Mathematics – Part 2'. This was a part of the
national project *Maths Assess* led by
Universities of Monash, Melbourne and Western Sydney. The main project aimed at
delivering mathematics assessment standards and a system of rubrics that
clearly identify the levels of standards which are applicable for all tertiary
institutions.

*The TEMPEST project (Advisory Group): *This is a national project targeting teachers of
mathematics K-12, and including the VET sector. It aims to build the capacity
of teachers to engage and inspire students through increased knowledge and
pedagogical skill. The project will support professional Mathematics teacher
development with aid of the national framework for the creation,
implementation, and evaluation of quality professional learning (PL) programs
and resources available through the AAMT's Portal.

### Current projects

Project (2015): 'Essential Algebra Skills Workshop for Tasmanian pre-tertiary students'. The project consists of four tutorial sessions for all Tasmanian students studying pre-tertiary maths unit Maths Methods. The aim is to enhance their fundamental algebraic skills which are very necessary to obtain high scores in pre-tertiary and tertiary mathematics.

Other Projects on Pure Mathematics and Operations Research :

- (1) Intertwining Numbers of Induced Representations
- (2) L
_{1 }Inducing (theory of Representations) - Change detection algorithms (a temporary title for an Honours project)

### Fields of Research

- Mathematics and Numeracy Curriculum and Pedagogy (130208)
- Group Theory and Generalisations (010105)
- Lie Groups, Harmonic and Fourier Analysis (010106)
- Curriculum and Pedagogy Theory and Development (130202)
- Operator Algebras and Functional Analysis (010108)
- Algebra and Number Theory (010101)

### Research Objectives

- Expanding Knowledge in the Mathematical Sciences (970101)
- Pedagogy (930201)
- Syllabus and Curriculum Development (930302)
- Learner and Learning Achievement (930101)

## Publications

Total publications

7

### Journal Article

(3 outputs)Year | Citation | Altmetrics |
---|---|---|

2019 | Dharmadasa HK, Moran W, 'A generalisation of the Frobenius Reciprocity theorem', Bulletin of the Australian Mathematical Society pp. 1-6. ISSN 0004-9727 (2019) [Refereed Article] | |

2018 | Dharmadasa HK, Moran W, 'An identity for cocycles on coset spaces of locally compact groups', Rocky Mountain Journal of Mathematics, 48, (1) pp. 269-277. ISSN 0035-7596 (2018) [Refereed Article] | |

2017 | Dharmadasa HK, Moran W, 'An identity for cocycles on coset spaces of locally compact groups', Rocky Mountain Journal of Mathematics pp. 1-5. ISSN 0035-7596 (2017) [Refereed Article] |

### Conference Publication

(3 outputs)Year | Citation | Altmetrics |
---|---|---|

2018 | Oates GN, Reaburn RL, Brideson MA, Dharmadasa HK, 'Understanding of limits and differentiation as threshold concepts in a first-year mathematics course', Proceedings of the Eleventh Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, 26 November - 1 December 2017, Rio Grande do Sul, Brazil, pp. 108-120. ISBN 978-85-8167-237-3 (2018) [Refereed Conference Paper] Co-authors: Oates GN; Reaburn RL; Brideson MA | |

2018 | Reaburn R, Oates G, Dharmadasa K, Brideson M, 'Relating Flexibility in Concept Image and Understanding of Limits and Derivatives', Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education, 7-11 May 2018, Taipei, Taiwan, pp. 239-247. ISBN 978-986-05-5784-8 (2018) [Refereed Conference Paper] Co-authors: Reaburn R; Oates G; Brideson M | |

2014 | Dharmadasa HK, Palmer D, 'Assessment and standards in undergraduate mathematics - Part 2', Proceedings of the Australian Conference on Science and Mathematics Education,, 29-30 September 2014, Sydney, Australia, pp. 20. ISBN 9780987183439 (2014) [Conference Extract] Co-authors: Palmer D |

### Thesis

(1 outputs)Year | Citation | Altmetrics |
---|---|---|

1995 | Dharmadasa HK, 'The theory of q _{ p } spaces' (1995) [PhD] |

## Research Supervision

Kumudini was the supervisor for the following Honours Thesis:

- Induced Representations and Frobenius Reciprocity Theorem (1998)
- Abstract Harmonic Analysis (2009)
- Multipliers and Tensor Products (2012)
- Applications of Group Representation Theory (2013)

Completed

2

### Completed

Degree | Title | Completed |
---|---|---|

Masters | Clifford Algebras and Geometry of Entanglement Candidate: Isamu Imahori | 2008 |

Masters | Applications of Representation theory Candidate: Abdul Rouf Alghofari | 1998 |