Science, Technology and Engineering

Department of Mathematics and Statistics, Bendigo

Mathematics Seminars 2007

Below is a list of seminars presented during 2007 in the Seminar Program of the Department of Mathematics and Statistics at La Trobe University's campus in Bendigo, Victoria.

Diane Itter	Cathrine Yaneff

Fibonacci and multiplication, by Diane Itter and Cathrine Yaneff (Faculty of Education, La Trobe University, Bendigo)

Scheduled: 12 noon, Monday 3 December 2007, in Room B2.09

Abstract: Fibonacci's seminal work "Liber Abaci", first published in 1202, made an enormous contribution to the introduction and dissemination of the Hindu number system and arithmetic throughout the western world. In this paper, we will explore Fibonacci's treatment of multiplication and examine Fibonacci's explanation of the method of checking by casting out nines. Furthermore, we will consider implications of Fibonacci's ideas for teaching multiplication in schools today. This is joint work with Christopher Lenard and Terry Mills.

Robert Hunting

Project One: Uncovering the Seeds of Mathematics in Children Aged 12-24 Months, by Dr Robert Hunting (School of Education, La Trobe University, Bendigo)

Scheduled: 12 noon, Friday 5 October 2007, in Room B2.15

Abstract: Mathematics is a human activity whose origins in the learner have both genetic and social roots. This presentation will discuss selected segments of video data of a toddler's spontaneous play showing evidence of pre-mathematical actions and activity. Such data, including commentary provided by the Investigator, is to be submitted for further analyses by an expert panel of mathematicians, if funded.

Chris Cope

Improving teaching and learning about confidence intervals, by Dr Chris Cope (Department of Computer Science and Computer Engineering, La Trobe University, Bendigo)

Scheduled: 12 noon, Friday 24 August 2007, in Room B2.15

Abstract: Threshold concepts are the keys to meaningful learning progression in a discipline but are particularly difficult to teach and learn. The seminar will report on a study which improved understanding of teaching and learning about confidence intervals (CIs), a threshold concept in the statistics discipline. The responses to an exam question of 100 first year undergraduate students were analysed qualitatively using a phenomenographic technique. The outcome space consisted of 7 distinctly different, but hierarchically related, ways of experiencing CIs. A logical analysis of the outcome space identified three educationally critical aspects of learning about CIs at the introductory level: CIs are based on repeated sampling, CIs relate to the success of the method, and CIs are an estimation tool for improving decision making in the real world. The seminar will include a discussion on the types of learning activities most likely to help students come to terms with these educationally critical aspects.

Aleesha Keogh	Adam Rosenow

Government expenditure on the Pharmaceutical Benefits Scheme, by Aleesha Keogh and Adam Rosenow (La Trobe University, Bendigo)

Scheduled: 12 noon, Monday 4 June 2007, in Room B2.32

Abstract: We will discuss recent trends in the cost of the Pharmaceutical Benefits Scheme (PBS) and the application of time series analysis for modelling and forecasting monthly PBS cost data. This work was carried out for the third-year undergraduate unit Topics in Statistics.

Robert Champion

Nonlinear springs – where Hooke got it wrong, by Dr Robert Champion (La Trobe University, Bendigo) [Co-author: Len Champion]

Scheduled: 12 noon, Friday 23 March 2007, in Room B2.15

Abstract: Models derived on the assumption that springs exhibit linear elastic behaviour are found to be inadequate for precisely fitting measurements of the static extension and periods of oscillation of a vertically suspended, loaded, helical spring. A nonlinear spring model, derived from the elasticity equations for a helical wire, is found to overcome the deficiencies in the linear models.

Terry Mills

Bernstein's inequality in probability, by Professor Terry Mills (La Trobe University, Bendigo)

Scheduled: 12 noon, Friday 23 February 2007, in Room B2.05

Abstract: In 1924, S.N. Bernstein (1880-1968) sought to improve an inequality in the theory of probability established by P.L. Chebyshev (1821-1894). Although Bernstein's inequality is a decided improvement of the result of Chebyshev, and was published 82 years ago, it is not as well known as the result of Chebyshev. Even books on probability do not give it much prominence. In this seminar I will outline Bernstein's result and its proof, and describe various improvements and extensions of this inequality. The story surrounding this inequality will illustrate how the theory of probability in general has developed over the last 80 years.

Joachim Gwinner

Variational Inequalities – a way to treat inequality-constrained problems in operations research and mechanics, by Professor Joachim Gwinner (Universität der Bundeswehr München)

Scheduled: 12 noon, Tuesday 13 February 2007, in Room B1.29

Abstract: Variational Inequalities (VI) are now established as a versatile mathematical model to treat inequality-constrained problems in various fields like operations research and mechanics. Here I discuss (dis)equilibria of distributed markets, traffic equilibria in networks, and elliptic boundary value problems with Signorini boundary conditions that arise in unilateral contact mechanics and in fluid flow in porous media.

By the VI approach not only can existence and stability results be obtained, but also efficient numerical methods can be developed in combination with variational discretisation methods for partial differential equations such as the Finite Element Method or the Boundary Element Method.

In this seminar, I will present a recent extension of the VI methodology to inequality-constrained problems with random data.

Deane Arganbright

Innovative Techniques in Mathematical Visualization with Microsoft Excel, by Dr Deane Arganbright

Scheduled: 12 noon, Thursday 18 January 2007, in Room B1.29 [This seminar is also part of the Seminar Program of the Department of Computer Science & Computer Engineering.]

Abstract: Excel is a natural tool for learning and implementing a wide range of mathematical concepts in a way that closely parallels the way one naturally approaches mathematics. It provides an easy-to-use graphic platform for interactive ways to visualize mathematical concepts and algorithms. Furthermore, since Excel is the principal mathematical tool of the workplace, one does not always need to use specialized software to do significant mathematics. Finally, this approach allows a number of topics ordinarily considered quite advanced to be understood by a very wide audience of people. Thus, Excel assists in making mathematical ideas more accessible.

Anyone with an interest in mathematics, mathematical modelling, or creative uses of spreadsheets in teaching might enjoy this seminar.

Deane Arganbright has just completed an appointment as visiting professor of mathematics at Korea Advanced Institute of Science and Technology, a leading technological research university. In the coming spring he will be a guest professor at the University of Vienna. He is a pioneer and an internationally recognized expert in the creative use of spreadsheets for mathematics and mathematics teaching. He has published three books and numerous articles on the subject and given many invited international presentations. He has taught at universities in the US, Austria, Australia, PNG and Korea.

An article about the seminar, titled "Learn to Excel at maths", appeared in Bendigo's The Advertiser newspaper of Thursday January 18, 2007.