It is clear that visualisation is an important tool for the mathematical sciences, but too often it does not play a prominent role in the teaching of mathematics. Also, with the increase of ‘big data’ and the mathematical tools to handle it, visualisation is of growing importance in many areas of mathematical research and applications.
This workshop brought together representatives of universities, schools, and the private sector, to explore how our common objective of maintaining and improving the health of the mathematical sciences can be furthered through better use of visualisation. As this was the second EViMS event, it was possible to have some speakers follow up on their presentations from two years ago to provide an update on the state of their research. In other cases, new speakers gave fresh insights into the importance of visualisation for teaching and research. At the heart of the conference was the understanding that there are three types of mathematical minds: an analytic type, a geometric type and a harmonic type and two components of thinking processes: verbal-logical that enables people to work with abstract problems, and visual-pictorial which requires visualisation. The most effective teaching will include elements that present the material in ways that can be accessed efficiently by all the different types of student minds. The same ideas also apply in research, especially when the research involves very large amounts of data.
Special presenters at EViMS 2 were:
- Professor Elias Wegert (TU Bergakemie Freiberg)
- Professor Andrei Tetenov (Gorno-Altaisk University)
- Professor Peter Eades (University of Sydney)
- Professor Christoph Bandt (University of Greisfwald)
The topics covered fell into two main areas:
Visualisation as an aid in mathematical research. Topics covered included:
- the importance of visualization when dealing with ‘big data’
- on visualizing floating point numbers as 3D walks
- on the use of ‘chaos game’ pictures to gain important intuitions for research
- on the use of IFSBuilder to check hypotheses
- using Matlab based Complex Function Explorer to explore complex functions using phase plots and how this relates to research on the Riemann zeta function
Visualisation as a tool in the teaching of mathematics and ‘outreach’ to the public. Topics covered included:
- Different types of ‘learners’ and how important it is to include visualisation in the teaching of mathematics to ensure all types of leaners are catered for in the teaching of calculus
- The use of visualisation in successful crowd funding and outreach to the public
- Using GeoGebra applets when teaching undergraduate economics and mathematics
- Quality metrics for graph “readability” and “faithfulness”
At the conclusion of EViMS 2 there was a great deal of enthusiasm from the participants and a strong message that a third EViMS should be organised in two years time. To help facilitate that, a special EViMS website will be set up at ANU to make the talks from EViMS 2 available and provide a forum for all interested parties to communicate on visualisation topics during the intervening months.