COMPUTER-ASSISTED RESEARCH MATHEMATICS AND ITS APPLICATIONS

Vale: Professor Jonathan M Borwein

These pages are part of the continuing legacy of Professor Jonathan M Borwein, CARMA's Founding Director, whose sudden and unexpected passing away on 2nd August 2016 caused shockwaves of sorrow to ripple around the mathematical world. Jon changed the way innumerable people think and feel about mathematics, and his contributions are celebrated and commemorated in events and blogs listed in this news item, including the Jonathan M Borwein Commemorative Conference

As a Laureate Professor at University of Newcastle, Jonathan Borwein would frequently gather his students and postdocs together in his office for meetings. In those meetings, he would talk with each person about their current projects and the challenges they were encountering. These meetings frequently led to fruitful collaborations between researchers who discovered unexpected commonality in their mathematical interests.

The Borwein Meetings are an attempt to carry on this part of his legacy by connecting early career researchers. Come or use Skype to share and discuss research, and to learn about what others are doing. RHD students may also want to use this relaxed setting as the opportunity to practice giving a research talk. Everyone (not just RHD students and postdocs) is encouraged to come or join via Skype. People can ask questions and participate in the discussion. If you would like to share some ideas, you can contact us.

Mathematical constants who can be represented by BBP-type formula have the property that their n-th digit can be directly calculated without needing to compute any of the first (n-1) digits. This online database presents a comprehensive compilation of both formal and experimental BBP-type formulae.

The Inverse Symbolic Calculator 2 (ISC2) uses a combination of lookup tables and integer relation algorithms in order to associate with a user-defined, truncated decimal expansion (represented as a floating point expression) a closed form representation for the real number.

This site is currently in hiatus.

Update May 2020: the Calculatrice de Recherche Inversée des Nombres uses the ISC look-up tables to provide searches. Interested users are directed to Simon Plouffe's much more comprehensive and up to date tables at plouffe.fr/ipgz/ (or archived on the Internet Archive), with 11.3 billion entries (compared to the ISC's 47.9 million).

CRI utilises the same lookup tables as the ISC did, "to associate ... user-defined, truncated decimal expansion[s] ... [with] a closed form representation".

A tribute, archive and biography, including a timeline of his life and archive of his publications.

The complete works of Kurt Mahler, collected in memory of Alf van der Poorten.

A four-lecture series by Prof Jeremy Avigad presented at CARMA in May 2015.

An archive of the AccessGrid website, containing information about this videoconferencing software which was in heavy use here for a number of years.

For a number of years, CARMA provided a portal for websites of the Australian Mathematical Sciences Student Conference, run annually around Australia. This is preserved here (formerly amssc.org).

"Developing Expertise and Fostering Thinking" is a Professional Development Project being co-created and undertaken by a group of university lecturers across diverse institutions and contexts. We are interested in how our students think, what they think about, and how we can be more effective and precise in fostering thinking amongst our cohorts.

Experimental mathematics is a raison d'être for CARMA; this page outlines a variety of current projects.

The IMSITE Project: "Inspiring Mathematics and Science in Teacher Education". The IMSITE team at the University of Newcastle focused on mathematics particularly within mathematics and science teacher education. The team consisted of academics from the Mathematics, Statistics, and Education disciplines and a project officer whose background includes school science teaching.

"A site created out of concern with the proliferation of quasi-mathematical investment claims and schemes in the past few years... which appear to be based on sophisticated mathematics, but which, upon more careful and rigorous analysis, are at best questionable."

• Backtest Overfitting: an interactive demonstration of the consequences of backtest overfitting on investment models and strategies, where investment strategies are developed based on general trading rules; for example seasonal opportunities.
• Tenure Maker: an interactive finance tool demonstrating the consequences of backtest overfitting on investment models and strategies, where investment strategies are developed based on forecasting equations; for example econometric models.

Inside you will find 12 famous mathematical contestants battling it out for supremacy.

There is a deep tradition within the mathematical sciences at the University of Newcastle of care and involvement in education at all levels. We have a critical mass of people invested in this tradition, and this page is intended to describe and promote our activities, and hopefully promote cooperation with other like-minded persons.

Pi Computation Working Document and bibliography.

An annual poster competition for school students across Australia, with almost 1,000 participants in 2017.

A collection of visualisation-related projects at CARMA.

A multimedia mathematics project.

Group theory research group.

• "The Mathematics of Symmetry" video