UCLIC, University College

London Interaction Centre

February 2004

It is usually very hard, both for designers and users, to reason reliably about user interfaces. This paper shows that 'push button' and 'point and click' user interfaces are algebraic structures. Users effectively do algebra when they interact, and therefore we can be precise about some important design issues and issues of usability. Matrix algebra, in particular, is useful for explicit calculation and for proof of various user interface properties.

With matrix algebra, we are able to undertake with ease unusally thorough reviews of real user interfaces: this paper examines a mobile phone, a handheld calculator and a digital multimeter as case studies, and draws general conclusions about the approach and its relevance to design.

**Keywords**: Matrix algebra, Usability analysis.

In postscript, in PDF. This paper defines the matrix approach, and examines a mobile phone, a handheld calculator and a digital multimeter as case studies. It draws general conclusions about the approach and its relevance to design and HCI research

- Jeremy Gow's MAUI system.
- Nokia 5110: in HTML, in
*Mathematica*. - Calculator: in HTML, in
*Mathematica*.

You can download a Mathematica reader from http://www.wolfram.com/mathreader/

Markov modelling, which uses matrices for probabilistic modelling, and introduces the 'knowledge/usability' graph.

Computer algebra approaches.

Nokia's web site. The paper discusses their
5110 mobile phone model. More details
of the 5110 user interface; and a *Mathematica*
paper on it.

Casio's web site. The paper discusses their HL-820LC, MS-70L and HS-8V calculator models. See also Thimbleby's other resources on calculators.

Fluke's web site. The paper discusses their 185 digital multimeter model. Note that (as of May 2003) their similar 187/189 model has a Flash virtual demo.