The role of spreadsheets in an investigation of Fibonacci numbers

We introduce a function Z(k) which measures the number of distinct ways in which a number can be expressed as the sum of Fibonacci numbers. Using a binary table and other devices, we explore the values that Z(k) can take and reveal a surprising relationship between the values of Z(k) and the Fibonacci numbers from which they were derived. The article shows the way in which standard spreadsheet functionalities makes it possible to reveal quite striking patterns in data.

Letters and numbers in Excel : fostering student engagement in fundamentals of maths & computing

The television quiz program Letters and Numbers, broadcast on the SBS network, has recently become quite popular in Australia. This paper considers an implementation in Excel 2010 and its potential as a vehicle to showcase a range of mathematical and computing concepts and principles.

Challenges for integrated design and delivery solutions

A new approach of integrated design and delivery solutions (IDDS) aims to radically improve the performance of the construction industries. IDDS builds upon recent trends in the construction industries that have seen the widespread adoption of technologies such as building information modelling (BIM) and innovative processes such as integrated project delivery. However, these innovations are seen to develop in isolation, with little consideration of the overarching interactions between people, process and technology. The IDDS approach is holistic in that it recognizes that it is only through a combination of initiatives such as skill development, process re-engineering, responsive information technology, enhanced interoperability and integrating knowledge management, among others, that radical change can be achieved. To implement IDDS requires step changes in many project aspects, and this gap between current performance and that required for IDDS is highlighted. The research required to bridge the gaps is identified in four major aspects of collaborative processes, workforce skills, integrated information and knowledge management.

A model of enterprise architecture evolution

Enterprise architectures are exposed to fast emerging business and information technology capabilities. A prominent example is the paradigm of service-orientation, which leads to its own architectural requirements and impacts the design and ongoing evolution of Enterprise Architectures. This thesis develops the first theoretical model describing enterprise architecture evolution and outcomes in light of a changing IT landscape such as service-oriented architectures. The developed theoretical model explains enterprise architecture evolution, its main stages and related capabilities. This model can be used to derive theoretical, sound guidelines to manage enterprise architectures in a changing environment.

Using a smartphone application for customer-centric banking

The banking industry is under pressure. In order to compete, banks should adapt to concentrating on the specific customer needs, following an outside-in perspective. This paper presents the design of a business model for banks that considers this development by providing flexible and comprehensive support for retail banking clients. It is demonstrated that the identification of customer processes and the consequent alignment of banking services to those processes implies great potential to increase customer retention in banking. It will be shown that information technology – especially smartphones – can serve as an interface between customer and suppliers to enable an alignment of offerings to customer processes. This approach enables the integration of banks into their customers’ lifestyle, creating emotional value added, improving the personal relationship and the customers’ affiliation with the bank. The paper presents the design of such a customer-process-centric smartphone application and derives success factors for implementation.

Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

Fun with Fibonacci

We introduce a function which measures the number of distinct ways in which a number can be expressed as the sum of Fibonacci numbers. Using a binary table and other devices, we explore the values that can take and reveal some interesting patterns. The article shows how standard spreadsheet functionalities make it possible to reveal quite striking patterns in data, and is intended to be used in the classroom.

The slumbarumba jumbuck problem

The potential for simple linear relationships arising from a computer game to build student modelling and "world problem" skills is explored. The fundamental capability of the spreadsheet to tabulate and graph possible solutions is used to lay bare the problem structure for the students.

Security analysis of the non-aggressive challenge response of the DNP3 Protocol using a CPN Model

Distributed Network Protocol Version 3 (DNP3) is the de-facto communication protocol for power grids. Standard-based interoperability among devices has made the protocol useful to other infrastructures such as water, sewage, oil and gas. DNP3 is designed to facilitate interaction between master stations and outstations. In this paper, we apply a formal modelling methodology called Coloured Petri Nets (CPN) to create an executable model representation of DNP3 protocol. The model facilitates the analysis of the protocol to ensure that the protocol will behave as expected. Also, we illustrate how to verify and validate the behaviour of the protocol, using the CPN model and the corresponding state space tool to determine if there are insecure states. With this approach, we were able to identify a Denial of Service (DoS) attack against the DNP3 protocol.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.