Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

Computationally sound automated proofs of cryptographic schemes

Proving security of cryptographic schemes, which normally are short algorithms, has been known to be time-consuming and easy to get wrong. Using computers to analyse their security can help to solve the problem. This thesis focuses on methods of using computers to verify security of such schemes in cryptographic models. The contributions of this thesis to automated security proofs of cryptographic schemes can be divided into two groups: indirect and direct techniques. Regarding indirect ones, we propose a technique to verify the security of public-key-based key exchange protocols. Security of such protocols has been able to be proved automatically using an existing tool, but in a noncryptographic model. We show that under some conditions, security in that non-cryptographic model implies security in a common cryptographic one, the Bellare-Rogaway model [11]. The implication enables one to use that existing tool, which was designed to work with a different type of model, in order to achieve security proofs of public-key-based key exchange protocols in a cryptographic model. For direct techniques, we have two contributions. The first is a tool to verify Diffie-Hellmanbased key exchange protocols. In that work, we design a simple programming language for specifying Diffie-Hellman-based key exchange algorithms. The language has a semantics based on a cryptographic model, the Bellare-Rogaway model [11]. From the semantics, we build a Hoare-style logic which allows us to reason about the security of a key exchange algorithm, specified as a pair of initiator and responder programs. The other contribution to the direct technique line is on automated proofs for computational indistinguishability. Unlike the two other contributions, this one does not treat a fixed class of protocols. We construct a generic formalism which allows one to model the security problem of a variety of classes of cryptographic schemes as the indistinguishability between two pieces of information. We also design and implement an algorithm for solving indistinguishability problems. Compared to the two other works, this one covers significantly more types of schemes, but consequently, it can verify only weaker forms of security.

Educational accountability tests, social and legal inclusion approaches to discrimination for students with disability : a national case study from Australia

The UN Convention on the Rights of Persons with Disability (CRPD) promotes equal and full participation by children in education. Equity of educational access for all students, including students with disability, free from discrimination, is the first stated national goal of Australian education (MCEETYA 2008). Australian federal disability discrimination law, the Disability Discrimination Act 1992 (DDA), follows the Convention, with the federal Disability Standards for Education 2005 (DSE) enacting specific requirements for education. This article discusses equity of processes for inclusion of students with disability in Australian educational accountability testing, including international tests in which many countries participate. The conclusion drawn is that equitable inclusion of students with disability in current Australian educational accountability testing in not occurring from a social perspective and is not in principle compliant with law. However, given the reluctance of courts to intervene in education matters and the uncertainty of an outcome in any court consideration, the discussion shows that equitable inclusion in accountability systems is available through policy change rather than expensive, and possibly unsuccessful, legal challenges.

Reasonable adjustments in assessment : putting law and policy into practice in Australia

The Australian Disability Standards for Education 2005 (Cth) require education providers to make reasonable adjustments in educational assessment so that students with disability can participate on the same basis as other students and be able to demonstrate what they know and can do. Reasonableness is governed by a determination of the balance of interests, benefits and detriment to the parties involved. The Standards require providers to consult with students and associates on adjustments, although guidance on how consultation should occur and how the views of students and associates are to be taken into account is vague. In this article, we identify three principles to be considered in order to put appropriate and effective reasonable adjustments in assessment into practice. While Australian law and assessment contexts are used to examine intentions, expectations and practices in educational assessment for students with disability, we argue that these three principles must be considered in any national education system to ensure equitable assessment practices and achieve equitable educational inclusion for students with disability.

The assessment of students with disabilities : the Australian law as to reasonable adjustment and academic integrity

This paper explains the legislation which underpins the right to reasonable adjustment in education for students with disabilities in Australian schools. It gives examples of the kinds of adjustment which may be made to promote equality of opportunity in the area of assessment. It also considers how the law has constructed the border between reasonable adjustment and academic integrity.

Planar difference functions

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.

Mutually unbiased bases as submodules and subspaces

Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with projective and affine planes. We propose a connection with higher dimensional projective geometries and projective Hjelmslev geometries. We show that this proposed geometric structure is present in several constructions of MUBs.

Repeating patterns : strategies to assist young students to generalise the mathematical structure

This paper focuses on very young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5-10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns.

Using formative feedback to identify and support first year chemistry students with missing or misconceptions. A Practice Report

Students entering tertiary studies possess a diverse range of prior experiences in their academic preparation for tertiary chemistry so academics need tools to enable them to respond to issues in diversity in conceptual models possessed by entering students. Concept inventories can be used to provide formative feedback to help students identify concepts that they need to address to improve construction of subsequent understanding enabling their learning. Modular, formative learning activities that can be administered inside or outside of class in first year chemistry courses have been developed. These activities address key missing and mis-conceptions possessed by incoming student. Engagement in these learning activities by students and academics will help shift the culture of diagnostic and formative assessment within the tertiary context and address issues around the secondary/tertiary transition. This diagnostic/intervention framework is currently being trialed across five Australian tertiary institutions encompassing a large heterogeneous sample of students.

Modelling the information seeking user by the decision they make

The article focuses on how the information seeker makes decisions about relevance. It will employ a novel decision theory based on quantum probabilities. This direction derives from mounting research within the field of cognitive science showing that decision theory based on quantum probabilities is superior to modelling human judgements than standard probability models [2, 1]. By quantum probabilities, we mean decision event space is modelled as vector space rather than the usual Boolean algebra of sets. In this way,incompatible perspectives around a decision can be modelled leading to an interference term which modifies the law of total probability. The interference term is crucial in modifying the probability judgements made by current probabilistic systems so they align better with human judgement. The goal of this article is thus to model the information seeker user as a decision maker. For this purpose, signal detection models will be sketched which are in principle applicable in a wide variety of information seeking scenarios.

A family of Alltop functions that are EA-inequivalent to the cubic function

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (\emph{IEEE Trans. Inf. Theory} 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these sequences were optimal with respect to the known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases (MUBs), a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called \emph{Alltop functions}. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs.

Perspectives on Reconceptualizing Early Mathematics Learning

This introductory section provides an overview of the different perspectives on reconceptualizing early mathematics learning. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualizing the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed. Although these themes are diffused throughout the chapters, we restrict our introduction to the core focus of each of the chapters.

Update on the inaugural Sydney Diabetic Foot Conference 2013

The first International Diabetic Foot Conference in Australia was hosted at Liverpool Hospital in Sydney during May 30-31, 2013. In response to the growing diabetes epidemic globally and more locally to Australia, the conference provided the perfect bridge for interaction between the multidisciplinary team members involved in diabetes care and the opportunity to assimilate the most up-to-date evidence-based medicine from some of the most respected researchers in the field.

An examination of how the military, the conservative press and ministerialist politicians generated support within Queensland for the war in South Africa in 1899 and 1900

This thesis examines the role of conservative newspaper proprietors and editors to generate support for war against the Boers in South Africa. The thesis utilises Rune Ottosen's theoretical model concerning newspapers creating a pro-war mentality, and S.E. Finer's theory on the influences of the military on civilian Government. The pivotal supportive roles of Governor Lamington and Premiers Dickson and Philp and the oppositional role of Premier Dawson are also examined.