Proposal of a mobile learning preferences model

A model consisting of five dimensions of mobile learning preferences – location, level of distractions, time of day, level of motivation and available time – is proposed in this paper. The aim of the model is to potentially increase the learning effectiveness of individuals or groups by appropriately matching and allocating mobile learning materials/applications according to each learner’s type. Examples are given. Our current research investigations relating to this model are described

A self-regulated learning approach : a mobile context-aware and adaptive learning schedule (mCALS) tool

Self-regulated students are able to create and maximize opportunities they have for studying or learning. We combine this learning approach with our Mobile Context-aware and Adaptive Learning Schedule (mCALS) tool which will create and enhance opportunities for students to study or learn in different locations. The learning schedule is used for two purposes, a) to help students organize their work and facilitate time management, and b) for capturing the users’ activities which can be retrieved and translated as learning contexts later by our tool. These contexts are then used as a basis for selecting appropriate learning materials for the students. Using a learning schedule to capture and retrieve contexts is a novel approach in the context-awareness mobile learning field. In this paper, we present the conceptual model and preliminary architecture of our mCALS tool, as well as our research questions and methodology for evaluating it. The learning materials we intend to use for our tool will be Java for novice programmers. We decided that this would be appropriate because large amounts of time and motivation are necessary to learn an object-oriented programming language such as Java, and we are currently seeking ways to facilitate this for novice programmers

Introducing Java : the case for fundamentals-first

Java has increasingly become the language of choice for teaching introductory programming. In this paper, we examine the different approaches to teaching Java (Objects-first, Fundamentals-first and GUI-first) to ascertain whether there exists an agreed ordering of topics and difficulty levels between nine relatively basic Java topics. The results of our literature survey and student questionnaire suggests that the Fundamentals-first approach may have benefits from the student's point of view and an agreed ordering of the Java topics accompanying this approach has been established

Universality for generalized Wigner matrices with Bernoulli distribution

The universality for the eigenvalue spacing statistics of generalized Wigner matrices was established in our previous work \cite{EYY} under certain conditions on the probability distributions of the matrix elements. A major class of probability measures excluded in \cite{EYY} are the Bernoulli measures. In this paper, we extend the universality result of \cite{EYY} to include the Bernoulli measures so that the only restrictions on the probability distributions of the matrix elements are the subexponential decay and the normalization condition that the variances in each row sum up to one. The new ingredient is a strong local semicircle law which improves the error estimate on the Stieltjes transform of the empirical measure of the eigenvalues from the order $(N \eta)^{-1/2}$ to $(N \eta)^{-1}$. Here $\eta$ is the imaginary part of the spectral parameter in the definition of the Stieltjes transform and $N$ is the size of the matrix.Comment: On Sep 17.2011 a small error in the condition of Lemma 6.1 was fixed and accordingly the proof of Thm 6.3 was slighly changed in page 29. (this last change was made after the paper was published, so this version corrects a small error in the published paper

Rigidity of Eigenvalues of Generalized Wigner Matrices

Consider $N\times N$ hermitian or symmetric random matrices $H$ with independent entries, where the distribution of the $(i,j)$ matrix element is given by the probability measure $\nu_{ij}$ with zero expectation and with variance $\sigma_{ij}^2$. We assume that the variances satisfy the normalization condition $\sum_{i} \sigma^2_{ij} = 1$ for all $j$ and that there is a positive constant $c$ such that $c\le N \sigma_{ij}^2 \le c^{-1}$. We further assume that the probability distributions $\nu_{ij}$ have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eigenvalue distribution of $H$ is given by the Wigner semicircle law uniformly up to the edges of the spectrum with an error of order $(N \eta)^{-1}$ where $\eta$ is the imaginary part of the spectral parameter in the Stieltjes transform. There are three corollaries to this strong local semicircle law: (1) Rigidity of eigenvalues: If $\gamma_j =\gamma_{j,N}$ denotes the {\it classical location} of the $j$-th eigenvalue under the semicircle law ordered in increasing order, then the $j$-th eigenvalue $\lambda_j$ is close to $\gamma_j$ in the sense that for any $\xi>1$ there is a constant $L$ such that $$\mathbb P \Big (\exists \, j : \; |\lambda_j-\gamma_j| \ge (\log N)^L \Big [ \min \big (\, j, N-j+1 \, \big) \Big ]^{-1/3} N^{-2/3} \Big) \le C\exp{\big[-c(\log N)^{\xi} \big]}$$ for $N$ large enough. (2) The proof of the {\it Dyson's conjecture} \cite{Dy} which states that the time scale of the Dyson Brownian motion to reach local equilibrium is of order $N^{-1}$. (3) The edge universality holds in the sense that the probability distributions of the largest (and the smallest) eigenvalues of two generalized Wigner ensembles are the same in the large $N$ limit provided that the second moments of the two ensembles are identical.Comment: 72 pages, no figures Sep 17,2011 a small error in the conditions of Lemma 5.1 was fixed and the argument in page 34-35 modified accordingly. On Oct 25 we added several explanation paragraphs and considerably expanded Section 7 to better illustrate the metho