## Development and Evaluation of an Internet-Based Tutorial Module (i-TModule) For Statistics Learning Among Postgraduate Students

Abstract: Because students’ ability to use statistics, which is mathematical in nature, is one of the concerns of instructors embedding within an e-learning system the pedagogical characteristics of learning is ‘value added’. It could facilitate the traditional method of learning mathematics which is usually a teacher-centered. Nowadays, many different types of online learning platform and Learning Management Systems, LMSs, (such as Moodle) are used in the teaching and learning process especially in universities, but there is a lack of innovation to adopt effective instructional approaches...

Read More## Quantitative multiple recurrence for two and three transformations.

Abstract: In this talk I will provide some counter examples for quantitative multiple recurrence problems for systems with more than one transformation. For instance, I will show that there exists an ergodic system $(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that \[ \mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell} \] for every $n \in \mathbb{N}$. The construction of such a system is based on the study of “big” subsets of $\mathbb{N}^2$ and $\mathbb{N}^3$ satisfying...

Read More## Limit distributions related to the Euler discretization error of Brownian motion about random times

Resumen: In this talk we study the simulation of barrier-hitting events and extreme events of one-dimensional Brownian motion. We call “barrier-hitting event” an event where the Brownian motion hits for the first time a deterministic “barrier” function; and call “extreme event” an event where the Brownian motion attains a minimum on a given compact time interval or unbounded closed time interval. To sample these events we consider the Euler discretization approach of Brownian motion; that is, simulate the Brownian motion on a discrete and equidistant times...

Read More## Stability of Hamiltonian systems which are close to integrable : introduction to KAM and Nekhoroshev theory

Abstract: We give a panorama of classical theories of stability of Hamiltonian systems close to integrable which are of two kind : – Stability in measure over infinite time (KAM theory). – Effective stability over finite but very long time (Nekhoroshev theory)

Read More## TOPOLOGICAL DYNAMICS OF PIECEWISE Λ-AFFINE MAPS OF THE INTERVAL

ABSTRACT: Let 0 < a < 1, 0 ≤ b < 1 and I = [0,1). We call contracted rotation the interval map φa,b : x ∈ I → ax+b mod1. Once a is fixed, we are interested in the dynamics of the one-parameter family φa,b, where b runs on the interval interval [0, 1). Any contracted rotation has a rotation number ρa,b which describes the asymptotic behavior of φa,b. In the first part of the talk, we analyze the numerical relation between the parameters a, b and ρa,b and discuss some applications of the map φa,b. Next, we introduce a generalization of contracted rotations. Let −1 < λ < 1 and f...

Read More## Recurrences for generating polynomials

Abstract: In this talk we consider sequences of polynomials that satisfy differential–difference recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. It is, therefore, of interest to understand the properties of such polynomials and their probabilistic consequences. We will be primarily interested in the limiting distribution of the corresponding random variables. As an illustration we give a few examples, leading...

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