A temporal Central Limit Theorem for real-valued cocycles over rotations

We consider deterministic random walks on the real line driven by irrational rotations, or equivalently, skew product extensions of a rotation by $\alpha$ where the skewing cocycle is a piecewise constant mean zero function with a jump by one at a point $\beta$. When $\alpha$ is badly approximable and $\beta$ is badly approximable with respect to $\alpha$, we prove a Temporal Central Limit theorem (in the terminology recently introduced by D.Dolgopyat and O.Sarig), namely we show that for any fixed initial point, the occupancy random variables, suitably rescaled, converge to a Gaussian random variable. This result generalizes and extends a theorem by J. Beck for the special case when $\alpha$ is quadratic irrational, $\beta$ is rational and the initial point is the origin, recently reproved and then generalized to cover any initial point using geometric renormalization arguments by Avila-Dolgopyat-Duryev-Sarig (Israel J., 2015) and Dolgopyat-Sarig (J. Stat. Physics, 2016). We also use renormalization, but in order to treat irrational values of $\beta$, instead of geometric arguments, we use the renormalization associated to the continued fraction algorithm and dynamical Ostrowski expansions. This yields a suitable symbolic coding framework which allows us to reduce the main result to a CLT for non homogeneous Markov chains.Comment: a few typos corrected, 28 pages, 4 figure

An investigation into the differing success rates of management accounting students in professional accounting examinations and undergraduate accounting students studying on cognate courses

This dissertation is concerned with the issue that students studying part-time for professional accounting examinations - specifically those in management accounting of the Association of Chartered Certified Accountants (ACCA) - at a London university suffer much higher failure rates than their counterparts taking degrees in Accounting at the same institution, who are entitled to exemptions from many of the professional accounting papers. Utilising the 'Student Approaches to Learning' (SAL) methodology, the differences between the students are examined in terms of factors affecting the presage to learning, the learning process, and the product of learning.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Reflection on Oral Quizzes

In this article we reflect on an instructional technique piloted in our discrete mathematics course this past semester. Motivated by a desire for students to better prepare for class and for them to receive adaptive feedback, we introduced oral quizzes as a check on preparation. We observed oral quizzes to be a good inspiration for out of class reading and practice, they forced students to practice oral and written communication of mathematics, and allowed us to tailor feedback to be appropriate for each student. We will discuss our motivation in more depth and detail oral quizzes as we implemented them. Finally we reflect on the instructional method and consider how oral quizzes can be improved and modified for other classes. We found oral quizzes to be very successful, and we believe they can be adapted to suit nearly any college math class