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Statistics is running the risk of appearing irrelevant to today's undergraduate students. Today's undergraduate students are familiar with data science projects and they judge statistics against what they have seen. Statistics, especially…
Computer programming was once thought of as a skill required only by professional software developers. But today, given the ubiquitous nature of computation and data science it is quickly becoming necessary for all scientists and engineers…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
These informal notes concern some basic themes of harmonic analysis related to representations of groups.
Depending on the point of view, modern machine learning is either providing an unprecedented boost to the numerical methods of particle physics, or it is transforming the way we do science with vast amounts of complex data. In any case, it…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
A calculator program has been written to give confidence intervals on branching ratios for rare decay modes (or similar quantities) calculated from the number of events observed, the acceptance factor, the background estimate and the…
The goal of Inductive Logic Programming (ILP) is to learn a program that explains a set of examples in the context of some pre-existing background knowledge. Until recently, most research on ILP targeted learning Prolog programs. Our own…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
These lectures provide an introduction to effective theories concentrating on the basic ideas and providing some simple applications
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
This is a brief exposition of the mathematical themes that motivate the special programme at the Newton Institute in 2009. It is mostly intended for the general public having mathematical training up to the level of secondary school.
These notes are an exposition of Galois Theory from the original Lagrangian and Galoisian point of view. A particular effort was made here to better understand the connection between Lagrange's purely combinatorial approach and Galois…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of statistical data to both undergraduate and postgraduate students, in particular in the…
A discussion of Lagrangian and Hamiltonian dynamics is presented at a level which should be suitable for advanced high school students. This is intended for those who wish to explore a version of mechanics beyond the usual Newtonian…
The aim of this study is to investigate the decisions and reasoning of undergraduate students when choosing simple measurement instruments in an introductory physics laboratory course. For this study, we have developed a questionnaire and…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation…
These informal notes deal with a number of questions related to sums and integrals in analysis.