Should we teach linear algebra through geometry?

AbstractCan geometry help students learn linear algebra? I study this question and demonstrate that there is no obvious clear answer: geometry can be an obstacle to learning linear algebra; or it can be helpful. Geometry is helpful only under certain conditions and with a specific use of drawings. These special requirements for using geometry are apparently not much recognized in our teaching of linear algebra courses, at least in France, where my educational studies have taken place

The fundamental constants and their variation: observational status and theoretical motivations

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on the variation of the fine structure constant, the gravitational, weak and strong interactions couplings and the electron to proton mass ratio are reviewed. This review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant and (3) to point out the underlying hypotheses. Such an investigation is of importance to compare the different results, particularly in view of understanding the recent claims of the detections of a variation of the fine structure constant and of the electron to proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories and other alternative theories and cosmological implications of these results are discussed. The links with the tests of general relativity are emphasized.Comment: 56 pages, l7 figures, submitted to Rev. Mod. Phy

Introducing PIONEER: a project to harness big data in prostate cancer research

Prostate Cancer Diagnosis and Treatment Enhancement Through the Power of Big Data in Europe (PIONEER) is a European network of excellence for big data in prostate cancer, consisting of 32 private and public stakeholders from 9 countries across Europe. Launched by the Innovative Medicines Initiative 2 and part of the Big Data for Better Outcomes Programme (BD4BO), the overarching goal of PIONEER is to provide high-quality evidence on prostate cancer management by unlocking the potential of big data. The project has identified critical evidence gaps in prostate cancer care, via a detailed prioritization exercise including all key stakeholders. By standardizing and integrating existing high-quality and multidisciplinary data sources from patients with prostate cancer across different stages of the disease, the resulting big data will be assembled into a single innovative data platform for research. Based on a unique set of methodologies, PIONEER aims to advance the field of prostate cancer care with a particular focus on improving prostate-cancer-related outcomes, health system efficiency by streamlining patient management, and the quality of health and social care delivered to all men with prostate cancer and their families worldwide.Prostate Cancer Diagnosis and Treatment Enhancement Through the Power of Big Data in Europe (PIONEER) is a European network of excellence for big data in prostate cancer, consisting of 32 private and public stakeholders from 9 countries across Europe. In this Perspectives article, the authors introduce the PIONEER project and describe its aims and plans for ultimately improving prostate cancer care through the use of big data