Literature Index

Two improvements in teaching linear regression are suggested. The first is to include the<br><br>population regression model at the beginning of the topic. The second is to use a geometric<br><br>approach: to interpret the regression estimate as an orthogonal projection and the estimation<br><br>error as the distance (which is minimized by the projection). Linear regression in finance is<br><br>described as an example of practical applications of the population regression model.<br><br>The paper also describes a geometric approach to teaching the topic of finding an optimal<br><br>portfolio in financial mathematics. The approach is to express the optimal portfolio through<br><br>an orthogonal projection in Euclidean space. This allows replacing the traditional solution of<br><br>the problem with a geometric solution, so the proof of the result is merely a reference to the<br><br>basic properties of orthogonal projection. This method improves the teaching of the topic by<br><br>avoiding tedious technical details of the traditional solution such as Lagrange multipliers and<br><br>partial derivatives. The described method is illustrated by two numerical examples

In South Australia mathematics students typically have had considerable exposure to calculus but little to probability on entering university. The amount of probability in school syllabuses has decreased, and our first year university students often associate the subject with fatuous but intricate examples. Some undertake a first year statistics subject, but many will come to a first course in applied probability/stochastic processes in second year applied mathematics without that background. They are ill at lease with any second year applied mathematics courses not based on calculus (forgetting the effort with which the comfort with calculus was won!) and will often demand evidence of meaningful applicability at an early stage. This creates some challenge and necessitates an examination of one's teaching philosophy.

This article presents two major paradoxical examples of one of the simplest statistics, the "average".

The purpose of this paper is to report on the conception and some results of a long-term<br>university research project in Budapest. The study is based on an innovative idea of teaching the basic notions<br>of classical and Bayesian inferential statistics parallel to each other to teacher students. Our research is driven<br>by questions like: Do students understand probability and statistical methods better by focussing on<br>subjective and objective interpretations of probability throughout the course? Do they understand classical<br>inferential statistics better if they study Bayesian ways, too? While the course on probability and statistics has<br>been avoided for years, the students are starting to accept the "parallel" design. There is evidence that they<br>understand the concepts better in this way. The results also support the thesis that students' views and beliefs<br>on mathematics decisively influence work in their later profession. Finally, the design of the course integrates<br>reflections on philosophical problems as well, which enhances a wider picture about modern mathematics and<br>its applications.