The goal the article is to answer the questions: "Why the probability theory and its applications should be studied?" and "What is the attitude of students to the study of probabilistic branches of mathematics?" The values of probabilistic branches of mathematics (stochastics) are revealed on the analysis of scientific…

Online software systems are extensively used to give students practice on course content, especially in mathematics and physics courses. They offer instant feedback, and several of these systems are open source or very economical compared with hiring graders for traditional paper-and-pencil-based homework (PPH). In this article, the authors…

Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

This article describes how a Brier score analysis can be used as an evaluative tool to estimate the predictive accuracy of a course placement policy that was established based on professional or subjective judgment. The policy being evaluated uses the score received on the mathematics portion of the SAT examination as the primary mechanism to…

Completing a PhD on time is a complex process, influenced by many interacting factors. In this paper we take a Bayesian Network approach to analyzing the factors perceived to be important in achieving this aim. Focusing on a single research group in Mathematical Sciences, we develop a conceptual model to describe the factors considered to be…

The use of open-book tests, closed-book tests, and notecards on tests in an introductory statistics course is described in this article. A review of the literature shows that open-book assessments are universally recognized to reduce anxiety. The literature is mixed however on whether deeper learning or better preparation occurs with open-book…

This paper surveys the fascinating mathematics of fair division, and provides a suite of examples using basic ideas from algebra, calculus, and probability which can be used to examine and test new and sometimes complex mathematical theories and claims involving fair division. Conversely, the classical cut-and-choose and moving-knife algorithms…

The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…

Within the set of points in the plane with integer coordinates, one point is said to be visible from another if no other point in the set lies between them. This study of visibility draws in topics from a wide variety of mathematical areas, including geometry, number theory, probability, and combinatorics.

A method of generating common statistical tables using canned statistical computer software is presented. This method allows instructors to provide statistical tables for their students, tailored to their needs. The four most common tables used in elementary college statistics courses are z (standard normal), t, F, and chi square. Specific…