Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Effect of two wild rootstocks of genus Passiflora L. on the content of antioxidants and fruit quality of yellow passion fruit

ABSTRACT The nutritional importance of the fruit of passionfruit has prompted studies to assess its composition and antioxidant content and to evaluate it as a functional food in fresh fruit and concentrated juice markets. Currently, the use of wild species as rootstock has been recommended mainly for their positive effects such as tolerance to disease attack and maintenance of fruit quality of grafted cultivars. The aim of this study was to determine the effect of wild species of Passiflora gibertii N.E. Br. and Passiflora mucronata Lam as rootstock on the content of antioxidants and fruit quality of Passiflora edulis f. flavicarpa. The experimental design was completely randomized with four treatments and 25 replications, with a total of 100 experimental units. As a control treatment, plants of P. edulis from seed and grafted on the same species were used. Significant correlations were observed among the contents of β-carotene, ascorbic acid, luminosity values, chroma and hue angle. For the combination P. edulis/P. gibertti, the contents of β-carotene and ascorbic acid were highly correlated with luminosity, chroma and hue angle of fruit juice. A similar behavior was observed for the combination P. edulis/P. mucronata Lam. The content of β-carotene in the fruit showed no statistical differences (p < 0.05), indicating no significant rootstock effect on the variables evaluated. The results indicate a potential wild rootstock use for its positive effects on grafted plants while maintaining the commercial quality of the fruits of passionfruit crops

Delays between the onset of symptoms and first rheumatology consultation in patients with rheumatoid arthritis in the UK: an observational study

Objective To investigate delays from symptom onset to rheumatology assessment for patients with a new onset of rheumatoid arthritis (RA) or unclassified arthritis. Methods Newly presenting adults with either RA or unclassified arthritis were recruited from rheumatology clinics. Data on the length of time between symptom onset and first seeing a GP (patient delay), between first seeing a general practitioner (GP) and being referred to a rheumatologist (general practitioner delay) and being seen by a rheumatologist following referral (hospital delay) were captured. Results 822 patients participated (563 female, mean age 55 years). The median time between symptom onset and seeing a rheumatologist was 27.2 weeks (IQR 14.1–66 weeks); only 20% of patients were seen within the first 3 months following symptom onset. The median patient delay was 5.4 weeks (IQR 1.4–26.3 weeks). Patients who purchased over-the-counter medications or used ice/heat packs took longer to seek help than those who did not. In addition, those with a palindromic or an insidious symptom onset delayed for longer than those with a non-palindromic or acute onset. The median general practitioner delay was 6.9 weeks (IQR 2.3–20.3 weeks). Patients made a mean of 4 GP visits before being referred. The median hospital delay was 4.7 weeks (IQR 2.9–7.5 weeks). Conclusion This study identified delays at all levels in the pathway towards assessment by a rheumatologist. However, delays in primary care were particularly long. Patient delay was driven by the nature of symptom onset. Complex multi-faceted interventions to promote rapid help seeking and to facilitate prompt onward referral from primary care should be developed

A direct heuristic algorithm for linear programming

An O(n^{\mathrn{3}}) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure

Solving linear differential equations as a minimum norm least squares problem with error-bounds

Linear ordinary/partial differential equations (DEs) with linear boundary conditions (BCs) are posed as an error minimization problem. This problem has a linear objective function and a system of linear algebraic (constraint) equations and inequalities derived using both the forward and the backward Taylor series expansion. The DEs along with the BCs are approximated as linear equations/inequalities in terms of the dependent variables and their derivatives so that the total error due to discretization and truncation is minimized. The total error along with the rounding errors render the equations and inequalities inconsistent to an extent or, equivalently, near-consistent, in general. The degree of consistency will be reasonably high provided the errors are not dominant. When this happens and when the equations/inequalities are compatible with the DEs, the minimum value of the total discretization and truncation errors is taken as zero. This is because of the fact that these errors could be negative as well as positive with equal probability due to the use of both the backward and forward series. The inequalities are written as equations since the minimum value of the error (implying error-bound and written/expressed in terms of a nonnegative quantity) in each equation will be zero. The minimum norm least-squares solution (that always exists) of the resulting over-determined system will provide the required solution whenever the system has a reasonably high degree of consistency. A lower error-hound and an upper error-bound of the solution are also included to logically justify the quality/validity of the solution