The work of lagrange in number theory and algebra

Joseph Louis Lagrange, a French mathematician, worked on a variety of topics — Algebra (classical and abstract), Number Theory, Dynamics, Functions of several variables, and Astronomy to mention a few. Here we give proofs of four theorems, three in number theory and one in group theory. It is said that post-Newtonian mathematics was dominated by two giants, Lagrange and Euler, in the eighteenth century. While Euler mainly contributed to pure mathematics, Lagrange contributed equally to mathematical physics and pure mathematics. Lagrange had special love for the theory of numbers and theory of polynomials.     

Social justice and political education through non-formal education

The New Policy will lay special emphasis on the removal of disparities and equalise educational opportunity by attending to the specific needs of those who have been denied equality so far.     

Euclid’s fifth postulate

In this article, we review the fifth postulate of Euclid and trace its long and glorious history. That after two thousand years, it led to so much discussion and new ideas speaks for itself. Renuka Ravindran was on the faculty of the Department of Mathematics, IISc, Bangalore. She was also Dean, Science Faculty at IISc. She has been a visiting Professor at various universities in USA and Germany.     

Parental Structuring in Response to Toddler Negative Emotion Predicts Children’s Later Use of Distraction as a Self-Regulation Strategy for Waiting

Structuring is a parental response to young children’s behavior that may foster children’s attempts to use cognitive skills to engage in self-regulation. Using a rural, economically strained sample, parental structuring in response to 127 eighteen-month-olds’ negative emotion was observed during a home visit. Children’s distraction, a useful cognitive strategy when waiting for a reward, was assessed during a laboratory wait task at 18, 24, 36, and 48 months. More frequent parental structuring at child age 18 months predicted more developmental growth in children’s use of distraction between 18 and 48 months, in contrast with parental directives. Consistent with Kopp’s (1989) framework, parental structuring may capitalize on children’s cognitive development to play a unique role in fostering children’s self-regulation of negative emotion.     

Arrow’s impossibility theorem

In this article a number of voting models are considered and the drawbacks of each are indicated. The aim is to develop a voting method, which is based on individual preferences and which finally represents the choice of society. Arrow’s theorem addresses this problem.     

Teachers and `Street Children': On Becoming a Teacher of Mathematics

The phenomenon of `street children' where youngpeople, for various reasons, live on thestreets of towns and cities is found all overthe world in varying degrees and forms. InSouth Africa, one approach to take care aboutthe plight of these children has been to set upand run what are referred to as `streetshelters'. One such street shelter, the onlyone exclusively for girls in the city ofDurban, is Tennyson House. In this paper Idescribe an innovative outreach programmeintegrated with a university curriculum inwhich a group of pre-service teachers takingmathematics education as a major were involvedin teaching mathematics to girls at TennysonHouse. From the vantage point of a mathematicsteacher educator in the programme, I describeand reflect on what was experienced and learnedfrom the intervention in terms of threeaspects: learning about learners; learningabout teaching (mathematics) and learning aboutrelationships.     

Lighthill and his art of mathematical modelling

Lighthill modeled the flow of blood through a narrow capillary involving the passage of individual red blood cells through it in a single file. The study involved the motion of relatively tightly fitting pellets of solid matter forced along distensible tubes. The equations governing the motion and suitable boundary conditions are formulated. The mathematical highlight of Lighthill’s model is the use of the method of matched asymptotic expansion in six layers.     

Gender,teaching and academic promotions in higher education

Teaching is increasingly being considered for inclusion in academic promotions in a number of universities. This raises questions about how teaching is appraised in relation to research; and which teaching criteria contribute to promotions outcomes. This article investigates these questions from a gender perspective by statistically analysing the actual promotions outcomes by rank levels at a South African university where teaching and research have been equally evaluated in academic promotions. The findings show that, overall, there was no statistically significant difference in promotions success rates between males and females and that more females achieved excellence in teaching with higher scores than males. Two of the 10 teaching criteria analysed – ‘ongoing study of tertiary education’ and ‘special recognition of teaching’ showed statistically significantly higher scores for females with high effect sizes, pointing to the importance of the Scholarship of Teaching and Learning in academic promotions for women. This study has implications for closing the gender gap in the senior ranks of universities.     

Sex hormone binding globulin in breast cancer

The present study was undertaken to determine the significance of sex hormone binding globulin, the major and specific binding protein for testosterone and estradiol, in breast cancer. Among breast cancer patients, lower serum levels of Sex hormone binding globulin and higher levels of testosterone were observed. Sex hormone binding globulin showed an inverse relationship with testosterone and total cholesterol, and a direct relation with HDL-cholesterol. By the western blot analyses, Sex hormone binding globulin was detected in all biological samples that we examined. In the breast tumor tissue sections, immuno-staining for Sex hormone binding globulin was confined in cell cytoplasm and 29% cases were positive, which showed no association with the investigated prognostic markers of breast cancer such as ER and HER-2/neu over-expression. In this study, decreased circulating levels of Sex hormone binding globulin in breast cancer patients possibly indicate higher bioavailable estrogens.