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.     

Telemedicine for patient education

Abstract

A telemedicine project was conducted to explore the delivery of childbirth preparation classes originating at a large regional hospital to a remote site at a small rural hospital. Over six months, three series of classes were included in the project, with twenty‐four participants at the originating site and twenty participants at the remote site. A two‐way, audio/video teleconferencing system with multiple cameras and monitors was employed for instruction. A registered nurse taught the class and a site facilitator assisted at the remote site. Evaluation of the project was done through surveys, interviews, and observations. The classes were well received by project participants at both sites. Principal advantages cited were increased availability of the programs, improved attendance, and convenience to rural participants. The principal disadvantages cited focused on technical problems, particularly audio quality.     

Redundant networks and minimum distance

Networks in which each node is directly linked to its nearest neighbors exhibit high reliability and message handling capability. The construction of such networks guaranteeing minimal length, for a given degree of redundancy, is formulated in zero-one integer linear programming terms. Initial feasible solutions to the programs are presented, but connectedness is not guaranteed. In the latter case further zero-one integer programs are proposed assuring connectedness, with given initial feasible solutions. The inefficiency of zero-one programs for large networks leads to consideration of alternate redundant connected networks, without guaranteed minimal length. These networks are based on “nearest- neighbor edge sets”, and are simple to construct. Various theorems on the properties of such networks are presented with applications to one-way communicability.     

Junior researchers’ experience of innovation in a multidisciplinary team environment

This paper describes junior researchers’ experience of innovative research, with the aim of encouraging fellow junior academics. Through the experience, the team recognised that context and flexibility are key factors in the research process. These factors are discussed in the light of three specific features of this project. First is the type of research the team engages in: meta-research, which includes looking at how research is managed. Second, the team is embedded in a larger organisation that holds a broad range of perspectives, from molecular scientists to sociologists. Third, the organisation offers unique opportunities not available through the traditional academic paradigm. Identification of these factors influenced the learning associated with engaging in innovative research, not in the least was the lesson that research does not follow a linear path. These concepts are framed by Blumer's theory of Symbolic Interactionism.     

A qualitative study of the academic,social, and cultural factors that influence students’ library use in a rural Ugandan village

The Kitengesa Community Library in rural Uganda is unique in that provides tailored collections and services for the community. This library, which was built in 2002, serves a small but diverse population including a large number of secondary school students who live in the area. Previous research on the impact of this library on the surrounding community revealed that the library influences reading habits, reading culture development, and the availability of locally relevant information. This is especially true for young adults, who represent Uganda's fastest growing population. Only 18 percent of girls and 20 percent of boys are enrolled in secondary school, rendering this group of students (ages 13–17) particularly vulnerable to a wide range of social and economic challenges. School libraries in Uganda are rare, and in this case, the Kitengesa Community Library serves as a de facto school library. Previous research by Dent and Yannotta (2005) revealed that secondary school students are among the heaviest users of the Kitengesa Community Library, and this qualitative study represents an attempt to characterize students' library use experiences across academic, social, and cultural domains. Findings suggest that the student experience consists of five factors – personal improvement, reading culture development, academic support, learning independence, and reducing isolation. There is a growing network of rural village libraries in Africa and the findings from this study will be used to inform development of additional library services and resources to better support student learning and interpersonal growth.     

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.