pp 1063-1063 Editorial
pp 1065-1068 Article in a Box
pp 1069-1069 Science Smiles
pp 1073-1091 General Article
Weyl was a universal mathematician whose fundamental contributionsto mathematics encompassed all areas, and provideda unification seldom seen. His work on the theory ofLie groups was motivated by his life-long interest in quantummechanics and relativity. When Weyl entered Lie theory,it mostly focussed on the infinitesimal, and he strove to bringin a global perspective. Time and again, Weyl’s ideas arisingin one context have been adapted and applied to wholly newcontexts. In 1925–26, Weyl wrote four epochal papers in representationtheory of Lie groups which solved fundamentalproblems, and also gave birth to the subject of harmonic analysisof semisimple Lie groups. In these papers, Weyl provedcomplete reducibility theorems and introduced many techniqueswhich have become the standard way to study representationsof Lie groups and their various generalizationsin the last seven decades. Weyl’s work covers several parts ofmathematics, as well as parts of physics. In this article, wediscuss mainly his contributions to the representation theoryof Lie groups via the four papers mentioned above.
pp 1093-1104 General Article
The symbiotic association between plant and fungi (mycorrhizalassociation) is an amazing phenomenon observed innature. The mycorrhizal association is one of nature’s boonsfor sustainable agriculture. In today’s changing environment,indiscriminate use of pesticides and chemicals pose a greatthreat to the existence of mycorrhizal species. There is a needto spread awareness in order to save mycorrhizal fungi fromextinction.
pp 1105-1117 General Article
Spin is a fundamental degree of freedom of matter and radiation.In quantum theory, spin is represented by Pauli matrices.Then the various algebraic properties of Pauli matricesare studied as properties of matrix algebra. What has beenshown in this article is that Pauli matrices are a representationof Clifford algebra of spin and hence all the propertiesof Pauli matrices follow from the underlying algebra. Cliffordalgebraic approach provides a geometrical and henceintuitive way to understand quantum theory of spin, and isa natural formalism to study spin. Clifford algebraic formalismhas lot of applications in every field where spin plays animportant role.
pp 1119-1133 Classroom
The Arithmetic Mean – Geometric Mean – Harmonic Meaninequality, AM–GM–HM inequality in short, is one of thefundamental inequalities in Algebra, and it is used extensivelyin olympiad mathematics to solve many problems. Theaim of this article is to acquaint students with the inequality,its proof and various applications.
pp 1135-1149 Classroom
E T Bell, the famous author of ‘Men of Mathematics’, hasdescribed mathematics as the ‘Queen of Arts and Servant ofScience’. What he meant is that mathematics serves scienceby entering into the picture as soon as a proper mathematicalmodel is set up by the scientist, and then after a purely mathematicalanalysis of the model, the final mathematical step isinterpreted scientifically. The purpose of the present articleis to convince the readers that sometimes the roles of scienceand mathematics are reversed, and a mathematical problemis interpreted as a physics problem; the laws of physics areutilized for a physical analysis, and the final result of thephysical analysis is interpreted mathematically. We shall illustratethis by means of few examples.
pp 1151-1151 Information and Announcements
pp 1153-1153 Flowering Trees