Complex numbers and plane geometry

The representation of complex numbers as points of the Euclidean plane naturally leads to a two-way interaction between geometry and numbers. The geometry of the plane has a very deep influence in the study complex analytic functions. In this article, we illustrate the other way aspect by a few simple-minded application of complex numbers to give elegant solutions of problems in plane geometry, such as Ptolemy’s Theorem, Euler-line and Nine-point Circle Theorem. Anant R Shastri is a Professor at IIT, Bombay. His research inerests are in algebraic topology and algebraic geometry. He is also keen in math education and music. This article is based on a talk given to an audience consisting mainly students of class IX and X, at Nehru Science Centre under the aegis of Bombay Association for Science Education and Bombay Math. Colloq. on 25th Jan. 2003. An earlier version of this article was published in Bona Mathematica, Vol.14 Nos.1–2, 2003.     

Beginnings of group cohomology

Cohomology theory is a powerful mathematical tool. This theory applied to topology is a part of algebraic topology, which associates algebraic invariants to topological spaces. In this article, we give a brief outline of group cohomology. R Sridharan has been an Adjunct Professor at the CMI, Chennai since retiring from TIFR, Bombay in 2000 where he was a senior professor. He is also an INSA senior scientist now. His scholarship permeates to literature (English and Sanskrit) and philosophy as well. Many of the algebraists in the country were his students. Dedicated to my teacher S Eilenberg     

Supporting Oral Second Language Use: A Learning Experience in a First Grade German Immersion Class

This article describes a learning context in which the first grade classroom teacher creates a learning community where she uses different teaching strategies to encourage children’s second language use and learning. The first graders share, discuss, and learn both the second language (German) and content.