pp 905-906 Editorial
pp 907-907 Science Smiles
pp 911-913 Article-in-a-Box
pp 915-933 General Article
The Hahn–Banach theorem is one of the major theoremsproved in any first course on functional analysis. It has plentyof applications, not only within the subject itself, but alsoin other areas of mathematics like optimization, partial differentialequations, and so on. This article will give a briefoverview of the Hahn–Banach theorem, its ramifications andindicate some applications.
pp 935-941 General Article
pp 943-953 General Article
Greeks used the method of cutting a geometric region intopieces and recombining them cleverly to obtain areas of figureslike parallelograms. In such problems, the boundaryis ignored. However, in our discussion, we will take everypoint of space into consideration. The human endeavour tocompute lengths, areas, and volumes of irregular complicatedshapes and solids created the subject of ‘measure theory’.The paradox of the title can be informally described as follows.Consider the earth including the inside stuff. It is possibleto decompose this solid sphere into finitely many piecesand apply three-dimensional rotations to these pieces suchthat the transformed pieces can be put together to form twosolid earths! The whole magic lies in the word ‘pieces’. Thepieces turn out to be so strange that they cannot be ‘measured’.
pp 955-960 Classroom
In this series of articles, the authors discuss various phenomenain fluid dynamics, which may be investigated via tabletopexperiments using low-cost or home-made instruments. Theeighth article in this series explores and demonstratesKelvin–Helmholtz instability.
pp 961-970 Classroom
There are several concepts in molecular thermodynamics whicheasily befuddle students. PV-type work done, presents onesuch example. Classifying the systematic mistakes made bystudents in response to a concept-based question on workdone in thermodynamics, and sharing them across a publicforum results in a paradigm of learning called the ‘mistakebased approach’. This approach is a subset of a populargenre in science education known as ‘student conceptionstudies’. It extends beyond thermodynamics itself, is particularlyamenable to undergraduate education and applies tomultiple disciplines of science and beyond.
pp 971-971 Information and Announcements
pp 972-972 Information and Announcements
pp 973-973 Information and Announcements
pp 974-974 Information and Announcements
pp 975-975 Information and Announcements
pp 976-976 Information and Announcements
pp 977-977 Information and Announcements
pp 978-978 Information and Announcements
pp 979-979 Flowering Trees