The Serre spectral sequence of a noncommutative fibration for de Rham cohomology

For differential calculi on noncommutative algebras, we construct a twisted de Rham cohomology using flat connections on modules. This has properties similar, in some respects, to sheaf cohomology on topological spaces. We also discuss generalised mapping properties of these theories, and relations of these properties to corings. Using this, we give conditions for the Serre spectral sequence to hold for a noncommutative fibration. This might be better read as giving the definition of a fibration in noncommutative differential geometry. We also study the multiplicative structure of such spectral sequences. Finally we show that some noncommutative homogeneous spaces satisfy the conditions to be such a fibration, and in the process clarify the differential structure on these homogeneous spaces. We also give two explicit examples of differential fibrations: these are built on the quantum Hopf fibration with two different differential structures.Comment: LaTeX, 33 page

Problem Based Learning (PBL) for Engineering Education in India: Need and Recommendations

Historical footprint of problem based learning (PBL) could be traced back at McMasters University, Canada 1968. Since then, PBL is enriched with development in the literature and multiple PBL models across the world. PBL, has gained importance in modern era of higher education as it has been implemented in many universities across the world in higher education. Although, world is weighing up for PBL and its positive outcomes, it could not extend much in Indian higher education. An objective of this manuscript is to give an overview of PBL across the world and in India. In addition to this, Indian higher education landscape and scope of PBL to Indian engineering education is discussed. Article ends with some recommendations to ensure growth of PBL in India.</p

Report on the Brauer-Thrall conjectures: Rojter's theorem and the theorem of Nazarova and Rojter (on algorithms for solving vectorspace problems. I)

Ringel CM. Report on the Brauer-Thrall conjectures: Rojter's theorem and the theorem of Nazarova and Rojter (on algorithms for solving vectorspace problems. I). In: Dlab V, Gabriel P, eds. Representation Theory I. Proceedings of the Workshop on the Present Trends in Representation Theory, Ottawa, Carleton University, August 13-18, 1979: No. 1. Lecture notes in mathematics. Vol 831. Berlin, Heidelberg: Springer; 1980: 104-136