These lecture notes discuss the extension problem and the MacWilliams identities for linear codes defined over finite modules.

These lecture notes on “Geometric Graphs, Triangulations and Polytopes” cover the material presented for half of the MPRI Master Course 2.38.1 entitled “Algorithmique et combinatoire des graphes géométriques”. The other half of the course, taught by Éric Colin de Verdière, focusses on “Algorithms for embedded graphs” [dV]. Announcements and further informations on the course are available onlin...

Introduction: Note taking while attending a PPT requires highactivity of memory and writing process which ultimately leadsto what is called “death by power point” referring to boredomand fatigue. To overcome this we planned to evaluate the impactof utilisation of uncompleted handouts given prior to PPTpresentations.Methods: Final year MBBS students were divided in 2 batches,batch A and batch B....

We often have to deal with situations involving hidden or unpredictable factors. Sometimes the unpredictability is an essential element of the phenomenon under investigation. For example, physicists regard radioactive decay as a purely random phenomenon caused by quantum fluctuations of the state of radioactive atoms. More often, the unpredictability is due to our lack of information of all the...

Looking at the examples in (2.1), we see that the degree of the first polynomial is 2, the second one has degree 16, etc. A number of operations can be performed with polynomials. Given a polynomial p(z) and a complex number c, the polynomial c p(z) is obtained by multiplying each coefficient in p(z) by c. Given two polynomials p(z) and q(z), their sum is defined by adding the coefficients of c...