By Titu Andreescu
This ebook is meant to aid scholars getting ready for all rounds of Mathematical Olympiads or the other major arithmetic contest.
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Extra info for 360 Problems for Mathematical Contests
An R0 of approximately 2 for HIV over an entire infectious duration of approximately 10 years, is quite different to an R0 of 2 or 3 for influenza or SARS over an infectious period of a couple of weeks [17, 18, 132, 133]. Regardless of the disease or method for estimating R0, all estimates in the literature of R0 for most diseases will almost always be reported to be around the same of 2-3 anyway! Further, how is an expression of ‘R0’= complex function of model parameters going to change policy?
Yet these models actually require a much more extensive parameter uncertainty analysis. Because of the large investment in development and implementation of the complex models, the practitioners are less likely to adapt or start afresh to meet new research problems but desire to use their existing model and find a problem to which it could be applied. Although there are many considerations that must be evaluated when one is developing a model, one must choose the approach that is most appropriate for the situation at hand.
Local minima in the sum of squares may produce a set of estimates for unknown parameters that are not representative of the true values of the parameters – multiple sets of parameter values in different regions of parameter space may produce similar (minimal) sum of square errors but only one set (or none of them) may reflect the true values. Furthermore, the fact that the model fits the data does not necessarily validate the model. By just adding extra parameters to be fitted for, it is possible to fit almost any data .