To most of the lectures I have added exercises. Quite a few ar
mine; but most are drawn or adapted from the cited references fo
their aptitude to reinforce the topic of the lecture. At this level o
discourse, various canonical exercises are pervasive in the pedagog
cal literature and can be found in multiple sources with only mino
variation: if these old standards are not de rigueur, then they are a
least very hard to improve on. I have therefore included a significan
number of them, and further problems, if necessary, may be foun
among the references (as indicated by endnotes). Only solutions o
hints for selected exercises appear at the end of the book, but mor
complete solutions are available from the
author.2
Finally, a word or two about notation. Just as modelling compel
tradeoffs among generality, precision and realism [36], so pedagog
compels tradeoffs among generality, rigor and transparency; and cen
tral to those tradeoffs is use of notation. At least two issues arise. Th
first is the subjectivity of signal-to-noise ratio. One person’s oasis o
terminological correctness may be another person’s sea of impenetra
ble clutter; and in any event, strict adherence to unimpeachably cor
rect notation entails encumbrances that often merely obscure. Th
second, and related, issue is that diversity is intrinsically valuabl
[46]. In the vast ecosystem of mathematical and scientific literature
polymorphisms of notation survive and prosper because, as in nature
each variant has its advantages and disadvantages, and none is un
versally adaptive. Aware of both issues, I use a mix of notation tha
suppresses assumed information when its relevance is not immediate
thus striving at all times to emphasize clarity over rigor.
2To
any instructor or bona fide independent user. For contact details, see
http://www.ams.org/bookpages/stml-50/index.html.
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