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.

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.