vi PREFACE
its use for a variety of course structures , for example to meet prerequisite
requirements for follow-on subjects. We found the lab classes to be particu-
larly important pedagogically, as students learn progra mming through their
own experimentation. Instructors may straightforwardly compile lab classes
by drawing on the numerous examples and exercis e s in the text, and these are
supplemented by the programming projects contained in Chapter
22, which
are based on assignments we gave our students.
Core content The following chapters contain our core material for a course
on scientific programming and simulation.
Part I: Core knowledge of R and progra mming concepts. Chapters
1–6.
Part II: Thinking about mathematics from a numerical point of view: applying
Part I concepts to root finding and numerical integration. Chapters
9–11.
Part III: Es sentials of probability, random variables, and expectation required
to understand simulation. Chapters
13–15 plus the uniform distribution.
Part IV: Stochastic modelling and simulatio n: rando m number generation,
Monte-Carlo integration, case studies and projects. Chapters
18.1–18.2, 19,
21.1–21.2 and 22.
Additional stochastic material The core outlined above only uses discrete
random varia bles, and for es timation only uses the concept of a sa mple average
converging to a mean. Chapters
16 and 17 add continuous random variables,
the Central Limit Theo rem and confidence intervals. Chapters
18.3–18.5 and
20 then look a t simulating continuous random variables and variance reduc-
tion. With some familiarity of continuous random variables the remaining case
studies, Chapter
21.3–21.4, become accessible.
Note that some of the pr ojects in Chapter
22 use continuous random variables,
but can be easily modified to us e discrete random variables instead.
Additional programming and numerical m aterial For the core material ba-
sic plotting of output is sufficient, but for those wanting to produce more
professional graphics we provide Chapter
7. Chapter 8, on further program-
ming, acts as a br idge to more spec ialised texts, for those who wish to pursue
programming more deeply.
Chapter
12 deals with univariate and multivariate optimisation. Sec tions 12.3–
12.7 on multivariate optimisation, a re harder than the r e st of the book, and
require a basic familiarity with vector ca lculus. This material is self-co ntained,
with the exc e ptio n of Example
17.1.2, which uses the optim function. However,
if you are prepared to use optim as a black box, then this exa mple is also quite
accessible without reading the multivariate optimisation sections.
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