id: 06202749
dt: b
an: 2014b.00551
au: Moore, Will H.; Siegel, David A.
ti: A mathematics course for political and social research.
so: Princeton, NJ: Princeton University Press (ISBN 978-0-691-15917-1/pbk;
978-0-691-15995-9/hbk; 978-1-4008-4861-4 /ebook). xix, 430~p. (2013).
py: 2013
pu: Princeton, NJ: Princeton University Press
la: EN
cc: H15 I15 K15 M15
ut: conceptions; basic mathematics; linear algebra; multivariate calculus;
optimization
ci:
li:
ab: This book is intended primarily for political scientists, not
mathematicians; if one needs to understand what mathematics is, what it
can tell, and how it can be useful to read this book. The authors aim
to provide a practical text that meets these intentions. The book is
divided into five parts. The first part covers the preliminaries and
topics which the reader should have learned in high school. In
particular, the chapter introduces variables, sets, operators,
relations, notations, and proofs. Other topics are basic algebra
including equation solving as well as functions and relations. The
second part covers calculus in one dimension including optimization.
Further, this part offers differentiation rules and derivatives of both
common and special functions. It introduces the indefinite and definite
integral, provides techniques of integration, and discusses the
fundamental theorem of calculus. At the end of this part, extreme
values of functions are defined, higher-order derivatives are
discussed, and concave and convex functions are considered. The third
part tackles probability from its basics to discrete and continuous
distributions. The fourth part is a primer on linear algebra. The fifth
and final part is the most complex part of the book. It introduces
selected topics in multivariate calculus including constrained and
unconstrained optimization and implicit differentiation. In each
chapter, the book gives reasons why a student should master particular
areas of mathematics. In spite of the fact that in political social
research game theory plays an important role, the subject is not
treated separately because the other chapters already introduce the
utility and the expected utility and discuss their maximization, which
is the heart of game theory. These actions form part of equilibrium
behavior, which means that each player is satisfied with his optimal
action, given everyone else’s optimal actions, and has no incentive
to change it. Each chapter concludes with a set of exercises designed
to develop mastery via practice. Detailed examples are included
throughout the highlighting of important concepts or techniques, aiming
at fostering a practical knowledge of mathematics that can be brought
into coursework and research. At the end of the book, online resources
are referenced.
rv: Fatima T. Adylova (Tashkent)