This brief monograph by one of the great mathematicians of the
early twentieth century offers a single-volume compilation of
propositions employed in proofs of Cauchy's theorem. Developing
an arithmetical basis that avoids geometrical intuitions, Watson
also provides a brief account of the various applications of the
theorem to the evaluation of definite integrals.
Author G. N. Watson begins by reviewing various propositions of... more...

Classic two-part work now available in a single volume assumes
no prior theoretical knowledge on reader's part and develops
the subject fully. Volume I is a suitable first course text for
advanced undergraduate and beginning graduate students. Volume
II requires a much higher level of mathematical maturity,
including a working knowledge of the theory of analytic
functions. Contents range from chapters on binary... more...

This lucid introductory text offers both an analytic and an
axiomatic approach to plane projective geometry. The analytic
treatment builds and expands upon students' familiarity with
elementary plane analytic geometry and provides a well-motivated
approach to projective geometry. Subsequent chapters explore
Euclidean and non-Euclidean geometry as specializations of the
projective plane, revealing the existence of an infinite number
of... more...

Starting with the fundamentals of number theory, this text
advances to an intermediate level. Author Harold N. Shapiro,
Professor Emeritus of Mathematics at New York University's
Courant Institute, addresses this treatment toward advanced
undergraduates and graduate students. Selected chapters,
sections, and exercises are appropriate for undergraduate
courses.
The first five chapters focus on the basic material of number
theory,... more...

Over 1500 problems on theory of functions of the complex
variable; coverage of nearly every branch of classical function
theory. Topics include conformal mappings, integrals and power
series, Laurent series, parametric integrals, integrals of the
Cauchy type, analytic continuation, Riemann surfaces, much
more. Answers and solutions at end of text. Bibliographical
references. 1965 edition.

The theory of ordinary differential equations in real and
complex domains is here clearly explained and analyzed. Not
only classical theory, but also the main developments of modern
times are covered. Exhaustive sections on the existence and
nature of solutions, continuous transformation groups, the
algebraic theory of linear differential systems, and the
solution of differential equations by contour integration are... more...

Combining three books into a single volume, this text comprises
Multicolor Problems, dealing with several of the
classical map-coloring problems; Problems in the Theory of
Numbers, an elementary introduction to algebraic number
theory; and Random Walks, addressing basic problems in
probability theory.
The book's primary aim is not so much to impart new information
as to teach an active, creative attitude toward mathematics. The... more...

Advanced undergraduates and graduate students studying quantum
mechanics will find this text a valuable guide to mathematical
methods. Emphasizing the unity of a variety of different
techniques, it is enduringly relevant to many physical systems
outside the domain of quantum theory.
Concise in its presentation, this text covers eigenvalue problems
in classical physics, orthogonal functions and expansions, the
Sturm-Liouville theory and... more...

The ultimate aim of the field of numerical analysis is to
provide convenient methods for obtaining useful solutions to
mathematical problems and for extracting useful information
from available solutions which are not expressed in tractable
forms. This well-known, highly respected volume provides an
introduction to the fundamental processes of numerical
analysis, including substantial grounding in the basic... more...

Exceptionally smooth, clear, detailed examination of uniform
spaces, topological groups, topological vector spaces,
topological algebras and abstract harmonic analysis. Also,
topological vector-valued measure spaces as well as numerous
problems and examples. For advanced undergraduates and beginning
graduate students. Bibliography. Index.