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These lecture notes begin with an introduction to topological
groups and proceed to a proof of the important Pontryagin-van
Kampen duality theorem and a detailed exposition of the structure
of locally compact abelian groups. Measure theory and Banach
algebra are entirely avoided and only a small amount of group
theory and topology is required, dealing with the subject in an
elementary fashion. With about a hundred exercises for the student,
it is a... more...

Ideal for courses that require the use of a graphing calculator,
ALGEBRA AND TRIGONOMETRY: REAL MATHEMATICS, REAL PEOPLE, 6th
Edition, features quality exercises, interesting applications, and
innovative resources to help you succeed. Retaining the book's
emphasis on student support, selected examples include notations
directing students to previous sections where they can review
concepts and skills needed to master the material at hand. The book
also... more...

A knowledge of matrix algebra is a prerequisite for the study of
much of modern statistics, especially the areas of linear
statistical models and multivariate statistics. This reference book
provides the background in matrix algebra necessary to do research
and understand the results in these areas. Essentially
self-contained, the book is best-suited for a reader who has had
some previous exposure to matrices. Solultions to the exercises are
available... more...

This book contains over 300 exercises and solutions that together
cover a wide variety of topics in matrix algebra. They can be used
for independent study or in creating a challenging and stimulating
environment that encourages active engagement in the learning
process. The requisite background is some previous exposure to
matrix algebra of the kind obtained in a first course. The
exercises are those from an earlier book by the same author
entitled... more...

Aimed primarily at graduate students and beginning researchers,
this book provides an introduction to algebraic geometry that is
particularly suitable for those with no previous contact with the
subject; it assumes only the standard background of undergraduate
algebra. The book starts with easily-formulated problems with
non-trivial solutions and uses these problems to introduce the
fundamental tools of modern algebraic geometry: dimension;... more...

This is a short text in linear algebra, intended for a one-term
course. In the first chapter, Lang discusses the relation between
the geometry and the algebra underlying the subject, and gives
concrete examples of the notions which appear later in the book. He
then starts with a discussion of linear equations, matrices and
Gaussian elimination, and proceeds to discuss vector spaces, linear
maps, scalar products, determinants, and eigenvalues. The book... more...

A presentation of outstanding achievements and ideas, of both
eastern and western scientists, both mathematicians and physicists.
Their presentations of recent work on quantum field theory,
supergravity, M-theory, black holes and quantum gravity, together
with research into noncommutative geometry, Hopf algebras,
representation theory, categories and quantum groups, take the
reader to the forefront of the latest developments. Other topics
covered... more...

Graph models are extremely useful for almost all applications and
applicators as they play an important role as structuring tools.
They allow to model net structures - like roads, computers,
telephones - instances of abstract data structures - like lists,
stacks, trees - and functional or object oriented programming. In
turn, graphs are models for mathematical objects, like categories
and functors. This highly self-contained book about algebraic graph... more...

The Weyr matrix canonical form is a largely unknown cousin of the
Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr
form outperforms the Jordan form in a number of mathematical
situations, yet it remains somewhat of a mystery, even to many who
are skilled in linear algebra.
Written in an engaging style, this book presents various advanced
topics in linear algebra linked through the Weyr form. Kevin
O'Meara, John Clark, and Charles... more...