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This work covers three important aspects of monomials ideals in the
three chapters "Stanley decompositions" by Jürgen Herzog, "Edge
ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez
Montaner. The chapters, written by top experts, include computer
tutorials that emphasize the computational aspects of the
respective areas. Monomial ideals and algebras are, in a sense,
among the simplest structures in commutative algebra and the main... more...

The book deals with the representation in series form of compact
linear operators acting between Banach spaces, and provides an
analogue of the classical Hilbert space results of this nature that
have their roots in the work of D. Hilbert, F. Riesz and E.
Schmidt. The representation involves a recursively obtained
sequence of points on the unit sphere of the initial space and a
corresponding sequence of positive numbers that correspond to the... more...

Michael Steele describes the fundamental topics in mathematical
inequalities and their uses. Using the Cauchy-Schwarz inequality as
a guide, Steele presents a fascinating collection of problems
related to inequalities and coaches readers through solutions, in a
style reminiscent of George Polya, by teaching basic concepts and
sharpening problem solving skills at the same time. Undergraduate
and beginning graduate students in mathematics, theoretical... more...

Computer algebra systems are now ubiquitous in all areas of science
and engineering. This highly successful textbook, widely regarded
as the 'bible of computer algebra', gives a thorough introduction
to the algorithmic basis of the mathematical engine in computer
algebra systems. Designed to accompany one- or two-semester courses
for advanced undergraduate or graduate students in computer science
or mathematics, its comprehensiveness and reliability... more...

"An excellent up-to-date introduction to the theory of groups. It
is general yet comprehensive, covering various branches of group
theory. The 15 chapters contain the following main topics: free
groups and presentations, free products, decompositions, Abelian
groups, finite permutation groups, representations of groups,
finite and infinite soluble groups, group extensions,
generalizations of nilpotent and soluble groups, finiteness... more...

The notes in this volume correspond to advanced courses given at
the Centre de Recerca Matemàtica (Bellaterra, Barcelona, Spain) as
part of the Research Programme in Arithmetic Geometry in the
2009-2010 academic year. They are now available in printed form due
to the many requests received by the organizers to make the content
of the courses publicly available. The material covers the theory
of p-adic Galois representations and Fontaine rings, Galois... more...

Nestled between number theory, combinatorics, algebra and
analysis lies a rapidly developing subject in mathematics
variously known as additive combinatorics, additive number
theory, additive group theory, and combinatorial number theory.
Its main objects of study are not abelian groups themselves, but
rather the additive structure of subsets and subsequences of an
abelian group, i.e., sumsets and subsequence sums. This text is a... more...

Linear algebra and matrix theory are fundamental tools in
mathematical and physical science, as well as fertile fields for
research. This new edition of the acclaimed text presents results
of both classic and recent matrix analysis using canonical forms as
a unifying theme, and demonstrates their importance in a variety of
applications. The authors have thoroughly revised, updated, and
expanded on the first edition. The book opens with an extended... more...

This completely revised and corrected version of the well-known
Florence notes circulated by the authors together with E.
Friedlander examines basic topology, emphasizing homotopy theory.
Included is a discussion of Postnikov towers and rational
homotopy theory. This is then followed by an in-depth look at
differential forms and de Tham’s theorem on simplicial complexes.
In addition, Sullivan’s results on computing the rational... more...