دانلود کتاب Algebra, Logic and Combinatorics

From the preface

The London Taught Course Centre (LTCC) for PhD students in the Mathematical
Sciences has the objective of introducing research students to a
broad range of advanced topics. For some students, these topics might
include one or two in areas directly related to their PhD projects, but the
relevance of most will be much less clear or even apparently non-existent.
However, all of us involved in mathematical research have experienced that
extraordinary moment when the penny drops and some tiny gem of information
from outside one’s immediate research field turns out to be the key
to unravelling a seemingly insoluble problem, or to opening up a new vista
of mathematical structure. By offering our students advanced introductions
to a range of different areas of mathematics, we hope to open their eyes to
new possibilities that they might not otherwise encounter.

Each volume in this series consists of chapters on a group of related
themes, based on modules taught at the LTCC by their authors. These
modules were already short (five two-hour lectures) and in most cases the
lecture notes here are even shorter, covering perhaps three-quarters of the
content of the original LTCC course. This brevity was quite deliberate on
the part of the editors: we asked contributors to keep their chapters short
in order to allow as many topics as possible to be included in each volume,
whilst keeping the volumes digestible. The chapters are “advanced introductions”,
and readers who wish to learn more are encouraged to continue
elsewhere. There has been no attempt to make the coverage of topics comprehensive.
That would be impossible in any case — any book or series of
books which included all that a PhD student in mathematics might need
to know would be so large as to be totally unreadable. Instead, what we
present in this series is a cross-section of some of the topics, both classical
and new, that have appeared in LTCC modules in the nine years since it
was founded.

The present volume covers the general area of algebra, logic and
combinatorics. The main readers are likely to be graduate students and
more experienced researchers in the mathematical sciences, looking for
introductions to areas with which they are unfamiliar. The mathematics
presented is intended to be accessible to first year PhD students, whatever
their specialised areas of research, though we appreciate that how “elementary”
or “advanced” any particular chapter appears to be will differ
widely from reader to reader. Whatever your mathematical background,
we encourage you to dive in, and we hope that you will enjoy reading these
concise introductory accounts written by experts at the forefront of current
research.