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This book is mainly intended for first-year University students who
undertake a basic abstract algebra course, as well as instructors.
It contains the basic notions of abstract algebra through solved
exercises as well as a 'True or False' section in each chapter.
Each chapter also contains an essential background section, which
makes the book easier to use.
This book is mainly intended for first-year University students who
undertake a basic abstract algebra course, as well as instructors.
It contains the basic notions of abstract algebra through solved
exercises as well as a 'True or False' section in each chapter.
Each chapter also contains an essential background section, which
makes the book easier to use.
'The book is well written, and there is a welcome breadth in the
choice of topics. I think this book is a valuable resource.
Students who meticulously work through all the problems in the book
in an intelligent way, will surely gain considerable insight into
the subject; teachers who donaEURO (TM)t tell their students about
it will find it a valuable source for exam questions.'The
Mathematical GazetteThe book offers a good introduction to topology
through solved exercises. It is mainly intended for undergraduate
students. Most exercises are given with detailed solutions.In the
second edition, some significant changes have been made, other than
the additional exercises. There are also additional proofs (as
exercises) of many results in the old section 'What You Need To
Know', which has been improved and renamed in the new edition as
'Essential Background'. Indeed, it has been considerably beefed up
as it now includes more remarks and results for readers'
convenience. The interesting sections 'True or False' and 'Tests'
have remained as they were, apart from a very few changes.
'The book is well written, and there is a welcome breadth in the
choice of topics. I think this book is a valuable resource.
Students who meticulously work through all the problems in the book
in an intelligent way, will surely gain considerable insight into
the subject; teachers who donaEURO (TM)t tell their students about
it will find it a valuable source for exam questions.'The
Mathematical GazetteThe book offers a good introduction to topology
through solved exercises. It is mainly intended for undergraduate
students. Most exercises are given with detailed solutions.In the
second edition, some significant changes have been made, other than
the additional exercises. There are also additional proofs (as
exercises) of many results in the old section 'What You Need To
Know', which has been improved and renamed in the new edition as
'Essential Background'. Indeed, it has been considerably beefed up
as it now includes more remarks and results for readers'
convenience. The interesting sections 'True or False' and 'Tests'
have remained as they were, apart from a very few changes.
The book offers a good introduction to topology through solved
exercises. It is mainly intended for undergraduate students. Most
exercises are given with detailed solutions.
This book is for third and fourth year university mathematics
students (and Master students) as well as lecturers and tutors in
mathematics and anyone who needs the basic facts on Operator Theory
(e.g. Quantum Mechanists). The main setting for bounded linear
operators here is a Hilbert space. There is, however, a generous
part on General Functional Analysis (not too advanced though).
There is also a chapter on Unbounded Closed Operators.The book is
divided into two parts. The first part contains essential
background on all of the covered topics with the sections: True or
False Questions, Exercises, Tests and More Exercises. In the second
part, readers may find answers and detailed solutions to the True
or False Questions, Exercises and Tests.Another virtue of the book
is the variety of the topics and the exercises and the way they are
tackled. In many cases, the approaches are different from what is
known in the literature. Also, some very recent results from
research papers are included.
This text is the first of its kind exclusively devoted to
counterexamples in operator theory and includes over 500 problems
on bounded and unbounded linear operators in Hilbert spaces. This
volume is geared towards graduate students studying operator
theory, and the author has designated the difficulty level for each
counterexample, indicating which ones are also suitable for
advanced undergraduate students. The first half of the book focuses
on bounded linear operators, including counterexamples in the areas
of operator topologies, matrices of bounded operators, square
roots, the spectrum, operator exponentials, and non-normal
operators. The second part of the book is devoted to unbounded
linear operators in areas such as closedness and closability,
self-adjointness, normality, commutativity, and the spectrum,
concluding with a chapter that features some open problems.
Chapters begin with a brief “Basics” section for the readers’
reference, and many of the counterexamples included are the
author’s original work. Counterexamples in Operator Theory
can be used by students in graduate courses on operator theory and
advanced matrix theory. Previous coursework in advanced linear
algebra, operator theory, and functional analysis is assumed.
Researchers, quantum physicists, and undergraduate students
studying functional analysis and operator theory will also find
this book to be a useful reference.
This book is essentially a survey of results on the Fuglede-Putnam
theorem and its generalizations in a wide variety of directions.
Presenting a broad overview of the results obtained in the field
since the early 1950s, this is the first monograph to be dedicated
to this powerful tool and its variants. Starting from historical
notes and classical versions with their different proofs, the book
then explores asymptotic versions, generalizations to non-normal
operators, generalizations to unbounded operators, counterexamples,
applications, intertwining relations, and conjectures. A rich
collection of applications is included. Aimed at postgraduate
students as well as researchers interested in operator theory, this
book could also be taught as a specialized course.
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