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'I like the authorsaEURO (TM) taste in footnotes, what with their
frequent emphasis on history, i.e. the minutiae of the lives of
many mathematicians appearing in these pages. Their remarks add a
particular dimension of fun and pleasure to what I think is a very
good book. ItaEURO (TM)s pitched at the right level, it does a lot
of serious stuff in preparation for what is coming the
studentsaEURO (TM) way in the future, and it does it well.'MAA
ReviewsThis comprehensive two-volume book deals with algebra,
broadly conceived. Volume 1 (Chapters 1-6) comprises material for a
first year graduate course in algebra, offering the instructor a
number of options in designing such a course. Volume 1, provides as
well all essential material that students need to prepare for the
qualifying exam in algebra at most American and European
universities. Volume 2 (Chapters 7-13) forms the basis for a second
year graduate course in topics in algebra. As the table of contents
shows, that volume provides ample material accommodating a variety
of topics that may be included in a second year course. To
facilitate matters for the reader, there is a chart showing the
interdependence of the chapters.
'I like the authorsaEURO (TM) taste in footnotes, what with their
frequent emphasis on history, i.e. the minutiae of the lives of
many mathematicians appearing in these pages. Their remarks add a
particular dimension of fun and pleasure to what I think is a very
good book. ItaEURO (TM)s pitched at the right level, it does a lot
of serious stuff in preparation for what is coming the
studentsaEURO (TM) way in the future, and it does it well.'MAA
ReviewsThis comprehensive two-volume book deals with algebra,
broadly conceived. Volume 1 (Chapters 1-6) comprises material for a
first year graduate course in algebra, offering the instructor a
number of options in designing such a course. Volume 1, provides as
well all essential material that students need to prepare for the
qualifying exam in algebra at most American and European
universities. Volume 2 (Chapters 7-13) forms the basis for a second
year graduate course in topics in algebra. As the table of contents
shows, that volume provides ample material accommodating a variety
of topics that may be included in a second year course. To
facilitate matters for the reader, there is a chart showing the
interdependence of the chapters.
'I like the authorsaEURO (TM) taste in footnotes, what with their
frequent emphasis on history, i.e. the minutiae of the lives of
many mathematicians appearing in these pages. Their remarks add a
particular dimension of fun and pleasure to what I think is a very
good book. ItaEURO (TM)s pitched at the right level, it does a lot
of serious stuff in preparation for what is coming the
studentsaEURO (TM) way in the future, and it does it well.'MAA
ReviewsThis comprehensive two-volume book deals with algebra,
broadly conceived. Volume 1 (Chapters 1-6) comprises material for a
first year graduate course in algebra, offering the instructor a
number of options in designing such a course. Volume 1, provides as
well all essential material that students need to prepare for the
qualifying exam in algebra at most American and European
universities. Volume 2 (Chapters 7-13) forms the basis for a second
year graduate course in topics in algebra. As the table of contents
shows, that volume provides ample material accommodating a variety
of topics that may be included in a second year course. To
facilitate matters for the reader, there is a chart showing the
interdependence of the chapters.
'I like the authorsaEURO (TM) taste in footnotes, what with their
frequent emphasis on history, i.e. the minutiae of the lives of
many mathematicians appearing in these pages. Their remarks add a
particular dimension of fun and pleasure to what I think is a very
good book. ItaEURO (TM)s pitched at the right level, it does a lot
of serious stuff in preparation for what is coming the
studentsaEURO (TM) way in the future, and it does it well.'MAA
ReviewsThis comprehensive two-volume book deals with algebra,
broadly conceived. Volume 1 (Chapters 1-6) comprises material for a
first year graduate course in algebra, offering the instructor a
number of options in designing such a course. Volume 1, provides as
well all essential material that students need to prepare for the
qualifying exam in algebra at most American and European
universities. Volume 2 (Chapters 7-13) forms the basis for a second
year graduate course in topics in algebra. As the table of contents
shows, that volume provides ample material accommodating a variety
of topics that may be included in a second year course. To
facilitate matters for the reader, there is a chart showing the
interdependence of the chapters.
This is the only book that deals comprehensively with fixed point
theorems throughout mathematics. Their importance is due, as the
book demonstrates, to their wide applicability. Beyond the first
chapter, each of the other seven can be read independently of the
others so the reader has much flexibility to follow his/her own
interests. The book is written for graduate students and
professional mathematicians and could be of interest to physicists,
economists and engineers.
This book begins with the basics of the geometry and topology of
Euclidean space and continues with the main topics in the theory of
functions of several real variables including limits, continuity,
differentiation and integration. All topics and in particular,
differentiation and integration, are treated in depth and with
mathematical rigor. The classical theorems of differentiation and
integration such as the Inverse and Implicit Function theorems,
Lagrange's multiplier rule, Fubini's theorem, the change of
variables formula, Green's, Stokes' and Gauss' theorems are proved
in detail and many of them with novel proofs. The authors develop
the theory in a logical sequence building one result upon the
other, enriching the development with numerous explanatory remarks
and historical footnotes. A number of well chosen illustrative
examples and counter-examples clarify matters and teach the reader
how to apply these results and solve problems in mathematics, the
other sciences and economics. Each of the chapters concludes with
groups of exercises and problems, many of them with detailed
solutions while others with hints or final answers. More advanced
topics, such as Morse's lemma, Sard's theorem, the Weierstrass
approximation theorem, the Fourier transform, Vector fields on
spheres, Brouwer's fixed point theorem, Whitney's embedding
theorem, Picard's theorem, and Hermite polynomials are discussed in
stared sections.
This book begins with the basics of the geometry and topology of
Euclidean space and continues with the main topics in the theory of
functions of several real variables including limits, continuity,
differentiation and integration. All topics and in particular,
differentiation and integration, are treated in depth and with
mathematical rigor. The classical theorems of differentiation and
integration such as the Inverse and Implicit Function theorems,
Lagrange's multiplier rule, Fubini's theorem, the change of
variables formula, Green's, Stokes' and Gauss' theorems are proved
in detail and many of them with novel proofs. The authors develop
the theory in a logical sequence building one result upon the
other, enriching the development with numerous explanatory remarks
and historical footnotes. A number of well chosen illustrative
examples and counter-examples clarify matters and teach the reader
how to apply these results and solve problems in mathematics, the
other sciences and economics. Each of the chapters concludes with
groups of exercises and problems, many of them with detailed
solutions while others with hints or final answers. More advanced
topics, such as Morse's lemma, Sard's theorem, the Weierstrass
approximation theorem, the Fourier transform, Vector fields on
spheres, Brouwer's fixed point theorem, Whitney's embedding
theorem, Picard's theorem, and Hermite polynomials are discussed in
stared sections.
Complex analysis is a beautiful subject - perhaps the single most
beautiful; and striking; in mathematics. It presents completely
unforeseen results that are of a dramatic; even magical; nature.
This invaluable book will convey to the student its excitement and
extraordinary character. The exposition is organized in an
especially efficient manner; presenting basic complex analysis in
around 130 pages; with about 50 exercises. The material constantly
relates to and contrasts with that of its sister subject; real
analysis. An unusual feature of this book is a short final chapter
containing applications of complex analysis to Lie theory.Since
much of the content originated in a one-semester course given at
the CUNY Graduate Center; the text will be very suitable for first
year graduate students in mathematics who want to learn the basics
of this important subject. For advanced undergraduates; there is
enough material for a year-long course or; by concentrating on the
first three chapters; for one-semester course.
'I like the authorsaEURO (TM) taste in footnotes, what with their
frequent emphasis on history, i.e. the minutiae of the lives of
many mathematicians appearing in these pages. Their remarks add a
particular dimension of fun and pleasure to what I think is a very
good book. ItaEURO (TM)s pitched at the right level, it does a lot
of serious stuff in preparation for what is coming the
studentsaEURO (TM) way in the future, and it does it well.'MAA
ReviewsThis comprehensive two-volume book deals with algebra,
broadly conceived. Volume 1 (Chapters 1-6) comprises material for a
first year graduate course in algebra, offering the instructor a
number of options in designing such a course. Volume 1, provides as
well all essential material that students need to prepare for the
qualifying exam in algebra at most American and European
universities. Volume 2 (Chapters 7-13) forms the basis for a second
year graduate course in topics in algebra. As the table of contents
shows, that volume provides ample material accommodating a variety
of topics that may be included in a second year course. To
facilitate matters for the reader, there is a chart showing the
interdependence of the chapters.
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