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In this classic work, Anthony W. Knapp offers a survey of
representation theory of semisimple Lie groups in a way that
reflects the spirit of the subject and corresponds to the natural
learning process. This book is a model of exposition and an
invaluable resource for both graduate students and researchers.
Although theorems are always stated precisely, many illustrative
examples or classes of examples are given. To support this unique... more...

With a visual, graphical approach that emphasizes connections among
concepts, this text helps students make the most of their study
time. The authors show how different mathematical ideas are tied
together through their zeros, solutions, and x-intercepts theme;
side-by-side algebraic and graphical solutions; calculator screens;
and examples and exercises. By continually reinforcing the
connections among various mathematical concepts as well as... more...

This book concerns the use of dioid algebra as (max, +) algebra
to treat the synchronization of tasks expressed by the maximum of
the ends of the tasks conditioning the beginning of another task
– a criterion of linear programming. A classical example is the
departure time of a train which should wait for the arrival of
other trains in order to allow for the changeover of
passengers.
The content focuses on the modeling of a class of... more...

A reader-friendly, systematic introduction to Fourier
analysis
Rich in both theory and application, Fourier Analysis
presents a unique and thorough approach to a key topic in
advanced calculus. This pioneering resource tells the full story
of Fourier analysis, including its history and its impact on the
development of modern mathematical analysis, and also discusses
essential concepts and today's applications.
Written at a rigorous... more...

Since abstract algebra is so important to the study of advanced
mathematics, it is critical that students have a firm grasp of its
principles and underlying theories before moving on to further
study. To accomplish this, they require a concise, accessible,
user-friendly textbook that is both challenging and stimulating. A
First Graduate Course in Abstract Algebra is just such a
textbook.
Divided into two sections, this book covers both the standard... more...

The book begins at the level of an undergraduate student
assuming only basic knowledge of calculus in one variable. It
rigorously treats topics such as multivariable differential
calculus, Lebesgue integral, vector calculus and differential
equations. After having built on a solid foundation of topology and
linear algebra, the text later expands into more advanced topics
such as complex analysis, differential forms, calculus of
variations,... more...

This volume provides a clear and self-contained introduction to
important results in the theory of rings and modules. Assuming only
the mathematical background provided by a normal undergraduate
curriculum, the theory is derived by comparatively direct and
simple methods. It will be useful to both undergraduates and
research students specialising in algebra. In his usual lucid style
the author introduces the reader to advanced topics in a manner
which... more...

Explore the foundations and modern applications of Galois
theory
Galois theory is widely regarded as one of the most elegant areas
of mathematics. A Classical Introduction to Galois Theory
develops the topic from a historical perspective, with an
emphasis on the solvability of polynomials by radicals. The book
provides a gradual transition from the computational methods
typical of early literature on the subject to the more abstract... more...

This book investigates the geometry of the quaternion and octonion
algebras. Following a comprehensive historical introduction, the
special properties of 3- and 4-dimensional Euclidean spaces are
illuminated using quaternions, leading to enumerations of the
corresponding finite groups of symmetries. The second half of the
book discusses the less familiar octonion algebra, concentrating on
its remarkable "triality symmetry" after an appropriate study... more...

This milestone work on the arithmetic theory of linear algebraic
groups is now available in English for the first time. Algebraic
Groups and Number Theory provides the first systematic
exposition in mathematical literature of the junction of group
theory, algebraic geometry, and number theory. The exposition of
the topic is built on a synthesis of methods from algebraic
geometry, number theory, analysis, and topology, and the result is
a systematic... more...