Unterberger, Andre
The Fourfold Way in Real Analysis
An Alternative to the Metaplectic Representation
Series: Progress in Mathematics, Vol. 250
2006, Approx. 255 p., Hardcover
ISBN: 3-7643-7544-2
About this book
The usual eigenfunctions of the harmonic oscillator L make up a
total set in L2(R): the structure they reveal is interwoven with
such representation-theoretic objects as the Fourier
transformation and the Heisenberg and metaplectic representations.
The book develops a substitute for the usual analysis that starts
with the consideration of eigenfunctions of L of an unusual (non
square-summable) species: new concepts of integral on the real
line, of Fourier transformation, of (indefinite) pseudoscalar
product are needed, also leading to an alternative to the
metaplectic representation. Up to some point, the construction
extends to the n-dimensional case.
Table of contents
Introduction.- 1. The One-dimensional Anaplectic Representation.-
2. The n-dimensional Anaplectic Analysis.- 3. Towards the
Anaplectic Symbolic Calculi.- 4. The Fourfold Way.- Bibliography.-
Index
Andreescu, Titu, Andrica, Dorin, Sunik, Zoran
Essential Linear Algebra with Applications
A Problem-Solving Approach
2007, Approx. 350 p. 40 illus., Hardcover
ISBN: 0-8176-4360-5
About this textbook
Rooted in a pedagogically successful problem-solving approach to
linear algebra, this work fills a gap in the literature that is
sharply divided between, on the one end, elementary texts with
only limited exercises and examples, and, at the other extreme,
books too advanced in prerequisites and too specialized in focus
to appeal to a wide audience. Instead, "Essential Linear
Algebra" clearly develops the theoretical foundations of
vector spaces, linear equations, matrix algebra, eigenvectors,
and orthogonality, while simultaneously emphasizing applications
and connections to fields such as biology, economics, computer
graphics, electrical engineering, cryptography, and political
science.
Table of contents
Preface * Linear Phenomena and Euclidean Spaces of Small
Dimension * Concrete Vector Spaces * Vector Spaces and Subspaces
* Linear Transformations * More Matrix Algebra and Determinants *
General Theory of Linear Equations * Eigenvectors * Orthogonality
* Forms * Vector Spaces over Finite Fields * Appendix A: Complex
Numbers * Appendix B: Polynomials over Complex Numbers *
References * Index
Andreescu, Titu, Mortici, Cristinel
Mathematical Bridges
2007, Approx. 300 p. 20 illus., Softcover
ISBN: 0-8176-4394-X
About this textbook
Building bridges between classical results and contemporary
nonstandard problems, Mathematical Bridges embraces important
topics in analysis and algebra from a problem-solving perspective.
Blending old and new techniques, tactics and strategies used in
solving challenging mathematical problems, readers will discover
numerous genuine mathematical gems throughout that will heighten
their appreciation of the inherent beauty of mathematics.
Most of the problems are original to the authors and are
intertwined in a well-motivated exposition driven by
representative examples. The book is structured to assist the
reader in formulating and proving conjectures, as well as
devising solutions to important mathematical problems by making
connections between various concepts and ideas from different
areas of mathematics.
Instructors and educators teaching problem-solving courses or
organizing mathematics clubs, as well as motivated mathematics
students from high school juniors to college seniors, will find
Mathematical Bridges a useful resource in calculus, linear and
abstract algebra, analysis and differential equations. Students
desiring to hone and develop their mathematical skills or with an
interest in mathematics competitions must have this book in their
personal libraries.
Table of contents
Preface * Glossary of Notation * Cardinality * Density * Lemma of
the Closed Intervals * Sequences Given by Implicit Relations *
Recurrence Relations * Complementary Sequences * Quadratic
Functions, Quadratic Equations * Polynomial Functions Involving
Determinants * A Decomposition Theorem Related to the Rank of a
Matrix * Intermediate Value Property * Uniform Continuity *
Toeplitz Theorem * Derivatives and Functions Variation *
Weierstrass Theorem * The Number e * Riemann Sums, Darboux Sums *
References * Subject Index
Biran, Paul; Cornea, Octav; Lalonde, Francois (Eds.)
Morse Theoretic Methods in Nonlinear Analysis and in
Symplectic Topology
Proceedings of the NATO Advanced Study Institute on Morse
Theoretic Methods in Nonlinear Analysis and in Symplectic
Topology, held in Montreal, Canada, from 21 June to 2 July 2004.
Series: NATO Science Series II: Mathematics, Physics and
Chemistry, Vol. 217
2006, Approx. 480 p.,
Softcover ISBN: 1-4020-4273-6
Hardcover ISBN: 1-4020-4272-8
About this book
This volume contains contributions to the Seminaire de
Mathematiques Superieures ? NATO Advanced Study Institute on
"Morse theoretic Methods in non-linear Analysis and
Symplectic Topology" which was held at the Universite de
Montreal in the summer of 2004.
The recent years have witnessed the emergence of a deeper and
more general formalism of the main geometric ideas in these
fields. The surveys and research papers in this volume are a
striking example of this trend. They provide an up-to-date
overview of some of the most significant advances in these topics.
The text is of high relevance for graduate students as well as
for more senior mathematicians with interest in a wide range of
topics going from symplectic topology to dynamical systems and
from algebraic and differential topology to variational methods.
Table of contents