Hardback (ISBN-13: 9780521766654)
Paperback (ISBN-13: 9780521154055)
150 b/w illus. 200 exercises
Page extent: 350 pages
Size: 228 x 152 mm
Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.
* At last, this book is back in print, with updated references and redesigned illustrations * Numerous examples introduce the main theorems of homology theory, enabling the reader to understand basic concepts and gradually develop their understanding * No prerequisites beyond elementary algebra
Preface to the third edition; Preface to the first edition; List of notation; Introduction; 1. Graphs; 2. Closed surfaces; 3. Simplicial complexes; 4. Homology groups; 5. The question of invariance; 6. Some general theorems; 7. Two more general theorems; 8. Homology modulo 2; 9. Graphs in surfaces; Appendix. Abelian groups; References; Index.
Series: Encyclopedia of Mathematics and its Applications (No. 74)
Paperback (ISBN-13: 9780521155670)
Page extent: 670 pages
Size: 234 x 156 mm
Originally published in 2000, this is the first volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which is unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 1 includes the abstract parabolic theory for the finite and infinite cases and corresponding PDE illustrations as well as various abstract hyperbolic settings in the finite case. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.
* In-depth, comprehensive coverage * Wealth of illustrative examples * Continuous theory and numerical approximation theory
Introduction; Part I. Analytic Semigroups: 1. The optimal quadratic cost problem over a preassigned finite time interval: the differential Riccati equation; 2. The optimal quadratic cost problem over a preassigned finite time interval: the algebraic Riccati equation; 3. Illustrations of the abstract theory of chapters 1 and 2 to PDEs with boundary/point controls; 4. Numerical approximations of algebraic Riccati equations; 5. Illustrations of the numerical theory of chapter 4 to parabolic-like boundary/point control PDE problems; 6. Min-max game theory over an infinite time interval and algebraic Riccati equations.
Series: Encyclopedia of Mathematics and its Applications (No. 75)
Paperback (ISBN-13: 9780521155687)
Page extent: 649 pages
Size: 234 x 156 mm
Originally published in 2000, this is the second volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which unifies across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.
* In-depth, comprehensive coverage * Wealth of illustrative examples * Continuous theory and numerical approximation theory
1. Categories; 2. Categories and exact sequences; 3. Change of rings; 4. The Morita theory; 5. Limits in categories; 6. Localization; 7. Local-global methods.
Paperback
ISBN 978-3-11-022673-7
Series: de Gruyter Textbook
This textbook on Combinatorics and Graph Theory systematically implements the following approach: Every section begins with simple model problems. Following their detailed analysis, the reader is led through the derivation of all definitions, concepts and methods for solving typical problems. Theorems are then formulated, proved and illustrated by more problems. Topics covered are elementary counting, graphs and trees, hierarchical clustering, enumerative combinatorics, existence theorems.
For a one- or two-semester undergraduate or an entry-level graduate course
Also suitable for self-study
Over 700 problems, some of them with answers or tips
24 x 17 cm
Approx. 350 pages
Languages: English
Type of Publication: Textbook
Cours Specialises--Collection SMF, Number: 17
2010; 332 pp; hardcover
ISBN-13: 978-2-85629-278-5
This book presents a part of the theory of (complex) representations of p-adic reductive groups. Starting from fundamentals accessible to graduate students, it culminates with the "Bernstein center" theory and the Langlands classification of smooth irreducible representations.
This book contains seven chapters. Chapters VI and VII are at the heart of the book. Chapter VI deals with the study of the category of smooth representations of a p-adic reductive group and the author establishes, among other things, Bernstein's decomposition theorem and the description of the center. Chapter VII deals with square integrable and temperate representations and contains the proof of Langland's classification theorem.
The first four chapters are more general and deal with: the study of algebras of idempotents, the one of locally compact totally discontinuous spaces and groups, smooth representations of the latter and specific representation classes (compact, unitary, square integrable). Chapter V is a reminder of structural results for reductive p-adic groups.
An appendix provides category theory notions necessary for reading this text.
A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in representations of $p$-adic reductive groups.
Algebres a idempotents
Espaces et groupes totalement discontinous
Representations des groupes totalement discontinous
Representations compactes, de carre integrable, unitaires
Structure des groupes reductifs p-adiques
Representations des groupes reductifs p-adiques
Classification de Langlands
Elements de theorie des categories
Theoreme d'Amitsur et corollaires
Algebre lineaire
Bibliographie