ISBN: 0-201-71090-0
Copyright: 2003
Format: Cloth; 304 pp
Published: 05/28/2002
Status: Instock
Description
Mathematical Proofs is designed to prepare students for the more
abstract mathematics courses that follow calculus. This text
introduces students to proof techniques and writing proofs of
their own. As such, it is an introduction to the mathematics
enterprise providing solid introductions to relations, functions,
and cardinalities of sets.
Table of Contents
0. Communicating Mathematics.
1. Sets.
2. Logic.
3. Direct Proof and Proof by Contrapositive.
4. More on Direct Proof and Proof by Contrapositive.
5. Proof by Contradiction.
6. Prove or Disprove.
7. Equivalence Relations.
8. Functions.
9. Mathematical Induction.
10. Cardinalities of Sets.
11. Proofs in Number Theory.
12. Proofs in Calculus.
13. Proofs in Group Theory.
Answers and Hints to Selected Odd-Numbered Exercises.
References Index of Symbols.
Index of Mathematical Terms.
ISBN: 0-201-72634-3
Publisher: Addison-Wesley
Copyright: 2004
Format: Cloth
Published: 07/17/2003
Status: Instock
Description
This fifth edition continues to improve on the features that have
made it the market leader. The text offers a flexible
organization, enabling instructors to adapt the book to their
particular courses. The book is both complete and careful, and it
continues to maintain its emphasis on algorithms and applications.
Excellent exercise sets allow students to perfect skills as they
practice. This new edition continues to feature numerous computer
science applications-making this the ideal text for preparing
students for advanced study.
Table of Contents
PART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS.
1. Fundamental Principles of Counting.
2. Fundamentals of Logic.
3. Set Theory.
4. Properties of the Integers: Mathematical Induction.
5. Relations and Functions.
6. Languages: Finite State Machines.
7. Relations: The Second Time Around.
8. The Principle of Inclusion and Exclusion.
9. Generating Functions.
10. Recurrence Relations.
11. An Introduction to Graph Theory.
12. Trees.
13. Optimization and Matching.
14. Rings and Modular Arithmetic.
15. Boolean Algebra and Switching Functions.
16. Groups, Coding Theory, and Polya's Theory of Enumeration.
17. Finite Fields and Combinatorial Designs.
Appendices.
Solutions.
Index.
ISBN: 0-321-12164-3
Copyright: 2004
Format: Cloth; 912 pp
Published: 10/02/2003
Status: Instock
Description
Elementary Differential Equations with Boundary Value Problems
integrates the underlying theory, the solution procedures, and
the numerical/computational aspects of differential equations in
a seamless way. For example, whenever a new type of problem is
introduced (such as first-order equations, higher-order
equations, systems of differential equations, etc.) the text
begins with the basic existence-uniqueness theory. This provides
the student the necessary framework to understand and solve
differential equations. Theory is presented as simply as possible
with an emphasis on how to use it. The Table of Contents is
comprehensive and allows flexibility for instructors.
Table of Contents
1. Introduction to Differential Equations.
2. First Order Linear Differential Equations.
3. First Order Nonlinear Differential Equations.
4. Second Order Linear Differential Equations.
5. Higher Order Linear Differential Equations.
6. First Order Linear Systems.
7. Laplace Transforms.
8. Nonlinear Systems.
9. Numerical Methods.
10. Series Solution of Differential Equations.
11. Linear Two-Point Boundary Value Problems.
12. First Order Partial Differential Equations and the Method of
Characteristics.
13. Second Order Linear Partial Differential Equations.
Appendix on Matrix Theory.
Series: Encyclopedia of Mathematics and its Applications, vol.101
Hardback | 500 pages 90 figures | ISBN: 0-521-82476-1
With the growing interest in the use of symmetry methods in
applied mathematics, this book presents a comprehensive overview
of the differential geometric view of the subject. The authors
begin with a background chapter on calculus on manifolds, and
then proceed to more advanced topics and applications, especially
concerning singularities of the Monge-Ampere equations that
describe many phenomena in geophysical fluid dynamics, for
example. The authors describe many application areas and include
computer code for implementing some of the techniques they
describe. The book is richly illustrated.
Contents
Introduction; Part I. Symmetries and Integrals: 1. Distributions; 2. Ordinary differential equations; 3. Model differential equations and Lie superposition principle; Part II. Symplectic Algebra: 4. Linear algebra of symplectic vector spaces; 5. Exterior algebra on symplectic vector spaces; 6. A Symplectic classification of exterior 2-forms in dimension 4; 7. Symplectic classification of exterior 2-forms; 8. Classification of exterior 3-forms on a 6-dimensional symplectic space; Part III. Monge-Ampere Equations: 9. Symplectic manifolds; 10. Contact manifolds; 11. Monge-Ampere equations; 12. Symmetries and contact transformations of Monge-Ampere equations; 13. Conservation laws; 14. Monge-Ampere equations on 2-dimensional manifolds and geometric structures; 15. Systems of first order partial differential equations on 2-dimensional manifolds; Part IV. Applications: 16. Non-linear acoustics; 17. Non-linear thermal conductivity; 18. Meteorology applications; Part V. Classification of Monge-Ampere Equations: 19. Classification of symplectic MAEs on 2-dimensional manifolds; 20. Classification of symplectic MAEs on 2-dimensional manifolds; 21. Contact classification of MAEs on 2-dimensional manifolds; 22. Symplectic
Publication is planned for January 2005 | Hardback | 300 pages
| ISBN: 0-521-83703-0
The representation theory of the symmetric group is of perennial
interest since it touches on so many areas of mathematics. This
book contains some of the modern theory, to which Alexander
Kleshchev was one of the main contributors. He brings the reader
to the frontiers of the subject in a work which will be an
invaluable resource for graduate students and researchers.
Description
This volume contains two articles. Both deal with generalizations
of Michael Harris' and Richard Taylor's work on the cohomology of
P.E.L. type Shimura varieties of signature (1,n-1) and on the
cohomology of Lubin-Tate spaces. They are based on the work of
Robert Kottwitz on those varieties in the general signature case,
and on the work of Michael Rapoport and Thomas Zink on moduli
spaces of p-divisible groups generalizing the one of Lubin-Tate
and Drinfeld.
In the first article it is proved that the ell-adique etale
cohomology of some of those "supersingular" moduli
spaces of p-divisible groups realizes some cases of local
Langlands correspondences. For this the author establishes a
formula linking the cohomology of those spaces to the one of the
"supersingular" locus of a Shimura variety. Then he
proves that the supercuspidal part of the cohomology of those
varieties is completely contained in the one of the "supersingular"
locus.
The second article links the cohomology of a Newton stratum of
the Shimura variety, for example the "supersingular"
stratum, to the cohomology of the attached local moduli space of
p-divisible groups and to the cohomology of some global varieties
in positive characteristic named Igusa varieties that generalize
the classical Igusa curves attached to modular curves.
The book is suitable for graduate students and research
mathematicians interested in number theory and algebraic geometry.
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.
Contents
L. Fargues. Cohomologie des espaces de modules de groupes p-divisibles
et correspondances de Langlands locales
Introduction
Varietes de Shimura de type P.E.L. non ramifiees
Espaces de Rapoport-Zink
Uniformisation des varietes de Shimura de type P.E.L.
Une suite spectrale de Hochschild-Serre pour l'uniformisation de
Rapoport-Zink
Formule de Lefschetz sur la fibre speciale
Formule de Lefschetz sur la fibre generique
Contribution de la cohomologie de la strate basique
Application a la cohomologie des espaces Rapoport-Zink de type E.L.
et P.E.L.
Appendices
References
E. Mantovan. On Certain Unitary Shimura Varieties
Introduction
Preliminaries
Igusa varieties
A system of covers of the Newton polygon strata
Group action on cohomology
Formally lifting to characteristic zero
Shimura varieties with level structure at p
The cohomology of Shimura varieties
References
Details:
Series: Asterisque, Number: 291
Publication Year: 2004
ISBN: 2-85629-150-3
Paging: 331 pp.
Binding: Softcover