ISBN: 0-07-291006-2
ISBN: 0-07-124339-9(paperback)
c2005 | 1st Edition | 304 pages , Hardcover
Description:
Sheldon Davis' text is designed for the contemporary course in
topology, and is written by one of the best-known topologists in
the field. It is divided into two parts for first- and second-semester
topology courses, but the author has built flexibility into the
topic coverage to accomodate the different ways the standard
topology course is organized at various schools. It is written
for undergraduate students, but can also be used with beginning
graduate topology courses.
This text is part of the Walter Rudin Student Series in Advanced
Mathematics.
New Features:
An emphasis on Point Set Topology, a branch of topology developed
at Miami University of Ohio.
Emphasis on Connectivity.
A well-known author and respected researcher in the field.
Appropriate for a one or two semester course.
Table of Contents:
Part I
1 Sets, Functions, Notation
2 Metric Spaces
3 Continuity
4 Topological Spaces
5 Basic Constructions: New Spaces From Old
6 Separation Axioms
7 Compact Spaces
8 Locally Compact Spaces
9 Connected Spaces
10 Other Types of Connectivity
11 Continua
12 Homotopy
Part II
13 A Little More Set Theory
14 Topological Spaces II
15 Quotients and Products
16 Convergence
17 Separation Axioms II
18 Compactness and Countability Properties
19 Stone-Cech Compactification
20 Paracompact Spaces
21 Metrization
ISBN: 0-07-242229-7
ISBN: 0-07-111151-4(paperback)
c2005 | 1st Edition | 688 pages , Hardcover
Description:
Ledder's innovative, student-centered approach reflects recent
research on successful learning by emphasizing connections
between new and familiar concepts and by engaging students in a
dialogue with the material. Though streamlined, the text is also
flexible enough to support a variety of teaching goals, in part
through optional topics that give instructors considerable
freedom in customizing their courses. Linear algebra is presented
in self-contained sections to accommodate both courses that have
a linear algebra prerequisite and those that do not. Throughout
the text, a wide variety of examples from the physical, life and
social sciences, among other areas, are employed to enhance
student learning. In-depth Model Problems drawn from everyday
experience highlight the key concepts or methods in each section.
Other innovative features of the text include Instant Exercises
that allow students to quickly test new skills and Case Studies
that further explore the powerful problem-solving capability of
differential equations. Readers will learn not only how to solve
differential equations, but also how to apply their knowledge to
areas in mathematics and beyond.
New Features:
FLEXIBLE ORGANIZATION: Allows high degree of customization of
course content and structure
OPTIONAL CASE STUDIES: Strengthen students' mathematical modeling
skills through in-depth explorations of real-world modeling
problems
MODEL PROBLEMS: Motivate the mathematics in each section by
focusing attention on examples that illustrate the key methods or
theories presented
VARIED EXAMPLES: Engage students' interest and build connections
with previous and subsequent material
INSTANT EXERCISES: Enable students to quickly check that they
understand what they have just learned (often by working a
problem that mimics an example) before proceeding to new material
BALANCED EXERCISE SETS: Help students quickly check that they
understand what they have just learned (often by working a
problem that mimics an example) before proceeding to new material
TECHNOLOGY USAGE: Exercises marked with technology icon give
students practice in using graphing calculators and computer
algebra systems for problem solving
Table of Contents:
1 Introduction
1.1 Natural Decay and Natural Growth
1.2 Differential Equations and Solutions
1.3 Mathematical Models and Mathematical Modeling
Case Study 1 Scientific Detection of Art Forgery
2 Basic Concepts and Techniques
2.1 A Collection of Mathematical Models
2.2 Separable First-Order Equations
2.3 Slope Fields
2.4 Existence of Unique Solutions
2.5 Euler's Method
2.6 Runge-Kutta Methods
Case Study 2 A Successful Volleyball Serve
3 Homogeneous Linear Equations
3.1 Linear Oscillators
3.2 Systems of Linear Algebraic Equations
3.3 Theory of Homogeneous Linear Equations
3.4 Homogeneous Equations with Constant Coefficients
3.5 Real Solutions from Complex Characteristic Values
3.6 Multiple Solutions for Repeated Characteristic Values
3.7 Some Other Homogeneous Linear Equations
Case Study 3 How Long Should Jellyfish Hold their Food?
4 Nonhomogeneous Linear Equations
4.1 More on Linear Oscillator Models
4.2 General Solutions for Nonhomogeneous Equations
4.3 The Method of Undetermined Coefficients
4.4 Forced Linear Oscillators
4.5 Solving First-Order Linear Equations
4.6 Particular Solutions for Second-Order Equations by Variation
of Parameters
Case Study 4 A Tuning Circuit for a Radio
5 Autonomous Equations and Systems
5.1 Population Models
5.2 The Phase Line
5.3 The Phase Plane
5.4 The Direction Field and Critical Points
5.5 Qualitative Analysis
Case Study 5 A Self-Limiting Population
6 Analytical Methods for Systems
6.1 Compartment Models
6.2 Eigenvalues and Eigenspaces
6.3 Linear Trajectories
6.4 Homogeneous Systems with Real Eigenvalues
6.5 Homogeneous Systems with Complex Eigenvalues
6.6 Additional Solutions for Deficient Matrices
6.7 Qualitative Behavior of Nonlinear Systems
Case Study 6 Invasion by Disease
7 The Laplace Transform
7.1 Piecewise-Continuous Functions
7.2 Definition and Properties of the Laplace Transform
7.3 Solution of Initial-Value Problems with the Laplace Transform
7.4 Piecewise-Continuous and Impulsive Forcing
7.5 Convolution and the Impulse Response Function
Case Study 7 Growth of a Structured Population
8 Vibrating Strings: A Focused Introduction to Partial
Differential Equations
8.1 Transverse Vibration of a String
8.2 The General Solution of the Wave Equation
8.3 Vibration Modes of a Finite String
8.4 Motion of a Plucked String
8.5 Fourier Series
Case Study 8 Stringed Instruments and Percussion
A Some Additional Topics
A.1 Using Integrating Factors to Solve First-Order Linear
Equations (Chapter 2)
A.2 Proof of the Existence and Uniqueness Theorem for First-Order
Equations (Chapter 2)
A.3 Error in Numerical Methods (Chapter 2)
A.4 Power Series Solutions (Chapter 3)
A.5 Matrix Functions (Chapter 6)
A.6 Nonhomogeneous Linear Systems (Chapter 6)
A.7 The One-Dimensional Heat Equation (Chapter 8)
A.8 Laplace's Equation (Chapter 8)
Included in series
Les Houches Summer School Proceedings, Volume 79
Description
It has been recognised recently that the strange features of the
quantum world could be used for new information transmission or
processing functions such as quantum cryptography or, more
ambitiously, quantum computing. These fascinating perspectives
renewed the interest in fundamental quantum properties and lead
to important theoretical advances, such as quantum algorithms and
quantum error correction codes. On the experimental side,
remarkable advances have been achieved in quantum optics, solid
state physics or nuclear magnetic resonance. This book presents
the lecture notes of the Les Houches Summer School on ?Quantum
entanglement and information processing?. Following the long
tradition of the les Houches schools, it provides a comprehensive
and pedagogical approach of the whole field, written by renowned
specialists. One major goal of this book is to establish
connections between the communities of quantum optics and of
quantum electronic devices working in the area of quantum
computing. When two communities share the same goals, the
universality of physics unavoidably leads to similar developments.
However, the communication barrier is often high, and few
physicists are able to overcome it. This school has contributed
to bridge the existing gap between communities, for the benefit
of the future actors in the field of quantum computing. The book
thus combines introductory chapters, providing the reader with a
sufficiently wide theoretical framework in quantum information,
quantum optics and quantum circuits physics, with more
specialized presentations of recent theoretical and experimental
advances in the field. This structure makes the book accessible
to any graduate student having a good knowledge of basic quantum
mechanics, and extremely useful to researchers.
Audience
Quantum mechanics teachers, Researchers and Graduate students.
Contents
Course 1. Principles of quantum computation, by Isaak Chuang
Course 2. Mesoscopic state superpositions and decoherence in
quantum optics, by S. Haroche Course 3. Cavity quantum
electrodynamics, by M. Brune Course 4. Quantum optical
implementation of quantum information processing, by P. Zoller, J.I.
Cirac, Luming Duan and J.J. Garcia-Ripoll Course 5. Quantum
information processing in ion traps I, by R. Blatt, H. Haffner, C.F.
Roos, C. Becher and F. Schmidt-Kaler Course 6. Quantum
information processing in ion traps II, by D.J. Wineland Course 7.
Quantum cryptography with and without entanglement, by N. Gisin
and N. Brunner Course 8. Quantum cryptography: from one to many
photons, by Philippe Grangier Course 9. Entangled photons and
quantum communication, by M. Aspelmeyer, C. Brukner and A.
Zeilinger Course 10. Nuclear magnetic resonance quantum
computation, by J.A. Jones Course 11. Introduction to quantum
conductors, by D.C. Glattli Course 12. Superconducting qubits, by
Michel H. Devoret and John M. Martinis Course 13. Superconducting
qubits and the physics of Josephson junctions, by John M.
Martinis Course 14. Josephson quantum bits based on a Cooper pair
box, by Denis Vion Course 15. Quantum tunnelling of magnetization
in molecular nanomagnets, by W. Wernsdorfer Course 16. Prospects
for srtong cavity quantum electrodynamics with superconducting
cirquits, by S.M. Girvin, R.-S. Huang, A. Blais, A. Wallraff andf
R.J. Schoelkopf
Hardbound, ISBN: 0-444-51728-6, 638 pages, publication date: 2004
0-19-856692-1(Paperback)
0-19-856691-3(Hardback)
Publication date: 27 January 2005
200 pages, 65 line drawings, 234mm x 156mm
Contains numerous exercises, figures, hints and solutions
Teaches essential mathematical skills
Ideal for training for competitions such as the Mathematical
Olympiad
Description
Containing numerous exercises, illustrations, hints and
solutions, presented in a lucid and thought-provoking style, this
text provides a wide range of skills required in competitions
such as the Mathematical Olympiad. With more than fifty problems
in Euclidean geometry, it is ideal for Mathematical Olympiad
training and also serves as a supplementary text for students in
pure mathematics, particularly number theory and geometry.
Readership: Students (both high school and undergraduate) and
teachers in pure mathematics and also Mathematical Olympiad
competitors and other recreational mathematicians.
Contents/contributors
Preface
Glossary of Symbols
1 Integer-sided Triangles
2 Circles and Triangles
3 Lattices
4 Rational Points on Curves
5 Shapes and Numbers
6 Quadrilaterals and Triangles
7 Touching Circles and Spheres
8 More on Triangles
9 Solids
10 Circles and Conics
11 Finite geometries
Appendix: Areal Co-ordinates
Answers to Exercises
References