Graph Theory 2nd ed
2000. Approx. 315 pp. 103 figs.
0-387-95014-1
This concise -- yet carefully written --
introduction to modern
graph theory contains all major recent
developments, and can be used both as a reliable
textbook for an
introductory course and as a
graduate text. For each topic it covers all
the basic material in
full detail, and adds one or two
deeper results to illustrate the more advanced
methods of that
field. This second edition offers a
thoroughly revised and updated chapter on
graph minors, which now
includes full new proofs of two
of the central Robertson-Seymour theorems,
and there is now a
section of hints for all the
exercises, to enhance their value for both
individual study and
classroom use.
Contents: The Basics.- Matching.- Connectivity.-
Planar Graphs.-
Colouring.- Flows.-
Substructures in Dense Graphs.- Ramsey Theory
for Graphs.-
Hamilton Cycles.- Random Graphs.-
Minors, Trees, and WQO.
Series: Graduate Texts in Mathematics.VOL.
173
Fields: Combinatorial Mathematics/Graph Theory
and Discrete
Mathematics
Written for: Graduate mathematics students,
mathematicians
Book category: Graduate Textbook
Publication language: English
Hecht, K.T., University of Michigan, Ann Arbor, MI, USA
Quantum Mechanics
2000. Approx. 660 pp. 101 figs.
0-387-98919-6
Intended for beginning graduate students,
this text takes the
reader from the familiar coordinate
representation of quantum mechanics to the
modern algebraic
approach, emphasizing symmetry
principles throughout. After an introduction
to the basic
postulates and techniques, the book
discusses time-independent perturbation theory,
angular momentum,
identical particles,
scatteering theory, and time-dependent perturbation
theory. The
whole is rounded off with several
lectures on relativistic quantum mechanics
and on many-body
theory.
Contents: Background.- The Motion of Wave
Packets.- The
Schrodinger Wave Equation.-
Schrodinger Theory.- Harmonic Oscillator
Calculations.- Further
Interpretation of Wave Eq.- The
Eigenvalue Problem.- Spherical Harmonics.-
l-Step Operators.- The
Radial Functions.- Shape
Invariant Potentials.- The Darboux Method.-
The Vector Space
Interpretation.- The Angular
Momentum Eigenvalue Rigid Rotators.- Transformation
Theory.-
Another Example.-Transformation
Theory.- Time dependence of a...- Perturbation
Theory.- The
Slightly Anharmonic.- Example 1.-
Perturbation Theory for- The Case of Neary
Degenerate Level.-
Magnetic Field Peturbations.- Fine
Structure and Zeeman...- Angular Momentum
Coupling Theory.-
Symmetry Properties.- Invariance
of...- The Clebsch-Gordon Series.- Spherical
Tensor Operators.-
The Wigner-Eckart Theorem.-
Nuclear Hyperfine Structure.- Angular Momentum...-
Perturbed
Coulomb Problem.- The Wkb
Approximation Applications of WKB.- The Two-Electron
Atom.-
n-Identical Particle.-The Variational
Method.- Introducing Scattering Theory.-
The
Rayleigh-Faxen-Holtzman Parital...- A Specific
Example.
Series: Graduate Texts in Contemporary Physics.
Fields: Physics, general
Written for: Graduate students
Book category: Graduate Textbook
Publication language: English
Ribenboim, P., Queen's University, Kingston, Ont., Canada
My Numbers, My Friends
2000. Approx. 450 pp.
0-387-98911-0
PRELIMINARTY TEXT. DO NOT USE. This is a
selection of expository
essays by Paulo
Ribenboim, the author of such popular titles
as "The New
Book of Prime Number Records" and
"The Little Book of Big Primes".
The book contains
essays on Fibonacci numbers, prime numbers,
Bernoulli numbers, and historical presentations
of the main
problems pertaining to elementary
number theory, such as for instance Kummer's
work on Fermat's
Last Theorem. The essays are
written in a light and humorous language
without secrets and are
thoroughly accessible to everyone
with an interest in numbers.
Contents: 1 Fibonacci Numbers and the Arctic
Ocean 2
Representations of Real Numbers by
Means of Fibonacci Numbers 3 Prime Number
Records 4 Selling
Primes 5 Euler's Famous
Polynomial and the Class Number of Imaginary
Quadratic Fields 6
Gauss and the Class Number
Problem 7 Consecutive Powers 8 1093 9 Powerless
Facing Powers 10
The Classical Bernoulli
Numbers 11 Galimatias Arithmetica 12 The
Work of Kummer on
Fermat's Last Theorem 13 An
Essay on Irrational Numbers
Fields: Number Theory
Written for: Math students, mathematicians,
math teachers
Book category: Monograph
Publication language: English
Bhatti, M.A., University of Iowa, Iowa City, IA, USA
Practical Optimization Methods
With Mathematica Applications
2000. Approx. 770 pp. 176 figs., with CD-ROM.
0-387-98631-6
This introductory textbook adopts a practical
and intuitive
approach, rather than emphasizing
mathematical rigor. Computationally oriented
books in this area
generally present algorithms alone,
and expect readers to perform computations
by hand, and are often
written in traditional computer
languages, such as Basic, Fortran or Pascal.
This book, on the
other hand, is the first text to use
Mathematica to develop a thorough understanding
of optimization
algorithms, fully exploiting
Mathematica's symbolic, numerical and graphic
capabilities.
Contents: Optimization Problem Formulation.-
Graphical
Optimization.- Mathematical
Preliminaries.- Optimality Conditions.- Unconstrained
Problems.-
Linear Programming.- Interior
Point Methods.- Quadratic Programming.- Nonlinear
Constrained
Problems.- Appendix.-
Introduction to Mathematica.
Fields: Operations Research/Decision Theory
Written for: Upper div. undergraduates, reference
for engineers
Book category: Undergraduate Textbook
Publication language: English
Hassani, S.
Mathematical Methods
for Students of Physics and Related Fields
2000. Approx. 650 pp. 179 figs.
0-387-98958-7
Intended to follow the usual introductory
physics courses, this
book has the unique feature of
addressing the mathematical needs of sophomores
and juniors in
physics, engineering and other
related fields. Many original, lucid, and
relevant examples from
the physical sciences, problems at
the ends of chapters, and boxes to emphasize
important concepts
help guide the student through
the material.
Beginning with reviews of vector algebra
and differential and
integral calculus, the book continues
with infinite series, vector analysis, complex
algebra and
analysis, ordinary and partial differential
equations. Discussions of numerical analysis,
nonlinear dynamics
and chaos, and the Dirac delta
function provide an introduction to modern
topics in mathematical
physics.
Contents: Coordinate Systems and Vectors.-
Differentiation.-
Integration.- Vectors.- Infinite Series.-
Integrals and Series as Functions.- Dirac
Delta Functions.-
Vector Analysis.- Complex Arithmetic.-
Complex Analysis.- Differential Equations.-
Laplace's Equation.-
Other PDEs of Mathematical
Physics.- Nonlinear Dynamics.- Index.
Series: Undergraduate Texts in Contemporary
Physics.
Fields: Mathematical and Computational Methods;
Mathematics,
general
Written for: Physicists, graduate students,
applied
mathematicians
Book category: Graduate Textbook
Publication language: English