Hardback (ISBN-13: 9780521825658)
Paperback (ISBN-13: 9780521532723)
This treatment provides an exposition of discrete time dynamic
processes evolving over an infinite horizon. Chapter 1 reviews
some mathematical results from the theory of deterministic
dynamical systems, with particular emphasis on applications to
economics. The theory of irreducible Markov processes, especially
Markov chains, is surveyed in Chapter 2. Equilibrium and long run
stability of a dynamical system in which the law of motion is
subject to random perturbations is the central theme of Chapters
3-5. A unified account of relatively recent results, exploiting
splitting and contractions, that have found applications in many
contexts is presented in detail. Chapter 6 explains how a random
dynamical system may emerge from a class of dynamic programming
problems. With examples and exercises, readers are guided from
basic theory to the frontier of applied mathematical research.
* Ideal for undergraduate and graduate courses on dynamic
economics, Markov processes, Stochastic processes/probability
* Authors are internationally renowned for their work in this
field
* Full of examples with many solutions, drawn from both applied
mathematics and econometrics/statistics
Contents
1. Dynamical systems; 2. Markov processes; 3. Random dynamical
systems; 4. Random dynamical systems: special structures; 5.
Invariant distributions: estimations and computation; 6.
Discounted dynamic programming under uncertainty; 7. Appendix.
Series: Spectrum
Hardback (ISBN-13: 9780883855584)
Celebrating the 300th birthday of Leonhard Euler (1707-1783), one
of the brightest stars in the mathematical firmament, this book
stands as a testimonial to a mathematician of unsurpassed
insight, industry, and ingenuity. The collected articles, aimed
at a mathematically literate audience, address aspects of Euler's
life and work, from the biographical to the historical to the
mathematical. The oldest of these was written in 1872, and the
most recent dates to 2006. Some of the papers focus on Euler and
his world, others describe a specific Eulerian achievement, and
still others survey a branch of mathematics to which Euler
contributed significantly. Among the 34 contributors are some of
the most illustrious mathematicians and mathematics historians of
the past century, e.g. Florian Cajori, Carl Boyer, George Polya,
Andre Weil, and Paul Erdos. And there are a few poems and a
mnemonic just for fun.
* Celebrates the 300th birthday of Euler - one who has been
rightly called 'the master of us all'
* Contributions from an illustrious list of mathematicians and
mathematics historians
* A truly great record of the life and work of a truly great
mathematician
Contents
Acknowledgments; Preface; About the authors; Part I. Biography
and Background: 1. Introduction to Part I; 2. Leonhard Euler B. F.
Finkel; 3. Leonhard Euler, supreme geometer (abridged) C.
Truesdell; 4. Euler (abridged) Andre Weil; 5. Frederick the Great
on mathematics and mathematicians (abridged) Florian Cajori; 6.
The Euler-Diderot anecdote B. H. Brown; 7. Ars expositionis:
Euler as writer and teacher G. L. Alexanderson; 8. The foremost
textbook of modern times Carl Boyer; 9. Leonhard Euler, 1707-1783
J. J. Burckhardt; 10. Euler's output, a historical note W. W.
Rouse Ball; 11. Discoveries (a poem) Marta Sved and Dave
Logothetti; 12. Bell's conjecture (a poem) J. D. Memory; 13. A
response to 'Bell's conjecture' (a poem) Charlie Marion and
William Dunham; Part II. Mathematics: 14. Introduction to Part
II; 15. Euler and infinite series Morris Kline; 16. Euler and the
zeta function Raymond Ayoub; 17. Addendum to 'Euler and the Zeta
Function' A. G. Howson; 18. Euler subdues a very obstreperous
series (abridged) E. J. Barbeau; 19. On the history of Euler's
constant J. W. L. Glaisher; 20. A mnemonic for Euler's constant
Morgan Ward; 21. Euler and differentials Anthony Ferzola; 22.
Leonhard Euler's integral: a historical profile of the gamma
function Philip Davis; 23. Change of variables in multiple
integrals: Euler to Cartan Victor Katz; 24. Euler's vision of a
general partial differential calculus for a generalized kind of
function Jesper Lutzen; 25. On the calculus of variations and its
major influences on the mathematics of the first half of our
century Erwin Kreyszig; 26. Some remarks and problems in number
theory related to the work of Euler Paul Erdos and Underwood
Dudley; 27. Euler's pentagonal number theorem George Andrews; 28.
Euler and quadratic reciprocity Harold Edwards; 29. Euler and the
fundamental theorem of algebra William Dunham; 30. Guessing and
proving George Polya; 31. The truth about Konigsberg Brian
Hopkins and Robin Wilson; 32. Graeco-Latin squares and a mistaken
conjecture of Euler Dominic Klyve and Lee Stemkoski; Glossary
Schattschneider et. al.; About the editor.
Series: Spectrum
Hardback (ISBN-13: 9780883855591)
Describes Euler's early mathematical works - the 50 mathematical
articles he wrote before he left St. Petersburg in 1741 to join
the Academy of Frederick the Great in Berlin. These works contain
some of Euler's greatest mathematics: the Konigsburg bridge
problem, his solution to the Basel problem, his first proof of
the Euler-Fermat theorem. Also presented are important results
that we seldom realize are due to Euler: that mixed partial
derivatives are equal, our f(x) notation, and the integrating
factor in differential equations. The book is a portrait of the
world's most exciting mathematics between 1725 and 1741, rich in
technical detail, woven with connections within Euler's work and
with the work of other mathematicians in other times and places,
laced with historical context.
* Woven with the connections between different aspects of Euler's
work, giving insight into the many strands in this beautiful web
of mathematics
* Through the papers considered we see Euler grow in power and
sophistication as a mathematician
* Published to celebrate Euler's 300th birthday
Contents
Preface; Part I. 1725-1727: 1. Construction of isochronal curves
in any kind of resistant; 2. Method of finding reciprocal
algebraic trajectories; Part II. 1728: 3. Solution to problems of
reciprocal trajectories; 4. A new method of reducing innumerable
differential equations of the second degree to equations of the
first degree: Integrating factor; Part III. 1729-1731: 5. On
transcendental progressions, or those for which the general term
cannot be given algebraically; 6. On the shortest curve on a
surface that joins any two given points; 7. On the summation of
innumerably many progressions; Part IV. 1732: 8. General methods
for summing progressions; 9. Observations on theorems that Fermat
and others have looked at about prime numbers; 10. An account of
the solution of isoperimetric problems in the broadest sense;
Part V. 1733: 11. Construction of differential equations which do
not admit separation of variables; 12. Example of the solution of
a differential equation without separation of variables; 13. On
the solution of problems of Diophantus about integer numbers; 14.
Inferences on the forms of roots of equations and of their
orders; 15. Solution of the differential equation axn dx = dy + y2dx;
Part VI. 1734: 16. On curves of fastest descent in a resistant
medium; 17. Observations on harmonic progressions; 18. On an
infinity of curves of a given kind, or a method of finding
equations for an infinity of curves of a given kind; 19.
Additions to the dissertation on infinitely many curves of a
given kind; 20. Investigation of two curves, the abscissas of
which are corresponding arcs and the sum of which is algebraic;
Part VII. 1735: 21. On sums of series of reciprocals; 22. A
universal method for finding sums which approximate convergent
series; 23. Finding the sum of a series from a given general
term; 24. On the solution of equations from the motion of pulling
and other equations pertaining to the method of inverse tangents;
25. Solution of a problem requiring the rectification of an
ellipse; 26. Solution of a problem relating to the geometry of
position; Part VIII. 1736: 27. Proof of some theorems about
looking at prime numbers; 28 Further universal methods for
summing series; 29. A new and easy way of finding curves enjoying
properties of maximum or minimum; Part IX. 1737: 30. On the
solution of equations; 31. An essay on continued fractions; 32.
Various observations about infinite series; 33. Solution to a
geometric problem about lunes formed by circles; Part X. 1738: 34.
On rectifiable algebraic curves and algebraic reciprocal
trajectories; 35. On various ways of closely approximating
numbers for the quadrature of the circle; 36. On differential
equations which sometimes can be integrated; 37. Proofs of some
theorems of arithmetic; 38. Solution of some problems that were
posed by the celebrated Daniel Bernoulli; Part XI. 1739: 39. On
products arising from infinitely many factors; 40. Observations
on continued fractions; 41. Consideration of some progressions
appropriate for finding the quadrature of the circle; 42. An easy
method for computing sines and tangents of angles both natural
and artificial; 43. Investigation of curves which produce
evolutes that are similar to themselves; 44. Considerations about
certain series; Part XII. 1740: 45. Solution of problems in
arithmetic of finding a number, which, when divided by given
numbers leaves given remainders; 46. On the extraction of roots
of irrational quantities: gymnastics with radical signs; Part
XIII. 1741: 47. Proof of the sum of this series 1 + 1/4 + 1/9 + 1/16
+ 1/25 + 1/ 36 + etc; 48. Several analytic observations on
combinations; 49. On the utility of higher mathematics; Topically
related articles; Index; About the author.
Hardback (ISBN-13: 9780521839747)
We live in a three-dimensional space; what sort of space is it
* Can we build it from simple geometric objects
* The answers to such questions have been found in the last 30
years, and Outer Circles describes the basic mathematics needed
for those answers as well as making clear the grand design of the
subject of hyperbolic manifolds as a whole. The purpose of Outer
Circles is to provide an account of the contemporary theory,
accessible to those with minimal formal background in topology,
hyperbolic geometry, and complex analysis. The text explains what
is needed, and provides the expertise to use the primary tools to
arrive at a thorough understanding of the big picture. This
picture is further filled out by numerous exercises and
expositions at the ends of the chapters and is complemented by a
profusion of high quality illustrations. There is an extensive
bibliography for further study.
* Up-to-date introduction to the topic written by a leading
figure in the theory of hyperbolic 3-manifolds
* Accessible to those with minimal formal background in topology,
hyperbolic geometry, and complex analysis
* Can serve as both an introductory text in the subject, and a
reference source for those looking for an accessible description
of individual topics, with extensive bibliography
Contents
List of illustrations; Preface; 1. Hyperbolic space and its
isometries; 2. Discrete groups; 3. Properties of hyperbolic
manifolds; 4. Algebraic and geometric convergence; 5. Deformation
spaces and the ends of manifolds; 6. Hyperbolization; 7. Line
geometry; 8. Right hexagons and hyperbolic trigonometry;
Bibliography; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 103)
Hardback (ISBN-13: 9780521854436)
The Langlands Program was conceived initially as a bridge between
Number Theory and Automorphic Representations, and has now
expanded into such areas as Geometry and Quantum Field Theory,
tying together seemingly unrelated disciplines into a web of
tantalizing conjectures. A new chapter to this grand project is
provided in this book. It develops the geometric Langlands
Correspondence for Loop Groups, a new approach, from a unique
perspective offered by affine Kac-Moody algebras. The theory
offers fresh insights into the world of Langlands dualities, with
many applications to Representation Theory of Infinite-dimensional
Algebras, and Quantum Field Theory. This accessible text builds
the theory from scratch, with all necessary concepts defined and
the essential results proved along the way. Based on courses
taught at Berkeley, the book provides many open problems which
could form the basis for future research, and is accessible to
advanced undergraduate students and beginning graduate students.
* The first account of local geometric Langlands Correspondence
* Suitable for advanced undergraduates and graduates in both
mathematics and theoretical physics
* Contains many open problems which could form the basis for
future research
Contents
Preface; 1. Local Langlands Correspondence; 2. Vertex algebras; 3.
Constructing central elements; 4. Opers and the center for a
general Lie algebra; 5. Free field realization; 6. Wakimoto
modules; 7. Intertwining operators; 8. Identification of the
center with functions on opers; 9. Structure of bg-modules of
critical level; 10. Constructing the local Langlands
Correspondence; Appendix; References.
Paperback (ISBN-13: 9780521701723)
In this fully revised second edition of Understanding
Probability, the reader can learn about the world of probability
in an informal way. The author demystifies the law of large
numbers, betting systems, random walks, the bootstrap, rare
events, the central limit theorem, the Bayesian approach and more.
This second edition has wider coverage, more explanations and
examples and exercises, and a new chapter introducing Markov
chains, making it a great choice for a first probability course.
But its easy-going style makes it just as valuable if you want to
learn about the subject on your own, and high school algebra is
really all the mathematical background you need.
* Fascinating probability problems (Monty Hall, birthday
surprise, lottery winners, and more) explained in a way that
anyone can understand
* Written with wit and clarity, this book offers a unique
informal style to explain mathematics
* This fully revised second edition now covers all material
usually taught in an introductory probability course, with many
more examples and exercises in almost every chapter
Contents
Preface; Introduction; Part I. Probability in Action: 1.
Probability questions; 2. The law of large numbers and
simulation; 3. Probabilities in everyday life; 4. Rare events and
lotteries; 5. Probability and statistics; 6. Chance trees and
Bayes' rule; Part II. Essentials of Probability: 7. Foundations
of probability theory; 8. Conditional probability and Bayes; 9.
Basic rules for discrete random variables; 10. Continuous random
variables; 11. Jointly distributed random variables; 12.
Multivariate normal distribution; 13. Conditional distributions;
14. Generating functions; 15. Markov chains; Appendix;
Recommended readings; Answers to odd-numbered problems;
Bibliography.
Reviews
'This book is eminently suitable for students undertaking a first
course in probability. It would be particularly useful for
service teaching where students are not aiming for a degree
classification in mathematics or statistics.' Significance
'… an extremely well-done result of carefully designing an
introduction to probability and an excellent choice … [for] …
a textbook for a first course in probability for students from a
wide area of disciplines.' Internationale Mathematische
Nachrichten
'This book gives an introduction to probability theory by using
motivating examples to illustrate the concepts.' Monatshefte fur
Mathematik
'The author clearly wants to stimulate the reader's interest in
probability, both as an academic subject and as a tool with which
to assess our daily world … The material on the history of the
subject, interspersed throughout, is a worthy inclusion. The
number of famous applications of probability included is
remarkable - the arcsine law for random walks, the drunkard's
walk in n dimensions, the Kelly betting system, the 'hot hand
theory', betting systems for roulette, the Pollaczek-Khintchine
queuing formula, Black-Scholes formula, and Benford's Law, just
to name a few. .. I would recommend this text for instructors who
may wish to try a fresh and very stimulating approach towards a
first course in probability.' Mark F. Schilling, California State
University
'The book is written in a narrative yet precise style which makes
it enjoyable to read. It is well suited for first courses in
probability for students of engineering or computer science. It
may also be used as additional material in other courses or for
self-study.' Zentralblatt MATH
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Hardback (ISBN-13: 9780521877275)
Numerical Solution of Hyperbolic Partial Differential Equations
is a new type of graduate textbook, with both print and
interactive electronic components (on CD). It is a comprehensive
presentation of modern shock-capturing methods, including both
finite volume and finite element methods, covering the theory of
hyperbolic conservation laws and the theory of the numerical
methods. The range of applications is broad enough to engage most
engineering disciplines and many areas of applied mathematics.
Classical techniques for judging the qualitative performance of
the schemes are used to motivate the development of classical
higher-order methods. The interactive CD gives access to the
computer code used to create all of the text's figures, and lets
readers run simulations, choosing their own input parameters; the
CD displays the results of the experiments as movies.
Consequently, students can gain an appreciation for both the
dynamics of the problem application, and the growth of numerical
errors.
* Textbook gives a comprehensive presentation of modern shock-capturing
methods, including both finite volume and finite element methods
* Innovative electronic component on accompanying CD allows the
reader to perform computations based upon the text, and view the
results as movies.
* Topic of interest to graduate students, academics and industry
Contents
Preface; 1. Introduction to partial differential equations; 2.
Scalar hyperbolic conservations laws; 3. Nonlinear scalar laws; 4,
Nonlinear hyperbolic systems; 5. Methods for scalar laws; 6.
Methods for hyperbolic systems; 7. Methods in multiple
dimensions; 8. Adaptive mesh refinement; Bibliography; Index.