Donald G. Saari, University of California, Irvine, CA
Chaotic Elections! A Mathematician Looks at Voting
Description
What does the 2000 U.S. Presidential Election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In Chaotic Elections!, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts or defective ballots, but are caused by the very way Americans vote for president.
This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These
consequences indicate that election outcomes--whether for president, the site of the next Olympics, the chair of a university department, or a prize winner--can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out that the mathematical structures of voting admit several strategic opportunities, which are described.
Finally, mathematics also helps identify positive results: By using mathematical symmetries, we can identify what the phrase "what the voters really want" might mean and obtain a unique voting method that satisfies these conditions.
Saari's book should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing anytime any group is making a choice using a voting procedure. Reading this book requires little more than high school
mathematics and an interest in how the apparently simple situation of voting can lead to surprising paradoxes.
Contents
A mess of an election
Voter preferences, or the procedure?
Chaotic election outcomes
How to be strategic
What do the voters want?
Other procedures; other assumptions
Bibliography
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Publication Year: 2001
ISBN: 0-8218-2847-9
Paging: 159 pp.
Binding: Softcover
Louis Nirenberg, New York University-Courant Institute of Mathematical Sciences, NY
Topics in Nonlinear Functional Analysis
Expected publication date is June 3, 2001
From reviews for the First Edition:
"These lecture notes are extremely stimulating."
-- Zentralblatt f・ Mathematik
"[The book] is short, concise, and to the point, and the proofs are unusually elegant, always with a geometric flavor and the best available."
-- Mathematical Reviews
Description
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references.
Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible
branching of solutions as parameters vary), including the proof of Rabinowitz's global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to
conjugacy problems.
After more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text.
Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Contents
Topological approach: Finite dimensions
Topological degree in Banach space
Bifurcation theory
Further topological methods
Monotone operators and the min-max theorem
Generalized implicit function theorems
Bibliography
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Courant Lecture Notes, Volume: 6
Publication Year: 2001
ISBN: 0-8218-2819-3
Paging: approximately 160 pp.
Binding: Softcover
Edited by: N. N. Uraltseva, Saint Petersburg State University, St. Petersburg, Russia
Proceedings of the St. Petersburg Mathematical Society Volume VII
Expected publication date is May 26, 2001
Description
The articles in this collection present new results in combinatorics, algebra, algebraic geometry, dynamical systems, analysis, and probability. Of particular interest is the survey article by A. N. Kirillov devoted to combinatorics of Young diagrams and related problems of representation theory. Also included are articles devoted to the eightieth birthday of renowned Russian mathematician, V. A. Rokhlin, "Remembrances of V. A. Rokhlin", by I. R. Shafarevich, and "An Unfinished Project of V.A. Rokhlin", by V. N. Sudakov. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.
Contents
A. M. Vershik and Yu. V. Yakubovich -- Continuous lattices of partitions and lattices of continuous partitions
A. N. Kirillov -- Combinatorics of Young tableaux and configurations B. Kunyavskii and B. Z. Moroz -- On integral models of affine toric varieties Ya. Yu. Nikitin and E. V. Ponikarov -- Rough asymptotics of probabilities of Chernoff type large deviations for von Mises functionals and $U$-statistics A. P. Petukhov -- Biorthogonal wavelet bases with rational masks A. L. Pirozerski and M. A. Semenov-Tian-Shansky -- $Q$-pseudodifference universal Drinfeld-Sokolov reduction A. L. Chistov -- Effective construction of local parameters of irreducible components of an algebraic variety I. R. Shafarevich -- Remembrances of V. A. Rokhlin V. N. Sudakov -- An unfinished project of V. A. Rokhlin
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: American Mathematical Society Translations--Series 2, Volume: 203
Publication Year: 2001
ISBN: 0-8218-2790-1
Paging: 253 pp.
Binding: Hardcover
Edited by: Katsumi Nomizu, Brown University, Providence, RI
Selected Papers on Classical Analysis
Expected publication date is June 15, 2001
Description
This volume contains papers that originally appeared in Japanese in the journal Sugaku. Ordinarily the papers would appear in the AMS translation of that journal,but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers here are in the general area of mathematical analysis
as it pertains to free probability theory.
Contents
F. Hiai -- Free products of operator algebras and free probability theory K. Matsuzaki -- Dynamics of Kleinian groups-The Hausdorff dimension of limit sets S. Nii -- Topological methods in stability analysis of travelling waves J.-i. Tanaka -- Extension of almost periodic functions and analyticity on flows H. Umemura -- Painlev・equations in the past 100 years M. Yamazaki -- The Navier-Stokes equation in various function spaces
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: American Mathematical Society Translations--Series 2, Publication Year: 2001
ISBN: 0-8218-2780-4
Paging: approximately 144 pp.
Binding: Hardcover
Edited by: Lo Yang, Chinese Academy of Sciences, Beijing, China,
and S.-T. Yau, Harvard University, Cambridge, MA
First International Congress of Chinese Mathematicians
Expected publication date is June 8, 2001
Description
The International Congress of Mathematicians was an historical event that was held at the Morningside Center of Mathematics of the Chinese Academy of Sciences (Beijing). It was the first occasion where Chinese mathematicians from all over the world gathered to present their research.
The Morningside Mathematics lectures were given by R. Borcherds, J. Coates, R. Graham, and D. Stroock. Other distinguished speakers included J.-P. Bourguignon, J. Jt, M. Taylor, and S. L. Lee. Topics covered in the volume include algebra and representation theory, algebraic geometry, number theory and
automorphic forms, Riemannian geometry and geometric analysis, mathematical physics, topology, complex analysis and complex geometry, computational mathematics, and combinatorics.
Contents
Morningside lectures
R. E. Borcherds -- Problems in moonshine
D. W. Stroock -- The Ornstein-Uhlenbeck process on a Riemannian manifold
Plenary addresses
W. E -- Stochastic PDEs in turbulence theory
H. Jiaxing -- Recent developments of realization of surfaces in $R^3$
H. D. Ceniceros and T. Y. Hou -- Numerical study of interfacial problems with small surface tension
J. Li -- Selected topics in moduli spaces
B. H. Lian and S.-T. Yau -- A tour of mirror symmetry
C.-S. Lin -- The scalar curvature equation on $S^n$
G. Tian -- Symplectic isotopy in four dimension
Z. Xia -- Stability in Hamiltonian dynamical systems
Z. Xin -- On the behavior of solutions to the compressible Navier-Stokes equations
H.-T. Yau -- Scaling limit of particle systems, incompressible Navier-Stokes equation and Boltzmann equation
S. Zhang -- Geometry of algebraic points
Invited addresses
C.-H. Chu -- Jordan structures in Banach manifolds
M.-c. Kang -- The rationality problem of finite group actions
Y. Zhu -- Hecke algebras and representation ring of Hopf algebras
M.-C. Chang -- On the Euler numbers of threefolds
W.-p. Li and Z. Qin -- Vector bundles, the $S$-duality conjecture of Vafa and Witten, and vertex algebras
S.-L. Tan -- Cayley-Bacharach property and $k$-very ampleness
K.-P. Lin and S. S.-T. Yau -- Sharp polynomial upper estimate of number of positive integral points in tetrahedron and coordinate free characterization of
homogeneous polynomials
L. Ji -- Spectral theory and geometry of locally symmetric spaces
J.-s. Li -- On the first eigenvalue of Laplacian for locally symmetric manifolds
H.-D. Cao and J. Zhou -- DGBV algebras and mirror symmetry
L.-f. Tam -- Harmonic maps on noncompact manifolds
J.-Y. Wu -- Curvature, bounded cohomology and path integrals
K. Liu -- Vanishing theorems for loop spaces
D. H. Phong -- Symplectic forms, 2+1 soliton equations, and supersymmetric gauge theories
X.-Y. Zhou -- Quotients, invariant version of Cartan's lemma, and the minimum principle
T.-C. Kuo and L. Paunescu -- an elementary expos・on equisingularities
W.-H. Lin -- A proof of the strong Kervaire invariant in dimension 62
X.-S. Lin -- Melvin-Morton conjecture: A survey
G. Meng -- The Seiberg-Witten equations and the Milnor torsion
S. Gong and X. Zheng -- The Bergman kernel function of some Reinhardt domains
X. Huang -- On some problems in serveral complex variables and CR geometry
C.-Q. Cheng -- A KAM theory for resonant tori and a generalization of Poincar・Birkhoff fixed point theorem
P. W. Bates, K. Lu, and C. Zeng -- Persistence of $C^k$ normally hyperbolic invariant manifolds for infinite dimensional dynamical systems
Y. Y. Li -- Fine analysis of blow up and applications
F. Lin -- Varifold type theory for Sobolev mappings
S.-S. Lin -- Cellular neural networks: Pattern and waves
X.-P. Zhu -- Long time behavior of curves evolving by curvature
G.-Q. Chen -- Discontinuous solutions to nonlinear evolutionary partial differential equations
T.-P. Liu -- Well-posedness theory for hyperbolic conservation laws
J. Li and T. Zhang -- Two-dimensional Riemann problems for conservation laws in gas dynamics
S. L. Lee and Q. Sun -- Boundedness of cascade algorithms in Besov spaces
R. H. Chan, M.-h. Yip, C.-w. Leung, and M. K. Ng -- Circulant preconditioners for ill-conditioned Hermitian Toeplitz matrices
R.-H. Wang -- What is computational geometry
G. J. Chang -- A survey on circular chromatic numbers of graphs
L. Ruan, D.-Z. Du, X. Hu, X. Jia, and D. Li -- Approximations for color-covering problems
List of participants
Details:
Publisher: American Mathematical Society, International Press
Distributor: American Mathematical Society
Series: AMS/IP Studies in Advanced Mathematics, Volume: 20
Publication Year: 2001
ISBN: 0-8218-2652-2
Paging: 518 pp.
Binding: Softcover