Alain Connes, Andrer Lichnerowicz, and Marcel Paul Schutzenberger
Triangle of Thoughts
Expected publication date is September 1, 2001
Description
In these "conversations", Connes, Lichnerowitz and Schutzenberger, all members of the French Academy, closely examine the relationships that connectmathematics, physics, and philosophy. The book may make you think again about things that you thought were familiar.
Contents
Logic and reality
The nature of mathematical objects
Physics and mathematics: The double-edged sword
Fundamental theory and real calculation
Mathematics and the description of the world
Cosmology and grand unification
Interpreting quantum mechanics
Reflections on time
Andre Lichernowicz
Marcel Paul Schotzenberger
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Publication Year: 2001
ISBN: 0-8218-2614-X
Paging: approximately 234 pp.
Binding: Hardcover
Edited by: Brian Conrad, University of Michigan, Ann Arbor, MI,
and Karl Rubin, Stanford University, CA
Arithmetic Algebraic Geometry
Expected publication date is August 1, 2001
Contents
B. Conrad and K. Rubin -- Introduction
Joe P. Buhler, Elliptic curves, modular forms, and applications
Preface
Elliptic curves
Points on elliptic curves
Elliptic curves over C
Modular forms of level 1
L-series; Modular forms of higher level
$l$-adic representations
The rank of elliptic curves over Q
Applications of elliptic curves
Bibliography
Alice Silverberg, Open questions in arithmetic algebraic geometry
Overview
Torsion subgroups
Conjectures of Birch and Swinnerton-Dyer
ABC and related conjectures
Some other conjectures
Bibliography
Kenneth A. Ribet and William A. Stein, Lectures on Serre's conjectures
Preface
Introduction to Serre's conjecture
Optimizing the weight
Optimizing the level
Exercises
Appendix by Brian Conrad: The Shimura construction in weight 2
Appendix by Kevin Buzzard: A mod $\ell$ multiplicity one result
Bibliography
Fernando Q. Gouvea, Deformations of Galois representations
Introduction
Galois groups and their representations
Deformations of representations
The universal deformation: Existence
The universal deformation: Properties
Explicit deformations
Deformations with prescribed properties
Modular deformations
$p$-adic families and infinite ferns
A criterion for existence of a universal deformation ring
An overview of a theorem of Flach
An introduction to the $p$-adic geometry of modular curves
Bibliography
Ralph Greenberg, Introduction to Iwasawa theory for elliptic curves
Preface
Mordell-Weil groups
Selmer groups
$\Lambda$-modules
Mazur's control theorem
Bibliography
John Tate, Galois cohomology
Galois cohomology
Bibliography
Wen-Ching Winnie Li, The arithmetic of modular forms
Introduction
Introduction to elliptic curves, modular forms, and Calabi-Yau varieties
The arithemtic of modular forms
Connections among modular forms, elliptic curves, and representations of Galois groups
Bibliography
Noriko Yui, Arithmetic of certain Calabi-Yau varieties and mirror symmetry
Introduction
The modularity conjecture for rigid Calabi-Yau threefolds over the field of rational numbers
Arithmetic of orbifold Calabi-Yau varieties over number fields
$K3$ surfaces, mirror moonshine phenomenon
Bibliography
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: IAS/Park City Mathematics Series,
Publication Year: 2001
ISBN: 0-8218-2173-3
Paging: 569 pp.
Binding: Hardcover
Solomon Friedberg and members of the Boston College Mathematics Case Studies Project Development Team, Boston College, Chestnut Hill, MA
Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom: GraduateStudent Edition
Expected publication date is June 16, 2001
Description
Progress in mathematics frequently occurs first by studying particular examples and then by generalizing the patterns that have been observed into far-reaching theorems. Similarly, in teaching mathematics one often employs examples to motivate a general principle or to illustrate its use. This volume uses the same idea in the
context of learning how to teach: By analyzing particular teaching situations, one can develop broadly applicable teaching skills useful for the professional mathematician. These teaching situations are the Case Studies of the title.
Just as a good mathematician seeks both to understand the details of a particular problem and to put it in a broader context, the examples presented here are chosen to offer a serious set of detailed teaching issues and to afford analysis from a broad perspective.
Each case raises a variety of pedagogical and communication issues that may be explored either individually or in a group facilitated by a faculty member. Teaching notes for such a facilitator are included for each Case in the Faculty Edition.
The methodology of Case Studies is widely used in areas such as business and law. The consideration of the mathematics cases presented here will help readers to develop teaching skills for their own classrooms.
This series is published in cooperation with the Mathematical Association of America.
Contents
Introduction
Fourteen case studies
Changing sections
Emily's test
Fundamental problems part I
Making the grade (College algebra version/Calculus I version/Multivariable calculus version)
Making waves
Order out of chaos
Pairing up
The quicksand of problem four
Salad days
Seeking points
Study habits
Studying the exam (College algebra questions/Calculus II questions/Multivariable calculus questions)
There's something about Ted part I
What were they thinking?
Details:
Publisher: American Mathematical Society, Mathematical Association of America
Distributor: American Mathematical Society
Series: CBMS Issues in Mathematics Education, ISSN:
Publication Year: 2001
ISBN: 0-8218-2823-1
Paging: approximately 75 pp.
Binding: Softcover
Edited by: Robert E. Reys, University of Missouri, Columbia, MO,
and Jeremy Kilpatrick, University of Georgia, Athens, GA
One Field, Many Paths: U. S. Doctoral Programs in Mathematics Education
Description
This book is the first to focus specifically on doctoral programs in mathematics education. It reflects the proceedings of a National Conference on Doctoral Programs in Mathematics Education (Lake Ozark, MO) which was sponsored by the National Science Foundation. This conference was proceeded by a comprehensive
survey of programs conducted over the preceding year. The meeting was designed to generate dialog regarding the nature of current doctoral programs in mathematics education, to discuss ways to strengthen such programs, and to detail suggestions and guidelines for faculty engaged in restructuring an existing program
or in creating a new one.
This volume outlines the results of the conference organized by the following sections:
Background, which includes papers providing different perspectives of doctoral programs in mathematics education in the U.S. and abroad.
Core Components, which highlights elements in common to most doctoral mathematic programs, including course work, research, education, and teaching.
Related Issues, which addresses the challenges of recruiting, organizing new programs, and restructuring existing programs.
Reactions and Reflections, which contains the thoughts of recent graduates regarding their doctoral programs and observations on the importance of integrating policy issues into doctoral programs.
Ideas for Action, which provides a brief synthesis of the conference and offers suggestions for future action to improve future doctoral programs.
This series is published in cooperation with the Mathematical Association of America.
Contents
Background
E. F. Donoghue -- Mathematics education in the United States: Origins of the field and the development of early graduate programs
R. E. Reys, B. Glasgow, G. A. Ragan, and K. W. Simms -- Doctoral programs in mathematics education in the U.S.: A status report
F. Fennell, D. Briars, T. Crites, S. Gay, and H. Tunis -- Reflections on the match between jobs and doctoral programs in mathematics education
A. J. Bishop -- International perspectives on doctoral studies in mathematics education
Core components
J. T. Fey -- Doctoral programs in mathematics education: Features, options, and challenges
F. K. Lester, Jr. and T. P. Carpenter -- The research preparation of doctoral students in mathematics education
J. A. Dossey and G. Lappan -- The mathematical education of mathematics educators in doctoral programs in mathematics education
N. C. Presmeg and S. Wagner -- Preparation in mathematics education: Is there a basic core for everyone?
D. V. Lambdin and J. W. Wilson -- The teaching preparation of mathematics educators in doctoral programs in mathematics education
L. V. Stiff -- Discussions on different forms of doctoral dissertations
G. Blume -- Beyond course experiences: The role of non-course experiences in mathematics education doctoral programs
Related issues
C. Thornton, R. H. Hunting, J. M. Shaughnessy, J. T. Sowder, and K. C. Wolff -- Organizing a new doctoral program in mathematics education
D. B. Aichele, J. Boaler, C. A. Maher, D. Rock, and M. Spikell -- Reorganizing and revamping doctoral programs--Challenges and results
K. C. Wolff -- Recruiting and funding doctoral students
C. E. Lamb -- The use of distance-learning technology in mathematics education doctoral programs
R. Lesh, J. A. Crider, and E. Gummer -- Emerging possibilities for collaborating doctoral programs
Reactions and reflections
J. M. Bay -- Appropriate preparation of doctoral students: Dilemmas from a small program perspective
A. Flores -- Perspectives from a newcomer on doctoral programs in mathematics education
T. Lingefjd -- Why I became a doctoral student in mathematics education in the United States
V. M. Long -- Policy--A missing but important element in preparing doctoral students
G. A. Ragan -- My doctoral program in mathematics education--A graduate student's perspective
Ideas for action
J. Hiebert, J. Kilpatrick, and M. M. Lindquist -- Improving U. S. doctoral programs in mathematics education
References
R. E. Reys and J. Kilpatrick -- References
Appendices
R. E. Reys and J. Kilpatrick -- List of participants
R. E. Reys and J. Kilpatrick -- Conference agenda
Details:
Publisher: American Mathematical Society, Mathematical Association of America
Distributor: American Mathematical Society
Series: CBMS Issues in Mathematics Education, Volume: 9
Publication Year: 2001
ISBN: 0-8218-2771-5
Paging: 192 pp.
Binding: Softcover
Edited by: I. M. Sigal and C. Sulem, University of Toronto, ON, Canada
Nonlinear Dynamics and Renormalization Group
Expected publication date is May 11, 2001
Description
This book contains the proceedings from the workshop, Nonlinear Dynamics and Renormalization Group, held at the Centre de recherches mathatiques (CRM) in Montreal (Canada), as part of the year-long program devoted to mathematical physics. In the book, active researchers in the fields of nonlinear partial differential
equations and renormalization group contribute recent results on topics such as Ginzburg-Landau equations and blow-up of solutions of the nonlinear Schroedinger equations, quantum resonances, and renormalization group analysis in constructive quantum field theory. This volume offers the latest research in the rapidly
developing fields of nonlinear equations and renormalization group.
Contents
S. Alama and L. Bronsard -- Analysis of some macroscopic models of high-$T_c$ superconductivity
N. D. Alikakos and G. Fusco -- The effect of distribution in space in Ostwald ripening
D. Auckly and L. Kapitanski -- Mathematical problems in the control of underactuated systems
O. I. Bogoyavlenskij -- Axially and helically symmetric global plasma equilibria
O. Costin, J. L. Lebowitz, and A. Rokhlenko -- On the complete ionization of a periodically perturbed quantum system
J. Dimock -- The sine-Gordon model at $\beta = 4\pi$
G. M. Graf -- Ground states of supersymmetric matrix models
S. J. Gustafson -- Some mathematical problems in the Ginzburg-Landau theory of superconductivity
M. K.-H. Kiessling -- Renormalization in radiation reaction: New developments in classical electron theory
C.-K. Lin -- Singular limit of the modified nonlinear Schringer equation
M. Merkli -- Dynamics of quantum resonances
H. Nawa -- Nelson diffusions and blow-up phenomena in solutions of the nonlinear Schringer equation with critical power
D. E. Pelinovsky and C. Sulem -- Embedded solitons of the DSII equation
G. Perelman -- On the blow up phenomenon for the critical nonlinear Schringer equation in 1D
S. Serfaty -- Vorticity for the Ginzburg-Landau model of superconductors in a magnetic field
A. Soffer -- Dissipation through dispersion
B. Vasilijevic -- Quantum tunneling at positive temperature
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: CRM Proceedings & Lecture Notes, Volume: 27
Publication Year: 2001
ISBN: 0-8218-2802-9
Paging: 192 pp.
Binding: Softcover