Publications

For the research mathematics community, the American Mathematical Society publishes the Park City Mathematics Series and the Park City Mathematics Subseries of the Student Mathematical Library.

Background of the IAS/Park City Mathematics Series:

The IAS/Park City Mathematics Institute (PCMI) was founded in 1991 as part of the “Regional Geometry Institute” initiative of the National Science Foundation.  In mid-1993 the program found an institutional home at the Institute for Advanced Study (IAS) in Princeton, New Jersey.

The IAS/Park City Mathematics Institute encourages both research and education in mathematics and fosters interaction between the two.  The three-week summer institute offers programs for researchers and postdoctoral scholars, graduate students, undergraduate students, high school teachers, undergraduate faculty, and researchers in mathematics education.  One of PCMI’s main goals is to make all of the participants aware of the total spectrum of activities that occur in mathematics education and research:  we wish to involve professional mathematicians in education and to bring modern concepts in mathematics to the attention of educators.  To that end the summer institute features general sessions designed to encourage interaction among the various groups.  In-year activities at the sites around the country form an integral part of the High School Teachers Program.

Each summer a different topic is chosen as the focus of the Research Program and Graduate Summer School.  Activities in the Undergraduate Summer School deal with this topic as well.  Lecture notes from the Graduate Summer School are being published each year in this series. (The first sixteen volumes can be found below and more volumes are in production.)

Some material from the Undergraduate Summer School is published as part of the Student Mathematical Library series of the American Mathematical Society.  We hope to publish material from other parts of the IAS/PCMI in the future.  This will include material from the Secondary School Teachers Program and publications documenting the interactive activities which are a primary focus of the PCMI.  At the summer institute late afternoons are devoted to seminars of common interest to all participants.  Many deal with current issues in education: others treat mathematical topics at a level which encourages broad participation.  The PCMI has also spawned interactions between universities and high schools at a local level.  We hope to share these activities with a wider audience in future volumes.

John C. Polking
Series Editor
April 2007

 


Current List of Publications – Park City Mathematics Series

The Park City Mathematics Series is published by the American Mathematical Society. Each volume contains the lectures for that year from the PCMI Graduate Summer School and, in some cases, the Mentoring Program for Women in Mathematics (now known as Women and Mathematics, co-sponsored by the Institute for Advanced Study and Princeton University).

  • Volume 1: Geometry and Quantum Field Theory (1991)
    Karen Uhlenbeck and Daniel Freed, Editors
  • Volume 2: Nonlinear Partial Differential Equations in Differential Geometry (1992)
    Robert Hardt and Michael Wolf, Editors
  • Volume 3: Complex Algebraic Geometry (1993)
    János Kollár, Editor
  • Volume 4: Gauge Theory and the Topology of Four-Manifolds (1994)
    Robert Friedman and John Morgan, Editors
  • Volume 5: Hyperbolic Equations and Frequency Interactions (1995)
    Luis Caffarelli and Weinan E, Editors
  • Volume 6: Probability Theory and Applications (1996)
    Elton P. Hsu and S.R.S. Varadhan, Editors
  • Volume 7: Symplectic Geometry and Topology (1997)
    Yakov Eliashberg and Lisa M. Traynor, Editors
  • Volume 8: Representation Theory of Lie Groups (1998)
    Jeffrey Adams and David Vogan, Editors
  • Volume 9: Arithmetic Algebraic Geometry (1999)
    Karl Rubin and Brian Conrad, Editors
  • Volume 10: Computational Complexity Theory (2000)
    Avi Wigderson and Stephen Rudich, Editors
  • Volume 11: Quantum Field Theory, Supersymmetry, and Enumerative Geometry (2001)
    Daniel S. Freed, David R. Morrison, and Isadore Singer, Editors
  • Volume 12: Automorphic Forms and their Applications (2002)
    Peter Sarnak and Freydoon Shahidi, Editors
  • Volume 13: Geometric Combinatorics (2004)
    Ezra Miller, Victor Reiner, and Bernd Sturmfels
  • Volume 14: Mathematical Biology (2005)
    Mark A. Lewis, Mark A. J. Chaplain, James P. Keener, and Philip K. Maini
  • Volume 15: Low Dimensional Topology (2006)
    Tomasz Mrowka and Peter Osváth
  • Volume 16: Statistical Mechanics (2007)
    Scott Sheffield and Thomas Spencer
  • Volume 17: Analytical and Algebraic Geometry (2008)
    Jeffrey McNeal and Mircea Mustaţă
  • Volume 18: Arthimatic of L-functions (2009)
    Cristian Popescu, Karl Rubin and Alice Silverberg
  • Volume 19: Mathematics in Image Processing (2010)
    Hongkai Zhao
  • Volume 20: Moduli Spaces of Riemann Surfaces (2011)
    Benson Farb, Richard Hain, and Eduard Looijenga
  • Volume 21: Geometric Group Theory (2012)
    Mladen Bestvina, Michah Sageev, and Karen Vogtmann

 


AMS Student Mathematical Library: Park City Mathematics Subseries

Each single volume in this subseries of the AMS Student Mathematical Library contains lectures from one of the PCMI Summer Session Undergraduate Program courses or the Mentoring Program for Women in Mathematics Undergraduate Course.

  • Lectures on Contemporary Probability; Gregory F. Lawler and Lester N. Coyle
    STML/2
  • An Introduction to the Mathematical Theory of Waves; Roger Knobel
    STML/3
  • Codes and Curves; Judy L. Walker
    STML/7
  • Lectures in Geometric Combinatorics; Rekha R. Thomas
    STML/33
  • Enumerative Geometry and String Theory; Sheldon Katz
    STML/32
  • Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots; Francis Bonahon
    STML/49
  • Differential Equations, Mechanics, and Computation; Richard S. Palais and Robert A. Palais
    STML/51
  • Elliptic Curves, Modular Forms, and Their L-functions; Álvaro Lozano-Robledo
    STML/58
  • Harmonic Analysis: From Fourier to Wavelets; María Cristina Pereyra and Lesley A. Ward
    STML/63
  • Algebraic Geometry: A Problem Solving Approach; Thomas Garrity, Richard Belshoff, Lynette Boos, Ryan Brown, Carl Lienert, David Murphy, Junalyn Navarra-Madsen, Pedro Poitevin, Shawn Robinson, Brian Snyder, and Caryn Werner
    STML/68

All AMS/PCMI volumes are available from the AMS Bookstore.

 


Resources for Mathematics Educators

Resources for educators (teachers and college faculty) are found on a special website created by the Math Forum at Drexel University: http://mathforum.org/pcmi/.

Specifically: