AMS Tutorial on Modeling:
An Introduction to Numerical and Statistical Modeling


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Sunday, January 4, 2009
9:00 a.m. to 4:30 p.m.
Washington Room 3, Marriott Wardman Hotel

Introduction and Description

This tutorial will be an introduction to both numerical and statistical modeling for those who are not currently studying computational science. It is especially designed for individuals who are considering non-academic employment.

The tutorial will be divided into two sessions. During the morning session, Professor Chi-Wang Shu of the Division of Applied Mathematics, Brown University, will present an introduction to numerical modeling. In the afternoon, Professor Wei Zhu, Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, will give an introduction to statistical modeling.

Introduction to Numerical Modeling

January 4, 2009
9:00 a.m. to 12:00 noon

Professor Chi-Wang Shu
Division of Applied Mathematics
Brown University

In today's job market, Ph.D. students in mathematics might improve their chances of getting employments if they consider jobs outside the traditional academic job market. Students who have expertise in numerical modeling are marketable to many different types of non-academic employers, including government research labs, research labs of large companies (such as the oil companies), and various computer software companies (such as those who write software for medical science and health industry or for financial markets). Even for students whose major expertise is not in numerical modeling, some knowledge of numerical modeling should enhance the chance to obtain employment from many non-academic employers.

This 3-hour tutorial is intended for graduate students who are not working in areas related to computational science (numerical analysis, scientific computing, computational engineering, etc.), but would be interested in an introduction to some fundamental ideas for entry level numerical modeling.

The tutorial will start with a general description of numerical modeling, and will explain the difference between a student in a mathematics department majoring in computational science and a student in computer science. While programming (in C or another language) is a necessary skill for any student in numerical modeling, it is the mathematical insight which allows mathematicians to design and improve algorithms that are stable, accurate and efficient for various applications.

The tutorial will then move to the description of a few selected topics in numerical modeling, including the solutions of large linear systems, the approximations of ordinary differential equations, and finite difference, finite element, and spectral methods for approximating partial differential equations. While it is impossible to give an in-depth coverage of so many topics within three hours, we will emphasize the fundamental concepts such as stability, accuracy and efficiency for these algorithms.

The tutorial will end with a list of references which will allow interested audience to follow up to gain more in-depth knowledge of the exciting area of numerical modeling.

The lecturer, Professor Chi-Wang Shu, has trained over twenty Ph.D.s at Brown University who are now employed both by academic and by non-academic employers. His research expertise is in scientific computing. In 2007 he was awarded the SIAM/ACM Prize in Computational Science and Engineering jointly by the Society for Industrial and Applied Mathematics, the major society for applied and computational mathematicians, and by the Association for Computing Machinery, the major association for computer scientists.

Introduction to Statistical Modeling

January 4, 2009
1:30 p.m. to 4:30 p.m.

Professor Wei Zhu
Department of Applied Mathematics and Statistics
State University of New York at Stony Brook

Statistics is a branch of the mathematical sciences that pertains to the collection and analysis of data. The goal of statistical inference is to make a probabilistic statement about the underlying population based on the given sample. A statistical model is usually one or a set of stochastic equations (often linear) linking the relevant population parameters to the data observed. For example, one may wish to establish a simple linear regression model predicting the height of a son based on the height of his father. To estimate the regression line, one can simply employ the least squares method developed by Gauss and Legendre. So far, it is all mathematics. The role of statistics is to make the subsequent statistical inference (including confidence intervals and hypothesis tests), estimating, for example, the range of the son's height with some certainty, say 95% confidence, for a given paternal statue. An immediate improvement upon such a model would be the addition of the mother's height as another predictor. With two predictors (often called regressors in statistics), one can now expand the simple linear regression model into a multiple linear regression model.

In this 3-hour workshop intended for Joint Mathematics Meetings attendees who wish to broaden their horizons (and job market if pertinent) by learning more statistics, we will start by introducing some popular probability problems from the Wall Street job interviews. We will then focus on some basic and yet most commonly used statistical models including the linear regression model, the logistic regression model, and the autoregressive time series model. We will conclude our workshop with an overview of major branches of modern statistics -- a list of reference books corresponding to these subjects will also be provided for the interested audience.

This workshop will be given by Professor Wei Zhu from the State University of New York at Stony Book. Professor Zhu has a B.S. in mathematics and a Ph.D. in Biostatistics. For the past 10 years, she has applied statistics to a wide spectrum of problems including brain imaging analysis, disease pathway studies, climate modeling and optimal design of experiments. She is an active educator whose former Ph.D. students are currently working in academia, and the pharmaceutical, internet and financial industries. She is the Data Core Director of the Alzheimer's Disease Research Center at New York University. She also collaborates closely with the Brookhaven National Laboratory and the Cold Spring Harbor Laboratory.


The fee for this tutorial is US$25. It is not necessary to register for the Joint Mathematics Meetings (JMM) in order to participate in the tutorial. Registration for the tutorial must be done separately. Please register by sending email to the Mathematics Meetings Service Bureau (MMSB) at and include your name, address, phone number and method of payment. If you would like to pay by check, please register first with the MMSB and then send the check by mail to: Mathematics Meetings Service Bureau, P.O. Box 6887, Providence, R.I., 02940-6887. If you are already registered for the JMM, please indicate this in your email so that this registration can be added to your current record.


If you have additional questions or concerns about the tutorial, please contact Ellen Maycock at 1-800-321-4267, Ext. 4101 or