AMS Tutorial on Modeling
January 11 - 12, 2010, Room 2006, 2nd Floor, Moscone Center West
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 nonacademic employment. The tutorial will be divided into two sessions, each lasting one day. The cost for both sessions is US$25. Click here to register.
Introduction to Numerical Modeling, Monday, 9:00 a.m. - noon and 1:30 p.m. - 4:30 p.m., presented by Chi-Wang Shu, Brown University.
In today's job market, Ph.D. students in mathematics might improve their chances of getting employment 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 one-day 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 in one day, 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. Professor Shu is Managing Editor of Mathematics of Computation and Editor-in-Chief of Journal of Scientific Computing.
Introduction to Statistical Modeling, Tuesday, 9:00 a.m. - noon and 1:30 p.m. - 4:30 p.m., presented by Wei Zhu, 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 classical statistical model is usually one or a set of stochastic equations (linear or nonlinear) linking the relevant variables 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 ordinary least squares (OLS) method developed by Gauss and Legendre. However, when randomness exists in both measurements, the OLS method will no longer be suitable. For instance, in gauging the relationship between the concentrations of organic aerosols and anthropogenic carbon monoxide, we found that both quantities, measured by the mass spectrometer and the UV fluorescence analyzer respectively, contain measurement errors and possibly other volatilities due to air dynamics, and thus the OLS method is obsolete in this situation. What are the alternative modeling methods?
In this one-day workshop intended for those who wish to broaden their horizons (and job market if pertinent) by learning more statistics, we will present a summary of classical as well as modern statistical modeling methods. Beginning with the simple linear regression introduced above, we will move on to the generalized linear models, categorical data analysis, time series models, survival analysis, and structural equation modeling (also called path analysis). We will discuss pertinent job markets and the knowledge/skills necessary for those markets. We will conclude the workshop by introducing the bootstrap resampling method and its role in modern statistical modeling and inference. A list of reference books corresponding to these subjects will be provided for the interested audience.
The lecturer, Professor Wei Zhu, has a B.S. in mathematics and a Ph.D. in Biostatistics. For the past decade, she has applied statistics to a wide spectrum of problems including brain imaging analysis, climate modeling, clinical trials, genetics and proteomics. She is an active educator whose former doctoral students are currently employed in academia, the pharmaceutical, Internet, and financial industries. She is the director of the Data Management and Statistical Analysis Core of the Alzheimer's Disease Research Center at New York University. She is also the director of the Bioinformatics Laboratory at the SBU Center of Excellence in Wireless and Information Technology. She collaborates closely with scientists from the Brookhaven National Laboratory, the Cold Spring Harbor Laboratory, and the National Institutes of Health.