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Linear Models: In 2005 Wiley, Inc published Introduction to Linear Models and Statistical Inference, co-authored by Steven Janke (Colorado College) and myself. This text is designed as either a first course in statistics for students undergraduates with sufficient backgrounds in mathematics or a second course in linear regression for undergraduates who have taken introductory statistics.
More information is available at http://faculty1.coloradocollege.edu/~sjanke/linearmodels/welcome.html
Mathematical Statistics and Computing:
The focus of most discussion on the teaching of statistics naturally is at the introductory level where a large majority of the students. Since its inception the personal computer has allowed practitioners and students alike to employ large data bases in their research. (Most refer to this use of computing as 'number crunching'.) As computing power increased, the ability to construct intricate graphics allowed users to illustrate their findings. Consequently, a voluminous literature along with the requisite number of conferences has blossomed in support of helping instructors incorporate this technology into their courses.
One manifestation of this change has been the emergence of an approach called 'resampling.' This pedagogy presumes the sample is exactly reflective of the population but makes no additional assumption about the shape of the underlying distribution. In fact, practitioners treat the sample as if it were an infinite population by sampling from it (with replacement). They draw a large number of samples (each of the same size as the original) to approximate the sampling distributions of the statistics of interest.
Advances have taken place in mathematical computing. In particular, the ability of machines to perform symbolic computations has touched most fields in abstract mathematics. In statistics one can mix symbolic and approximate computations to remove dependence upon traditional specific assumptions about underlying distributions. For small samples at least, the computer can compute distributions with reasonable precision for nearly arbitrary underlying distributions. A statistician need not rely on the typical normal approximations.
One goal is to develop for my advanced students useful techniques for analyzing data that require this kind of mathematical computing. I gave a talk about my progress at the Hawaii International Conference on Statistics, Mathematics, and Related Fields in Honolulu in January of 2008. The power point PDF slides from that talk are available below.
Power Point Presentation: