Credit: 0.5 QR
This is a basic course in statistics. The topics to be covered are the nature of statistical reasoning, graphical and descriptive statistical methods, design of experiments, sampling methods, probability, probability distributions, sampling distributions, estimation and statistical inference. Confidence intervals and hypothesis tests for means and proportions will be studied in the one- and two-sample settings. The course concludes with inference regarding correlation, linear regression, chi-square tests for two-way tables, and one-way ANOVA. Statistical software will be used throughout the course, and students will be engaged in a wide variety of hands-on projects. No prerequisite. Offered every semester.
Credit: 0.5 QR
Appropriate applications of statistical methods have changed the way some Major League Baseball teams manage the game. (see "Moneyball: The Art of Winning an Unfair Game".) Statistics are used in other sports to evaluate the performance of individual players or teams. The focus of this course will be on the proper application of statistical models in sports. Students will use appropriate methods to examine interesting questions such as: Are there unusual patterns in the performance statistics of "steroid sluggers" such as Barry Bonds and Mark McGwire or pitchers such as Roger Clemens? Other possible topics include the impact of a penalty kick in soccer, of home field advantage in football, of technological improvements in golf or cycling, and of training methods in marathon running. Although the sport and question of interest will change, the focus on proper applications of appropriate statistical methods will remain the same. Students will analyze data and present their results to the class. Oral and written reports will be expected. No prerequisite. Offered every other year.
Credit: 0.5 QR
This course focuses on choosing, fitting, assessing and using statistical models. Simple linear regression, multiple regression, analysis of variance, general linear models, logistic regression and discrete data analysis will provide the foundation for the course. Classical interference methods that rely on the normality of the error terms will be thoroughly discussed, and general approaches for dealing with data where such conditions are not met will be provided. For example, distribution-free techniques and computer-intensive methods, such as bootstrapping and permutation tests, will be presented. Students will use statistical software throughout the course to write and present statistical reports. The culminating project will be a complete data analysis report for a real problem chosen by the student. The MATH 106–206 sequence provides a thorough foundation for statistical work in economics, psychology, biology, political science and many other fields. Prerequisite: STAT 106 or 116 or a score of 4 or 5 on the Statistics AP exam. Offered every semester.
Credit: 0.5 QR
This course will focus on nonparametric and distribution-free statistical procedures. These procedures will rely heavily on counting and ranking techniques. In the one and two sample settings, the sign, signed-rank and Mann-Whitney-Wilcoxon procedures will be discussed. Correlation and one-way analysis of variance techniques also will be investigated. A variety of special topics will be used to wrap up the course, including bootstrapping, censored data, contingency tables and the two-way layout. The primary emphasis will be on data analysis and the intuitive nature of nonparametric statistics. Illustrations will be from real data sets and students will be asked to locate an interesting data set and prepare a report detailing an appropriate nonparametric analysis. Prerequisite: STAT 106, 116 or a score of 4 or 5 on the Statistics AP exam or permission of instructor. Offered every other year.
Credit: 0.5 QR
This course will focus on linear regression models. Simple linear regression with one predictor variable will serve as the starting point. Models, inferences, diagnostics and remedial measures for dealing with invalid assumptions will be examined. The matrix approach to simple linear regression will be presented and used to develop more general multiple regression models. Building and evaluating models for real data will be the ultimate goal of the course. Time series models, nonlinear regression models and logistic regression models also may be studied if time permits. Prerequisite: STAT 106, MATH 224 or permission of instructor. Offered every other spring.
Credit: 0.5 QR
This course follows MATH 336 and introduces the mathematical theory of statistics. Topics include sampling distributions, order statistics, point estimation, maximum likelihood estimation, methods for comparing estimators, interval estimation, moment generating functions, bivariate transformations, likelihood ratio tests and hypothesis testing. Computer simulations will accompany and corroborate many of the theoretical results. Course methods often will be applied to real data sets. Prerequisite: MATH 336. Offered every other spring.
Individual study is a privilege reserved for students who want to pursue a course of reading or complete a research project on a topic not regularly offered in the curriculum. It is intended to supplement, not take the place of, coursework. Individual study cannot be used to fulfill requirements for the major. Individual studies will earn 0.25 - 0.50 units of credit. To qualify, a student must identify a member of the mathematics department willing to direct the project. The professor, in consultation with the student, will create a tentative syllabus (including a list of readings and/or problems, goals and tasks) and describe in some detail the methods of assessment (e.g., problem sets to be submitted for evaluation biweekly; a 20-page research paper submitted at the course's end, with rough drafts due at given intervals, and so on). The department expects the student to meet regularly with his or her instructor for at least one hour per week. All standard enrollment/registration deadlines for regular college courses apply. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study preferably the semester before, so that there is time to devise the proposal and seek departmental approval before the registrar's deadline. Permission of instructor and department chair required. No prerequisite.
Credit: 0.25 QR
This course will consist largely of an independent project in which students read several sources to learn about a mathematical topic that complements material studied in other courses, usually an already completed depth sequence. This study will culminate in an expository paper and a public or semi-public presentation before an audience consisting of at least several members of the mathematics faculty as well as an outside examiner. Prerequisite: At least one "depth sequence" completed and permission of the department chair.