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.
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.
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.
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.
This course provides a mathematical introduction to probability and statistics using R statistical software. The primary goal of the course is to learn and apply Monte-Carlo simulation techniques to a wide variety of problems. We will focus on solving problems from a numerical point of view, with methods to complete numerical integration, root finding, curve fitting, variance reduction and optimization. Core knowledge of R and basic programming concepts will be introduced. Case studies and projects will be independently completed throughout the semester. This course will satisfy an intermediate-level elective for the math major (Column E: Statistical/Data Science) and it will satisfy an elective for the math and statistics minors as well. Prerequisite: STAT 106, STAT 116 or permission of instructor. Offered every other year.
Each offering of this course approaches the study of variability using a particular set of statistical tools (such as Bayesian Analysis, biostatistics, sports analytics, experimental design or statistical machine learning.) Specific statistical methodology within a subfield of the discipline will be examined. A large component of each offering will be intensive projects where students will be expected to determine which statistical methods are appropriate for a given setting before analyzing data. As part of these projects and daily activities, students will use R to analyze data to make inferences about the population characteristics of interest. Additionally, written and oral communication will be a regular part of the course. The course may be repeated for credit as long as the subfield is different. That is, students may receive credit for each specific subfield only once. This course will satisfy an upper-level elective for the math major (Column E: Statistical/Data Science) and it will satisfy an elective for the math and statistics minors as well. Prerequisite: any STAT course at the 200-level or higher or permission of the instructor. Offered every spring.
Additional Catalog information for different subfields:
STAT 306 Topics in Statistics: Bayesian Analysis
This course will focus on statistical inference using a Bayesian framework. Unlike many other statistical tools, Bayesian methods incorporate prior information with information derived through experimentation or observation. The course will begin with a review of the basic concepts of probability, which are critical to understanding the foundations of the subject. Other topics will include decision theory, loss functions, subjective and objective prior distributions, posterior distribution, estimation, testing, prediction, sensitivity analysis and hierarchical modeling. We will also compare and contrast Bayesian methods with classical methods. Students will use R regularly to make Bayesian inference from data.
STAT 306 Topics in Statistics: Biostatistics
Statistical methods are often used in medical studies. All of the examples, exercises and projects will deal with data from public health sectors, the World Health Organization, the CDC, the FDA or prospective or retrospective studies on patients. Survival functions will be introduced and inference methods based on the Kaplan-Meier estimator will be studied. Cox regression models and accelerated failure time models will be examined if time permits. R statistical software will be used heavily throughout the course.
STAT 306 Topics in Statistics: Sports Analytics
Sports analytics are being used more frequently to help managers and owners make important decisions. Billy Bean was one of the first general managers to implement statistical methods and models to MLB. Now, similar models and methods are being used in basketball, football, hockey, soccer, golf, swimming and other sports. Using data science techniques to scrape data from appropriate sources has been a game changer for many analysts who are always trying to get an advantage on their competitors. We will carefully examine the statistical methods that are being used. In addition to analyzing individual and team performance over time, we will look at the impact of rule changes and new guidelines or draft policies. Students will read current journal articles from sports statistics journals and analyze data to address open questions of interest. Oral and written communication about these technical models will be a regular part of the course. Students will regularly be using R to analyze data and make inferences. Statistical methods for analyzing time series data will be a major part of this course.
STAT 306 Topics in Statistics: Experimental Design
This course will focus on the design and analysis of experiments. Complete and fractional factorial designs, comp
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 and MATH 224. Offered every other spring.
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.
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. Permission of department chair required. Prerequisite: senior standing and at least one "depth sequence" completed.