Introduction to the application of elementary statistics to political analysis. A basic literacy subject, teaching the student how to read and interpret the quantitative literature in various subfields of political science and public policy. Students develop elementary statistical computation skills and learn to use a statistical computing package. From the course home page: This course provides students with a rigorous introduction to Statistics for Political Science. Topics include basic mathematical tools used in social science modeling and statistics, probability theory, theory of estimation and inference, and statistical methods, especially differences of means and regression. The course is often taken by students outside of political science, especially those in business, urban studies, and various fields of public policy, such as public health. Examples draw heavily from political science, but some problems come from other areas, such as labor economics.

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

his task is intended as a classroom activity. Student pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.

This task involves two aspects of statistical reasoning: providing a probabilistic model for the situation at hand, and defining a way to collect data to determine whether or not the observed data is reasonably likely to occur under the chosen model. When guessing between two choices, there is no reason to suspect that one outcome is more likely than the other. Thus, a model that assumes the two outcomes to be equally likely (such as flipping a coin) is appropriate.

This course focuses on the problem of supervised learning from the perspective of modern statistical learning theory starting with the theory of multivariate function approximation from sparse data. It develops basic tools such as Regularization including Support Vector Machines for regression and classification. It derives generalization bounds using both stability and VC theory. It also discusses topics such as boosting and feature selection and examines applications in several areas: Computer Vision, Computer Graphics, Text Classification and Bioinformatics. The final projects and hands-on applications and exercises are planned, paralleling the rapidly increasing practical uses of the techniques described in the subject.

Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.

This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes.

This course presents construction of sampling frames, area sampling, methods of estimation, stratified sampling, subsampling, and sampling methods for surveys of human populations. Students use STATA or another comparable package to implement designs and analyses of survey data.

Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third laws of thermodynamics. Numerous examples illustrating a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices. Concurrent enrollment in Quantum Physics I is recommended.

Statistical Reasoning in Public Health II provides an introduction to selected important topics in biostatistical concepts and reasoning through lectures, exercises, and bulletin board discussions. The course builds on the material in Statistical Reasoning in Public Health I , extending the statistical procedures discussed in that course to the multivariate realm, via multiple regression methods. New topics, such as methods for clinical diagnostic testing, and univariate, bivariate, and multivariate techniques for survival analysis will also be covered. These topics will be reinforced with many "real-life" examples drawn from recent biomedical literature. While there are some formulae and computational elements to the course, the emphasis is again on interpretation and concepts.

This course is an introduction to statistical data analysis. Topics are chosen from applied probability, sampling, estimation, hypothesis testing, linear regression, analysis of variance, categorical data analysis, and nonparametric statistics.

This 7-minute video lesson gives formulas for the Bernoulli Distribution Mean and Variance. [Statistics playlist: Lesson 42 of 85]

This 10-minute video lesson explains box and whisker plots. [Statistics playlist: Lesson 9 of 85]

This 10-minute video lesson shows how to calculate R-squared to see how well a regression line fits the data. [Statistics playlist: Lesson 70 of 85]

This 10-minute video lesson provides an introduction to the central limit theorem and the sampling distribution of the mean. [Statistics playlist: Lesson 35 of 85]

This 10-minute video lesson introduces the chi-square distribution. [Statistics playlist: Lesson 72 of 85]

This 3-minute video lesson provides clarification of the previous video on the confidence interval for difference of means. [Statistics playlist: Lesson 57 of 85]

This 11-minute video lesson compares population proportions (part 1). [Statistics playlist: Lesson 59 of 85]

This 10-minute video lesson compares population proportions (part 2). [Statistics playlist: Lesson 60 of 85]