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.

The R Project for statistical computing (R) is a programming language and environment for statistics and graphing. Another commonly used programming language for statistics and data mining is Python. Both Python and R are easy to learn. If the primary purpose is statistical analysis, then R is usually preferred.Why learn/teach R? One of the major reasons why R is becoming more popular (TIOBE,2018) is that it is an open-source (i.e. free) software. Also, when dealing with a large number of variables, multiple datasets, and large samples, R is also a more efficient tool than traditional drop-down menu software such as SPSS. Finally, R programming is now very easy to use with the development of helpful packages.This open text will introduce R packages and step-by-step codes for conducting common statistical analyses in psychological research and classrooms. Funding acknowledgment: The author would like to thank the Society for the Teaching of Psychology (STP), American Psychological Association Division 2 Instructional Resource Award for their generous support of this project. This resource is licensed under the Creative Commons Attribution-ShareAlike4.0 International license (CC BY-SA4.0)

Significant Statistics: An Introduction to Statistics was adapted and original content added by John Morgan Russell. It is adapted from content published by OpenStax Introductory Statistics, OpenIntro Statistics, and Introductory Statistics for the Life and Biomedical Sciences.

Significant Statistics: An Introduction to Statistics is intended for the one-semester introduction to statistics course for students who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermediate algebra. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a 'Your Turn' problem that is designed as extra practice for students.

Instructors reviewing, adopting, or adapting this textbook, please help us understand your use by filling out this form: https://bit.ly/stat-interest.

Table of Contents:

Chapter 1: Sampling and Data
Chapter 2: Descriptive Statistics
Chapter 3: Basics of Probability
Chapter 4: Discrete Random Variables
Chapter 5: Continuous Random Variables
Chapter 6: Foundations of Inference
Chapter 7: Inference for One Sample
Chapter 8: Inference for Two Samples
Chapter 9: Simple Linear Regression
Class Group Activities

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.

Table of Contents
1 Introduction to Probability
2 Applications of Probability
3 Random Sequences and Visualization
4 Introduction to Model Comparison
5 Applications of Model Comparison
6 Introduction to Parameter Estimation
7 Priors, Likelihoods, and Posteriors
8 Common Statistical Significance Tests
9 Applications of Parameter Estimation and Inference
10 Multi-parameter Models
11 Introduction to MCMC
12 Concluding Thoughts
Bibliography
Appendix A: Computational Analysis
Appendix B: Notation and Standards
Appendix C: Common Distributions and Their Properties
Appendix D: Tables

A discussion of how small probabilities license statistical inferences, and how frequentists C. S. Peirce, R. A. Fisher, J. Neyman, E. S. Pearson, and D. Mayo differ in their interpretations of the p-value of a statistical test. (Unpublished paper)

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 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.

Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.

Table of Contents
1 Introduction
2 Working with data
3 Probability
4 Summarizing data
5 Fitting models to data
6 Data Visualization
7 Sampling
8 Resampling and simulation
9 Hypothesis testing
10 Confidence intervals, effect sizes, and statistical power
11 Bayesian statistics
12 Modeling categorical relationships
13 Modeling continuous relationships
14 The General Linear Model
15 Comparing means
16 The process of statistical modeling: A practical example
17 Doing reproducible research

Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.

The purpose of this course is to provide background in the ways in which psychologists evaluate data collected from research projects. A researcher may gather many pieces of data that describe a group of research subjects and there are common ways in which these pieces of information are presented. Secondly, statistical tests can help investigators draw inferences about the relationship of the research sample to the general population it is supposed to represent. As a student of psychology or any other discipline that uses research data to explore ideas, it is important that you know how data is evaluated and that you gain an understanding of the ways in which these procedures help to summarize and clarify data.

This course introduces statistical tools and techniques that are routinely used by modern statisticians for a wide variety of applications. Upon successful completion of this course, the student will be able to: apply statistical hypothesis testing for one population; conduct statistical hypothesis testing and estimation for two populations; apply multiple regression analysis to analyze a multivariate problem; analyze the outputs for a multiple regression model and interpret the regression results; conduct test hypotheses about the significance of a multiple regression model and test the significance of the independent variables in the model; select appropriate multiple regression models using automatic model selection, forward selection, backward elimination, and stepwise selection; recognize and address issues when using multiple regression analysis; identify situations when nonparametric tests are appropriate; conduct nonparametric tests; explain the principles underlying General Linear Model, Multilevel Modeling, Data Mining, Machine Learning, Bayesian Belief Networks, Neural Network, and Support Vector Machine. This free course may be completed online at any time. (Mathematics 251)

This 12-minute video lesson looks at the T-Statistic Confidence Interval (for small sample sizes). [Statistics playlist: Lesson 52 of 85]

This 7-minute video lesson compares Z-statistics and T-statistics. [Statistics playlist: Lesson 49 of 85]

A whirl-wind tour of the statistics used in behavioral science research, covering topics including: data visualization, building your own null-hypothesis distribution through permutation, useful parametric distributions, the generalized linear model, and model-based analyses more generally. Familiarity with MATLABA, Octave, or R will be useful, prior experience with statistics will be helpful but is not essential. This course is intended to be a ground-up sketch of a coherent, alternative perspective to the "null-hypothesis significance testing" method for behavioral research (but don't worry if you don't know what this means).

This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.

The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.