Statistics and Data Science

SDS 1600 Introduction to Statistics

This course introduces students to the basic concepts of statistics, including the design of experiments, data organization, and statistical inference. Students will learn how the selection of sampling method and design of data collection processes can reduce bias and allow for generalizability. Students will use descriptive statistics as well as tables, graphs and frequency distributions to summarize important characteristics of datasets. Students will apply an understanding of elementary probability, measures of variability, and randomness to interpret confidence intervals and hypothesis tests.

Credit 3 units. A&S IQ: NSM, AN

Typical periods offered: Spring

SDS 1998 Statistics and Data Science Elective: 100-Level

Credit 3 units.

SDS 2010 Analytical Tools for Statistics and Data Science I

This is an 8 week short course. This is an introductory course in matrix algebra. The focus is on the concepts and computational aspects of matrix algebra using a high-level programming language or software, and its applications in Statistics and Data Science. Topics include the standard matrix and vector operations, inverses, determinants, system of linear equations, diagonalization (eigenvalues and eigenvectors), and other key matrix decompositions (LU, QR, and Cholesky).

Credit 2 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 2011 Analytical Tools for Statistics and Data Science II

This is an 8 week short course. The course covers some topics of multivariate calculus that are particularly relevant for Statistics and Data Science. The focus is on the ideas, concepts, and computational implementation of the theory. Whenever possible, we will show the use of mathematical and statistical software (e.g., Matlab, Maple, and R) to obtain symbolic, exact, or approximate solutions of the mathematical tools developed in class. Topics include generalities on functions in several variables (graphs, level curves, limits, continuity), linear and quadratic functions in two variables, partial differentiation, multivariate Chain Rule, multivariate Taylor’s approximation, local and global extrema, Lagrange multipliers, multiple integration, change of variables formula (Jacobians), and polar, cylindrical, and spherical coordinates.

Credit 2 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 2020 Elementary Probability and Statistics

An elementary introduction to statistical concepts, reasoning and data analysis. Topics include statistical summaries and graphical presentations of data, discrete and continuous random variables, the logic of statistical inference, design of research studies, point and interval estimation, hypothesis testing, and linear regression. Students will learn a critical approach to reading statistical analyses reported in the media, and how to correctly interpret the outputs of common statistical routines for fitting models to data and testing hypotheses. A major objective of the course is to gain familiarity with basic R commands to implement common data analysis procedures.  Students intending to pursue a major or minor in statistics or wishing to take 4000 level or above statistics courses should instead take SDS 3020 or SDS 3030.

Credit 3 units. A&S IQ: NSM, AN

Typical periods offered: Fall, Spring

SDS 2900 Directed Research in Statistics and Data Science

Introduces first-years and sophomores to research by engaging them in ongoing faculty research projects within the department. Under the direction of a faculty mentor, students take part in tasks that contribute to the mentor's research. Through this hands-on experience, students learn about the research process and build foundational research skills that can benefit their future academic experience and development. Faculty mentors provide regular guidance, training, and feedback to support students' understanding and growth. Students are registered by the department after approval from the faculty member leading the research project. The course may be taken for 1-3 credit hours based on the weekly hours required. Pass/No Pass only

Credit 1-3 units.

Typical periods offered: Fall, Spring

SDS 3020 Elementary to Intermediate Statistics and Data Analysis

An introduction to probability and statistics. Major topics include elementary probability, special distributions, experimental design, exploratory data analysis, estimation of mean and proportion, hypothesis testing and confidence, regression, and analysis of variance. Emphasis is placed on development of statistical reasoning, basic analytic skills, and critical thinking in empirical research studies. The use of the statistical software R is integrated into lectures and weekly assignments. Required for students pursuing a major or minor in statistics or wishing to take 4000 level or above statistics courses.Though Math 2130 is not essential, it is recommended.

Credit 3 units. A&S IQ: NSM, AN

Typical periods offered: Fall, Spring

SDS 3030 Statistics for Data Science I

This course starts with an introduction to R that will be used to study and explore various features of data sets and summarize important features using R graphical tools. It also aims to provide theoretical tools to understand randomness through elementary probability and probability laws governing random variables and their interactions. It integrates analytical and computational tools to investigate statistical distributional properties of complex functions of data. The course lays the foundation for statistical inference and covers important estimation techniques and their properties. It also provides an introduction to more complex statistical inference concepts involving testing of hypotheses and interval estimation. Required for students pursuing a major in Data Science. Prerequisite: Please check the eligibility rules. No prior knowledge of Statistics is required. NOTE: SDS 3030 (Math/SDS 3211) and SDS 3020 (Math/SDS 3200) can not both count towards any major or minor in the Statistics and Data Science Department.

Credit 3 units. A&S IQ: NSM, AN

Typical periods offered: Fall, Spring

SDS 3110 Biostatistics

A second course in elementary statistics with applications to life sciences and medicine. Review of basic statistics using biological and medical examples. New topics include incidence and prevalence, medical diagnosis, sensitivity and specificity, Bayes' rule, decision making, maximum likelihood, logistic regression, ROC curves and survival analysis. 

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 3111 Applied Linear Modeling

This course is an introduction to applied linear regression and analysis of variance. The course will cover simple linear regression, multiple linear regression, and simple experimental design. Emphasis will be placed on estimating, interpreting, and using statistical inference to answer scientific questions. This course is intended for students who would like to further their statistical knowledge past the level of introductory statistics, but without pursuing a statistics or data science major. This course will count as an elective for the minor in statistics, but not for the majors in statistics or data science. Statistics and data science majors should take SDS 439.

Credit 3 units. A&S IQ: NSM, AN

Typical periods offered: Fall

SDS 3115 Introduction to Computing For Statistical Sciences

This course is first course in computing using statistical software.
Topics covered include loading and modifying data, writing functions, and iteration. Emphasis
will be placed on data cleaning and data visualization. Students will be able to solve
practical problems using software. No previous experience with statistical software is required.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 3996 Statistics and Data Science Elective: 300-Level

Credit 3 units.

SDS 4000 Undergraduate Independent Study

 This course is for independent study. Approval of instructor required.

Credit 3 units.

Typical periods offered: Fall

SDS 4008 Nonparametric Statistics

Statistical methods that make few or no assumptions about the data distribution. Permutation tests of different types; nonparametric confidence intervals and correlation coefficients; jackknife and bootstrap resampling; nonparametric regressions. If there is time, topics chosen from density estimation and kernel regression. Short computer programs will be written in a language like R or C.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 4010 Probability

Mathematical theory and application of probability at the advanced undergraduate level; a calculus based introduction to probability theory. Topics include the computational basics of probability theory, combinatorial methods, conditional probability including Bayes' theorem, random variables and distributions, expectations and moments, the classical distributions, and the central limit theorem. permission of the instructor.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall, Spring

SDS 4020 Mathematical Statistics

Theory of estimation, minimum variance and unbiased estimators, maximum likelihood theory, Bayesian estimation, prior and posterior distributions, confidence intervals for general estimators, standard estimators and distributions such as the Student-t and F-distribution from a more advanced viewpoint, hypothesis testing, the Neymann-Pearson Lemma (about best possible tests), linear models, and other topics as time permits.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

SDS 4030 Statistics for Data Science II

This builds on the foundation from the first course (SDS 3030) and further develops the theory of statistical hypotheses testing. It also covers advanced computer intensive statistical methods, such as the Bootstrap, that will make extensive use of R. The emphasis of the course is to expose students to modern statistical modeling tools beyond linear models that allow for flexible and tractable interaction among response variables and covariates/feature sets. Statistical modeling and analysis of real datasets is a key component of the course. Prerequisites: Please see eligibility rules.

Credit 3 units. A&S IQ: NSM, AN

Typical periods offered: Fall, Spring

SDS 4070 Stochastic Processes

Content varies with each offering of the course. Past offerings have included such topics as random walks, Markov chains, Gaussian processes, empirical processes, Markov jump processes, and a short introduction to martingales, Brownian motion and stochastic integrals.

Credit 3 units. A&S IQ: NSM Art: NSM

Typical periods offered: Spring

SDS 4110 Experimental Design

A first course in the design and analysis of experiments, from the point of view of regression. Factorial, randomized block, split-plot, Latin square, and similar design.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

SDS 4120 Survival Analysis

Life table analysis and testing, mortality and failure rates, Kaplan-Meier or product-limit estimators, hypothesis testing and estimation in the presence of random arrivals and departures, and the Cox proportional hazards model. Techniques of survival analysis are used in medical research, industrial planning and the insurance industry.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

SDS 4130 Linear Statistical Models

Theory and practice of linear regression, analysis of variance (ANOVA) and their extensions, including testing, estimation, confidence interval procedures, modeling, regression diagnostics and plots, polynomial regression, collinearity and confounding, model selection, geometry of least squares, etc. The theory will be approached mainly from the frequentist perspective and use of the computer (mostly R) to analyze data will be emphasized. Prerequisite: Please see eligibility rules. If SDS 3030 (Math/SDS 3211) is taken, SDS 4010 (Math/SDS 493) is not required.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall, Spring

SDS 4135 Applied Statistics Practicum

This course develops critical thinking, practical data analysis skills, and effective communication by working on a series of data analysis projects. For each project, the instructor will give an introduction to the dataset and the desired outcome of the data analysis, along with a review of statistical methodology appropriate to each project. Students will be expected to produce written reports and give oral presentations for each project. The course will also cover how to collaborate on a data science project and produce information-rich data visualizations. We will also cover a number of practical skills for data analysis, including command line tools, version control, and reproducibility.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall, Spring

SDS 4140 Advanced Linear Statistical Models

Review of basic linear models relevant for the course; generalized linear models including logistic and Poisson regression (heterogeneous variance structure, quasilikelihood); linear mixed-effects models (estimation of variance components, maximum likelihood estimation, restricted maximum likelihood, generalized estimating equations), generalized linear mixed-effects models for discrete data, models for longitudinal data, optional multivariate models as time permits. The computer software R will be used for examples and homework problems. Implementation in SAS will be mentioned for several specialized models. Prerequisites: Math/SDS 439 and a course in linear algebra (such as Math 309 or 429).

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 4155 Time Series Analysis

Time series data types; autocorrelation; stationarity and nonstationarity; autoregressive moving average models; model selection methods; bootstrap condence intervals; trend and seasonality; forecasting; nonlinear time series; filtering and smoothing; autoregressive conditional heteroscedasticity models; multivariate time series; vector autoregression; frequency domain; spectral density; state-space models; Kalman filter. Emphasis on real-world applications and data analysis using statistical software.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

SDS 4210 Statistical Computation

Introduction to modern computational statistics. Pseudo-random number generators; inverse transform and rejection sampling. Monte Carlo approximation. Nonparametric bootstrap procedures for bias and variance estimation; bootstrap confidence intervals. Markov chain Monte Carlo methods; Gibbs and Metropolis-Hastings sampling; tuning and convergence diagnostics. Cross-validation. Time permitting, optional topics include numerical analysis in R, density estimation, permutation tests, subsampling, and graphical models. Prior knowledge of R at the level used in Math 494 is required. Acquaintance with fundamentals of programming in R is helpful.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

SDS 4215 Python for Data Science

Python has become the most popular programming language for data science and competency in Python is a critical skill for students interested in this area. This course introduces Python within the context of the closely related areas of statistics and data science. Topics include syntax and capabilities of Python, introduction to Spyder IDE and Jupyter notebooks, data wrangling using pandas library (cleaning, merging, reshaping, and summarizing/aggregating data), SQL databases, writing basic functions (handling missing data and common data cleaning tasks within the pandas framework), data visualization using Seaborn and Matplotlib, Statistical modeling with statsmodels, Machine learning with SKLearn (Tree Based Methods, Ensemble, SVM), Unsupervised Machine Learning with SkLearn (Clustering, K-means, Dimension Reduction, Principal Component Analysis), Introduction to NumPy, and Basics of Neural Network and PyTorch.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 4310 Bayesian Statistics

Introduces the Bayesian approach to statistical inference for data analysis in a variety of applications. Topics include: comparison of Bayesian and frequentist methods, Bayesian model specification, choice of priors, computational methods such as rejection sampling, and stochastic simulation (Markov chain Monte Carlo), empirical Bayes method, hands-on Bayesian data analysis using appropriate software.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 4425 Data Mining Methods and Applications

Data mining is the process of uncovering meaningful patterns and making predictions from data, often in large and complex datasets. This course provides both a practical and theoretical foundation in data mining, emphasizing computational techniques and statistical reasoning. Students will explore supervised and unsupervised learning methods, applying them to real-world datasets across different domains. The course balances conceptual understanding with hands-on programming, ensuring students grasp both the principles behind data mining algorithms and their implementation. Topics covered include essential data mining techniques, such as information retrieval and similarity measures, dimensionality reduction (PCA, MDS, Isomap, UMAP), clustering (k-means, hierarchical clustering), regression (linear regression, ridge regression, lasso), and classification (KNN, LDA, QDA, decision trees). Additional topics, including advanced clustering methods, ensemble learning techniques (bagging, boosting, random forests), and artificial neural networks, may be covered as time permits.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

SDS 4430 Statistical Learning

A modern course in multivariate statistics. Elements of classical multivariate analysis as needed, including multivariate normal and Wishart distributions. Clustering; principal component analysis. Model selection and evaluation; prediction error; variable selection; stepwise regression; regularized regression. Cross-validation. Classification; linear discriminant analysis. Tree-based methods. Time permitting, optional topics may include nonparametric density estimation, multivariate regression, support vector machines, and random forests.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 4440 Mathematical Foundations of Data Science

Mathematical foundations of data science. Core topics include: Probability in high dimensions; curses and blessings of dimensionality; concentration of measure; matrix concentration inequalities. Essentials of random matrix theory. Randomized numerical linear algebra. Data clustering. Depending on time and interests, additional topics will be chosen from: Compressive sensing; efficient acquisition of data; sparsity; low-rank matrix recovery. Divide, conquer and combine methods. Elements of topological data analysis; point cloud; Cech complex; persistent homology. Selected aspects of high- dimensional computational geometry and dimension reduction; embeddings; Johnson-Lindenstrauss; sketching; random projections. Diffusion maps; manifold learning; intrinsic geometry of massive data sets. Optimization and stochastic gradient descent. Random graphs and complex networks. Combinatorial group testing. A willingness to learn new mathematics as needed is essential.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Spring

SDS 4480 Topics in Statistics

Novel scientific discoveries are made nowadays by analyzing increasingly large and noisy biological datasets thanks to next-generation high-throughput technology. Machine learning methods which have been developed to extract complex patterns from image, text and speech datasets are now regularly being utilized to investigate conjectures in biology and medicine. The goal of this course will be to review some key concepts and methods in statistical learning and apply these to biological datasets. The course's focus is on the methods and applications rather than the theory and is intended for a broad audience. We will first explore predictive algorithms which perform classification and regression based on training datasets, such as logistic regression, decision trees, random forests, boosting, naive Bayes classifiers, Gaussian process regression, linear discriminant analysis and support vector machines. As much as time allows it, we will then review clustering algorithms and dimensionality reduction techniques used to identify patterns in large-scale biological datasets, such as hierarchical clustering, mixture models and principal component analysis.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall

SDS 4481 Special Topics in Statistics and Data Science: An Introduction in Python

At the end of the course, students will have a solid grasp of Python programming basics and have been exposed to the entire data science workflow. This includes interacting with SQL databases to query and retrieve data, through to data wrangling, reshaping, summarizing, analyzing and ultimately reporting results.The course will introduce and use popular Python libraries such as pandas, numpy, seaborn and matplotlib and use the Jupyter notebooks framework for coding. "Special Topics in Statistics and Data Science" is a variable-credit course that covers computational/practical methods or tools of broad interests in Statistics and Data Science. The title of the course will change from semester to semester.

Credit 1.5 units.

Typical periods offered: Spring

SDS 4482 Topics in Statistics

Topic changes each semester.

Credit 3 units. A&S IQ: NSM

Typical periods offered: Fall, Spring

SDS 4971 Topics in Statistics: Data Mining

Data mining is the process of uncovering meaningful patterns and making predictions from data, often in large and complex datasets. This course provides both a practical and theoretical foundation in data mining, emphasizing computational techniques and statistical reasoning. Students will explore supervised and unsupervised learning methods, applying them to real-world datasets across different domains. The course balances conceptual understanding with hands-on programming, ensuring students grasp both the principles behind data mining algorithms and their implementation. Topics covered include essential data mining techniques, such as information retrieval and similarity measures, dimensionality reduction (PCA, MDS, Isomap, UMAP), clustering (k-means, hierarchical clustering), regression (linear regression, ridge regression, lasso), and classification (KNN, LDA, QDA, decision trees). Additional topics, including advanced clustering methods, ensemble learning techniques (bagging, boosting, random forests), and artificial neural networks, may be covered as time permits. All programming throughout the course will be conducted in Python.

Credit 3 units. A&S IQ: NSM Art: NSM

Typical periods offered: Fall

SDS 4990 Study for Honors

Senior standing, a distinguished performance in upper level statistics courses, and permission of the Chair of the Undergraduate Committee. Register for the section (listed in department header) corresponding to your honors project supervisor.

Credit 3 units.

Typical periods offered: Fall, Spring

SDS 4996 Statistics and Data Science Elective: 400-Level

Credit 3 units.