Foundations of Data Science

Units: 3

Estimation and testing in full and non-full rank linear models. Normal theory distributional properties. Least squares principle and the Gauss-Markov theorem. Estimability, analysis of variance and co variance in a unified manner. Practical model-building in linear regression including residual analysis, regression diagnostics, and variable selection. Emphasis on use of the computer to apply methods with data sets. Credit not given for both ST 705 and ST 503. Note: this course will be offered in person [Spring] and online [Summer].

Offered in Spring and Summer

Units: 3

Course covers basic methods for summarizing and describing data, accounting for variability in data, and techniques for inference. Topics include basic exploratory data analysis, probability distributions, confidence intervals, hypothesis testing, and regression analysis. This is a calculus-based course. Statistical software is used; however, there is no lab associated with the course. Credit not given for this course and ST 511 or ST 513 or ST 515. This course does NOT count as an elective towards a degree or a minor in Statistics. Note: the course will be offered in person [Fall] and online [Fall and Summer].

Offered in Fall and Summer

Units: 3

Vector spaces, linear transformations and matrices, orthogonality, orthogonal transformations with emphasis on rotations and reflections, matrix norms, projectors, least squares, generalized inverses, definite matrices, singular values.

Offered in Fall and Spring

Units: 3

Introduction to uncertainty quantification for physical and biological models. Parameter selection techniques, Bayesian model calibration, propagation of uncertainties, surrogate model construction, local and global sensitivity analysis.

Offered in Fall and Spring

YEAR: Offered Alternate Even Years

Units: 3

Convex optimization methods and their applications in various areas of data science including, but not limited to, signal and image processing, inverse problems, statistical data analysis, machine learning and classification. Basic theory, algorithm design and concrete applications.

Offered in Fall Only

Units: 3

Algorithm design techniques: use of data structures, divide and conquer, dynamic programming, greedy techniques, local and global search. Complexity and analysis of algorithms: asymptotic analysis, worst case and average case, recurrences, lower bounds, NP-completeness. Algorithms for classical problems including sorting, searching and graph problems [connectivity, shortest paths, minimum spanning trees].

Offered in Fall Spring Summer

Units: 3

Advanced database concepts. Logical organization of databases: the entity-relationship model; the relational data model and its languages. Functional dependencies and normal forms. Design, implementation, and optimization of query languages; security and integrity, consurrency control, transaction processing, and distributed database systems.

Offered in Fall and Spring

Units: 3

This course will introduce common statistical learning methods for supervised and unsupervised predictive learning in both the regression and classification settings. Topics covered will include linear and polynomial regression, logistic regression and discriminant analysis, cross-validation and the bootstrap, model selection and regularization methods, splines and generalized additive models, principal components, hierarchical clustering, nearest neighbor, kernel, and tree-based methods, ensemble methods, boosting, and support-vector machines.

Offered in Summer

Units: 3

This course provides an introduction to concepts and methods for extracting knowledge or other useful forms of information from data. This activity, also known under names including data mining, knowledge discovery, and exploratory data analysis, plays an important role in modern science, engineering, medicine, business, and government. Students will apply supervised and unsupervised automated learning methods to extract patterns, make predictions and identify groups from data. Students will also learn about the overall process of data collection and analysis that provides the setting for knowledge discovery, and concomitant issues of privacy and security. Examples and projects introduce the students to application areas including electronic commerce, information security, biology, and medicine. Students cannot get credit for both CSC 422 and CSC 522.

Offered in Fall and Spring