This course introduces students to fundamental concepts and theorems in probability theory. Students will learn basic methods of counting, including permutations, combinations, and multinomial coefficients. Students will develop a deep understanding of probability, including conditional probabilities and Bayes’ Theorem. They will learn about probability distributions, highlighting many distributions that appear frequently in real-world problems, including the normal, binomial, Poisson, and exponential distributions. They will additionally learn mathematical tools for working with and describing probability distributions in general, including deriving expectations, variances, and covariances. Students will be introduced to the Central Limit Theorem.
Emphasis will be placed on concepts, derivations, and problem solving. Applications to business and to data analytics will be highlighted. Students will develop a deep understanding of the fundamentals of probability so as to develop the tools to approach novel problems and/or methodologies in their future careers.
This course introduces students to concepts and theorems in statistical theory. Building off of both their introductory statistics background and MATH 5111, we will examine the theoretical underpinnings of standard statistical tools to develop both a deeper understanding of these tools and an ability to work beyond the limitations of standard tools when necessary. Examples will emphasize potential applications to business and data analytics.
Students will study a variety of aspects of statistical estimation, beginning with principles of maximum likelihood estimation and confidence intervals, and then examining properties of statistical estimators such as sufficiency and consistency. Bayesian estimation will be discussed, and contrasted with traditional estimation in terms of both theory and practical use. Hypothesis testing will be examined from the principle of likelihood ratios - examples will focus on inferences about means, variances, proportions, and differences in means and proportions, while emphasizing the ability to generalize these tools to novel problems as well.
A survey of discrete modeling techniques used in data analysis. Topics covered include: propositional logic; set theory; algorithms; relations; finite state machines; graph theory.
Practical work in data science and analytics depends on efficient access to data from a variety of sources. This course will examine typical corporate data architectures with data warehouses that include both structured and unstructured data. Common storage techniques (including cloud) and retrieval strategies will be included. Advanced SQL, NoSQL, data cleaning, and ETL will also be covered. A start-to-finish implementation of a data warehouse will be developed by student project teams.
Prerequisites: BUAN 5305 or DATA 5212