This course introduces the mathematical background necessary to understand, design, and effectively deploy AI systems. It focuses on four key areas of mathematics: (1) linear algebra, which enables describing, storing, analyzing and manipulating large-scale data; (2) optimization theory, which provides a framework for training AI systems; (3) probability and statistics, which underpin many machine learning algorithms and systems; and (4) numerical analysis, which illuminates the behavior of mathematical and statistical algorithms when implemented on computers.

This course introduces students to Visual Analytics, or the science of analytical reasoning facilitated by interactive visual interfaces. Course lectures, reading assignments, and practical lab experiences will cover a mix of theoretical and technical Visual Analytics topics. Topics include analytical reasoning, human cognition and perception of visual information, visual representation and interaction technologies, data representation and transformation, production, presentation, and dissemination of analytic process results, and Visual Analytic case studies and applications. Furthermore, students will learn relevant Visual Analytics research trends such as Space, Time, and Multivariate Analytics and Extreme Scale Visual Analytics.

This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications.