MATHEMATICAL METHODS IN DATA SCIENCE

Prerequisites & course information

Requisites: ( MATH 320 , 340 , 341 , 345 , or 375 ) and ( STAT/MATH 309 , 431 , MATH 531 , or STAT 311 ) and ( MATH 322 , 341 , 375 , 421 , or 467 , or COMP SCI 577 ), graduate/professional standing, or declared in Mathematics VISP (graduate or undergraduate) Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. State and calculate eigenvalue, singular value and QR decompositions and apply them to data science techniques such as spectral clustering, principal components analysis and least-squares problems. Audience: Both Grad & Undergrad 2. State and derive properties of multivariate normal distributions and apply them to data science problems based on Gaussian models such as mixtures of Gaussians and Gaussian graphical models. Audience: Both Grad & Undergrad 3. Formulate certain machine learning and statistics problems as optimization problems, solve these problems using simple optimization algorithms such as first-order methods and state results about the convergence of these algorithms. Audience: Both Grad & Undergrad 4. State and derive basic properties of finite Markov chain models and apply them to data science techniques such as Markov chain Monte Carlo. Audience: Both Grad & Undergrad 5. Construct proofs of simple theorems in matrix factorizations, Gaussian modeling, optimization theory, and finite Markov chains. Audience: Both Grad & Undergrad 6. Implement data science methods based on matrix factorizations, Gaussian modeling, optimization theory, and finite Markov chains in a programming language such as Python. Audience: Both Grad & Undergrad 7. Identify and use course content in the context of current/modern research in mathematics and data science. Audience: Graduate Learning Outcomes: 1. State and calculate eigenvalue, singular value and QR decompositions and apply them to data science techniques such as spectral clustering, principal components analysis and least-squares problems. Audience: Both Grad & Undergrad 2. State and derive properties of multivariate normal distributions and apply them to data science problems based on Gaussian models such as mixtures of Gaussians and Gaussian graphical models. Audience: Both Grad & Undergrad 3. Formulate certain machine learning and statistics problems as optimization problems, solve these problems using simple optimization algorithms such as first-order methods and state results about the convergence of these algorithms. Audience: Both Grad & Undergrad 4. State and derive basic properties of finite Markov chain models and apply them to data science techniques such as Markov chain Monte Carlo. Audience: Both Grad & Undergrad 5. Construct proofs of simple theorems in matrix factorizations, Gaussian modeling, optimization theory, and finite Markov chains. Audience: Both Grad & Undergrad 6. Implement data science methods based on matrix factorizations, Gaussian modeling, optimization theory, and finite Markov chains in a programming language such as Python. Audience: Both Grad & Undergrad 7. Identify and use course content in the context of current/modern research in mathematics and data science. Audience: Graduate