Basic Information
Set Theory# Cardinality of Sets. Topological Tools# Open/closed Sets, Interior, Closure and Boundary of Sets, Convexity, Convex Hull Of Sets, Compact Spaces, Weak Topology. Metric Spaces# Compactness, Cauchy Sequences and Completeness. Measure Theory and Functional Analysis# -algebras. Borel Sets, Lebesgue Measure and Integral. Jensen S Inequality, Radon Nikodym Derivative and Conditional Expectation, Types of Convergence, Lp Spaces, Hilbert Spaces, Fourier Transform and Characteristic Functions. Learning Outcomes# At The End of The Class Students Would# 1. Be Able to Use Measure Theoretic Tools to Solve Problems In Problems Arising in Data Science Such As High Dimensional Probability And Statistics, Convex Optimization and Random Matrices. 2. Be Able to Model Conditioning On Random Information.
Faculty: Data and Decision Sciences
|Undergraduate Studies
|Graduate Studies
Pre-required courses
(94345 - Discrete Mathematics (for I.e) and 104032 - Calculus 2m and 104166 - Algebra Am) or (94345 - Discrete Mathematics (for I.e) and 104016 - Algebra 1/extended and 104022 - Differential and Integral Calculus 2m) or (94347 - Discrete Mathematics and 104016 - Algebra 1/extended and 104022 - Differential and Integral Calculus 2m)