MATH584B
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MATH584B - Theoretical Foundations of Applied Mathematics II
Course ID
041864
Course Description
Measure theory: Lebesque measures; Lebesgue Integral; Convergence theorems; Product measures; Differentiation.
Probability: Random numbers; Probability; Moments; Generating function; Independence; Law of large numbers; Central Limit Theorem; Large Deviation. Foundations of information theory: Multivariate distributions; Marginalization; Conditioning; Bayes theorem; Entropy; mutual information, comparison of probabilities; Shannon Theorem.
Markov Chains: Transition probabilities; Steady-State Analysis; Perron-Frobenius theorem. Fourier Analysis: Fourier series and convergence; applications to PDEs. Other topics as chosen by the instructor.
Probability: Random numbers; Probability; Moments; Generating function; Independence; Law of large numbers; Central Limit Theorem; Large Deviation. Foundations of information theory: Multivariate distributions; Marginalization; Conditioning; Bayes theorem; Entropy; mutual information, comparison of probabilities; Shannon Theorem.
Markov Chains: Transition probabilities; Steady-State Analysis; Perron-Frobenius theorem. Fourier Analysis: Fourier series and convergence; applications to PDEs. Other topics as chosen by the instructor.
Min Units
3
Max Units
3
Repeatable for Credit
No
Grading Basis
GRD - Regular Grades A, B, C, D, E
Career
Graduate
Course Attributes
CE - CL (Cross Listed), GIDP - APPL (Applied Mathematics)
Course Requisites
Math 584A
Cross Listed Courses
May be convened with
Component
Lecture
Optional Component
No