MATH 403
Measure and Ergodic Theory Fall 2024
Division III Quantitative/Formal Reasoning

Class Details

An introduction to measure theory and ergodic theory. Measure theory is a generalization of the notion of length and area, and has been used in the study of stochastic (probabilistic) systems. The course covers the construction of Lebesque and Borel measures, measurable functions, and Lebesque integration. Ergodic theory studies the probabilistic behavior of dynamical systems as they evolve through time, and is based on measure theory. The course will cover basic notions, such as ergodic transformations, weak mixing, mixing, Bernoulli transformations, and transformations admitting and not admitting an invariant measure. There will be an emphasis on specific examples such as group rotations, the binary odometer transformations, and rank-one constructions. The Ergodic Theorem will also be covered, and will be used to illustrate notions and theorems from measure theory.
The Class: Format: lecture
Limit: 25
Expected: 15-20
Class#: 1453
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation: Homework and exams
Prerequisites: MATH 350 or MATH 351 or permission of instructor
Enrollment Preferences: Mathematics majors
Unit Notes: senior major course
Distributions: Division III Quantitative/Formal Reasoning
QFR Notes: It is an advanced mathematics course.

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