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MATH6625 - Measure and Integration

Course Name: 
Measure and Integration
Course Code: 
MATH6625
Course Credits: 
4
Level: 
Graduate
Prerequisites: 
None
Course Description: 

We consider the limitations of the Riemann integral, and show that it is necessary to develop a precise mathematical notion of `length' and `area' in order to overcome them. Thus we develop the more abstract concept of measure, and use it to construct the more Lebesgue integral, and to investigate its properties. Finally we look at the role played by measure and Lebesgue integration in modern probability theory. This course is intended to develop the ability of students to work with abstract ideas.

 

Content: 
Introduction to Riemann Integral; Lebesgue Measure; Measurable functions; The Lebesgue integral; Applications to probability theory
Assessment: 
The course assessment has two components consisting of coursework (40%) and a final exam (60%): One in-course test – 20% of overall grade One Written assignment – 20% of overall grade; Final exam – 60% of overall grade
Categoryofcourses: 
Typeofcourse: 
Core Courses
coursedegree: 
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