- #1
thrillhouse86
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Hi All, I am a new phd student in engineering, working in signals analysis in neuroscience who seems to be doing a lot of work in statistics and probability theory. My uni is offering a course in measure theory. The course profile says:
"The course is an introduction to measure theory and Lebesgue integral. A sound knowledge of measure theory and the Lebesgue integral is a starting point to undertake advanced studies in partial differential equations, nonlinear analysis, the calculus of variations and probability theory."
The outcomes of the course are stated as:
"1 Appreciate the central role of sigma-algebras and measure in integration theory;
2 Work with measurable functions and understand their importance to the definition of the integral;
3 Work with the properties of the Lebesgue integral;
4 Generate measures including Stieltjes measures;
5 Use the relationship between the Riemann and Lebesgue integrals on the real line;
6 Understand the relationship between of functions of bounded variation and absolute continuity and the role they play in fundamental theorem of integral calculus;
7 Decompose measures and appreciate the role this decomposition plays in the Radon-Nikodym & Riesz representation theorems;
8 Gain a working knowledge of function spaces and modes of convergence;
9 Work with the integral on product spaces using the relationship with repeated integrals;
10 Apply results from integration theory to other areas of mathematics."
Given that I am not a pure mathematician would it be worth doing this course?
"The course is an introduction to measure theory and Lebesgue integral. A sound knowledge of measure theory and the Lebesgue integral is a starting point to undertake advanced studies in partial differential equations, nonlinear analysis, the calculus of variations and probability theory."
The outcomes of the course are stated as:
"1 Appreciate the central role of sigma-algebras and measure in integration theory;
2 Work with measurable functions and understand their importance to the definition of the integral;
3 Work with the properties of the Lebesgue integral;
4 Generate measures including Stieltjes measures;
5 Use the relationship between the Riemann and Lebesgue integrals on the real line;
6 Understand the relationship between of functions of bounded variation and absolute continuity and the role they play in fundamental theorem of integral calculus;
7 Decompose measures and appreciate the role this decomposition plays in the Radon-Nikodym & Riesz representation theorems;
8 Gain a working knowledge of function spaces and modes of convergence;
9 Work with the integral on product spaces using the relationship with repeated integrals;
10 Apply results from integration theory to other areas of mathematics."
Given that I am not a pure mathematician would it be worth doing this course?