This course continues the content covered in 18.100 Analysis I. Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and the other half to Fourier series and Fourier integrals. Topics covered in this course such as coin Tossing, Law of Large Numbers, Rademacher Functions, Measure Theory, Random Model, Boolean Rings, Lebesgue Spaces, Measurable Functions and Lebesgue Integral.
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
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Course Credit: MIT
|lec1 Coin Tossing, Law of Large Numbers, Rademacher Functions||00:20:00|
|lec2 Measure Theory, Random Models||00:15:00|
|lec3 Lebesgue Spaces, Inner Products||00:25:00|
|lec4 Hilbert Space, Midterm Review||00:30:00|
|lec5 Fourier Series and their Convergence1||00:30:00|
|lec6 Fourier Series and their Convergence 2||00:20:00|
|lec7 Applications of Fourier Series||00:30:00|
|lec8 Fourier Integrals||00:20:00|
|lec9 Fourier Integrals of Measures, Central Limit Theorem||00:30:00|
|lec10 Brownian Motion||00:35:00|
|Submit Your Assignment||00:00:00|
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