MATH 205 A Real Analysis
Autumn 2019
Lectures: TTh 9:00-10:20, 300-300
Instructor: Eugenia Malinnikova
Office: 383 Y
Office hours: T 3:30-5:30 pm, W 4:30-5:30 or by appointment
Course Assistant: Joey Zou
Office: 381 A
Office hours: T 12:30-1:30 pm and F 3:00-4:00 pm
Textbook and Course material
Folland, Real Analysis, Modern techniques and their applications, chapters 1-3, 6-8, part of 10
Lecture notes, by L. Ryzhik
Midterm and Final Exam
In class midterm, October 24
Final, Wednesday, December 11, 8:30-11:30 am
Homework
Weekly homework assignments are due each Thursday, the first one is due September 3rd. There will be 8 assignments during the quarter.
Assignment 1 (due 10/03) Assignment 5 (due 11/07)
Assignment 2 (due 10/10) Assignment 6 (due 11/14)
Assignment 3 (due 10/17) Assignment 7 (due 11/21)
Assignment 4 (due 10/24) Assignment 8 (due 12/05)
Final exam will consist of 7-8 problems and all but one will be either from homework assignments or from the list of 30 problems below.
Preliminary lecture plan:
Week 1: Sigma-algebras, measures, outer measures, Borel measures on the real line, Folland chapter 1 (Homework 1, due 10/3) Lecture notes (Lectures 1-3)
Week 2: Lebsegue measure, measurable functions, modes of convergence, Folland 1.5, 2.1, 2.4 (Homework 2 due 10/10)
Week 3: Integration, Product measures and integration, Folland 2.2-2.3, 2.5-2.6 Lecture notes (Lectures 4-6)
(Homework 3 due 10/17)
Week 4: Signed measures and Radon-Nidokym theorem, Differentiation in Euclidean space, Folland 3.1-3.2, 3.4 (Homework 4 due 10/24) Lecture notes (Lectures 7-10)
Week 5: Functions of bounded variation, absolutely continuous functions, (Folland 3.5) Repetition and Midterm
Week 6: Lebesgue spaces, introduction, Folland 6.1 (Homework 5, due 11/7) Lecture notes (Lecture 11-15)
Week 7: Lebesgue spaces, duality, Folland 6.2-6.4 (Homework 6, due 11/14)
Week 8: Interpolation theorems, applications, Folland 6.5 (Homework 7, due 11/21)
Week 9: Riesz representation theorem, Fourier transform, Folland 7.1,8.1 (Homework 8, due 12/5) Lecture notes (Lecture 16-17)
Week 10: Fourier transform and Fourier series, Folland 8.2-8.4