Lecture Time and Office Hours
About the Course
The Riemann integral poor convergence properties make it unsuitable for applications in probability, functional analysis and PDEs. A much more convenient and flexible theory was devised by Lebesgue at the beginning of the 20th century. In this course we will introduce Lebesgue integration theory and explore its applications to Lp spaces and related topics. This course is designed for students with a strong interest in real analysis and its applications to fields like probability, statistics, economics, functional analysis and PDEs among others.
The course will be based on the book "The Elements of Integration and Lebesgue Measure" by Robert Bartle. As complementary books, we will use "Real Analysis" by Halsey Royden and "Real Analysis: Modern Techniques and Applications" by Gerald Folland.
There will be a preliminary exam on Wednesday October 9th during lecture time, and a final exam on Thursday December 19th from 9:00-11:30 am at Malott 206. You will not be allowed to bring notes to any of the exams.
There will be a weekly homework to be handed in every Wednesday during lecture time. The homework with the lower score will be dropped before computing your final grade. You can check the homework for this week by clicking the appropriate link on the left or, if you are still reading this, you can just click here.
Final grades will be calculated either by using the formula:
20% Homework + 40% Preliminary Exam + 40% Final Exam
or the formula:
10% Homework + 30% Preliminary Exam + 60% Final Exam.
But don't worry, you don't have to choose. I will calculate both grades at the end and assign you the better one. Letter grades will be curved.