About The Course
In this class, I will explain the concepts of convergence and talk about topology. You will understand the difference between strong convergence and weak convergence. You will also see how these two concepts can be used.
You will learn about different types of spaces including metric spaces, Banach Spaces, Hilbert Spaces and what property can be expected. You will see beautiful lemmas and theorems such as Riesz and LaxMilgram and I will also describe Lp spaces, Sobolev spaces and provide a few details about PDEs, or Partial Differential Equations.
Frequently Asked Questions

Will I get a Statement of Accomplishment after completing this class?
Yes. Students who successfully complete the class will receive a Statement of Accomplishment signed by the instructor. 
What resources will I need for this class?
For this course, all you need is an Internet connection and the time to view the videos, understand the material, discuss the material with fellow classmates, take the quizzes and solve the problems. 
What pedagogy will be used?
This MOOC is in English but the math will be taught with a "French Touch". 
What does "teaching math with a French touch" mean?
France has a longstanding tradition where math is addressed from a theoretical standpoint and studied for its implicit value throughout high school and preparatory school for the highlevel entrance exams. This leads to a mindset based on proofs and abstraction. This mindset has consequences on problem solving that is sometimes referred to as the “French Engineer”. In contrast, other countries have a tradition where math is addressed as a computation tool. 
Does it mean it will abstract and complicated?
The approach will be rather abstract but I will be sure to emphasize the concepts over the technicalities. Above all, my aim is to help you understand the material and the beauty behind it.
Recommended Background
Because this is an online class, having advanced and nonadvanced students in a class will not be a problem; on the contrary we expect a wide range of interesting interactions. However, nonadvanced students may have to work a bit more.