Hello Quantum Formalists,
I'm delighted to announce that the start date for the long-due course on Measure Theory & Functional Analysis will be on Monday, August 29! I'll be doing my best to wrap up the group theory crash course by the latest first week of September!
New Course Format: We have decided to change the course format to help speed up the delivery. So instead of the current biweekly live lecture approach, we'll have the following:
Each Monday, we'll release a pre-recorded lecture on a playlist on our YouTube channel. Soon after, we'll upload the problem sheet to our GitHub repo. We'll try to stick to 2 - 3 problems per lecture!
At weekends, we'll host a live discussion forum about the previous lecture and the homework problems. We'll also upload the solutions to the problem sheet a few hours later.
Course Coverage: This 22-lecture course will start with a review of Calculus & Real Analysis, particularly integration theory. It is desirable that you still review some basics of calculus and analysis before showing up! We'll recommend refresher materials on the course's Discord channel over the coming days.
After the review above, we'll move on to topics such as; Measurable Functions, integration of non-negative functions, Monotone/Dominated convergence theorem, Fubini-Tonelli, Lebesgue Integrals vs Riemann Integrals.
Afterwards, we'll move on to topics such as; Normed Vector Spaces, Linear Functionals, Open Mapping Theorem, Topological Vector Spaces and then Hilbert Spaces.
Course Lecturer: We've drafted our good friend James Heffers to deliver this course. James is a Postdoctoral Assistant Professor at the University of Michigan who specialises in Several Complex Variables / Pluripotential Theory.
Community Initiative Scaling: This course is the beginning of our goal to scale our community initiatives, which means we'll have more courses running in parallel & delivered by multiple mathematicians.
Backseat Role: Due to my regular work commitments, I'll take more of a backseat role. However, I'll still work on the curriculum structure for all the upcoming courses. I'll also try to do occasional guest appearances on the applied side of each course, i.e. to show you how the abstract stuff you've just learned is being used!
Finally, please feel free to share the course registration https://www.quantumformalism.com/measure-theory-and-functional-analysis with anyone who may benefit from it. The mathematical topics covered will be helpful to those interested in 'Continuous Variable Quantum Information' and Machine Learning.
Happy rest of the week!
Bambordé