Greetings Quantum Formalists!
I am busily preparing for the start of our upcoming lecture series on Measure Theory and Functional Analysis, and in doing so want to provide you with a list of prerequisite information that would be helpful for you to get the most from the lessons. I would recommend seeking a copy of “Understanding Analysis” by Stephen Abbott (second edition). In general, reading Chapter 1, sections 2-5 will cover all the basics one would need. To provide a more specific list of topics, I’d look at:
Section 1.2
Sets
Functions
Example 1.2.5 (Triangle Inequality)
Logic and Proofs
Theorem 1.2.6
Induction
Section 1.3
Definition 1.3.1, 1.3.2 (Least Upper Bound/Greatest Lower Bound)
Lemma 1.3.8
Section 1.4
Theorem 1.4.3 (Density of the rationals in the reals) and Corollary 1.4.4
Section 1.5
Cardinality, Countable and Uncountable Sets
Definition 1.5.5, Theorem 1.5.6, Theorem 1.5.8.
For those who cannot easily access the book, you can still find the topics well explained on the web, and should seek out refreshers on at least sets/least upper bounds/greatest lower bounds/countable and uncountable. I will touch on these topics during the lectures as the need arises so if you do not currently have the time, worry not!
We will be holding a live Q&A session on August 20th at 11:00am Eastern time. You can register via https://www.crowdcast.io/c/mtfa-questions-and-answers.
Best,
James