UCB MFE UCB MFE Pre-program 2017 Participation!

Hello guys,

Even though deadline rounds were due, the application window is still open through November. Good luck to all still-applicants!
I am not applying to the UCB program coming-up Spring 2017, but I will take 1 of 3 pre-program courses; I intend to take only the math course. Purpose is to see myself if I am able to fit the top MFE programs like UCB.

About me:
status: international student
undergrad: Finance and Math (in a regular college in the U.S.)
work experience: (1) after graduation, I went back to my home country and worked for commercial banking industry, mainly on building scorecards both for retail and corporate portfolios, and also managing credit portfolios, and followed Basel II guideline. It's how I exposed myself to quanty problems in the real world about 1.6 years. They were pretty much all about lending industry, but involved some little-investment concepts along the way.
(2) then I have currently been a math-tutor for a college for a year or so now, teaching calculus, linear algebra and stuff like that.

I will only take the math course but this thread opened up is for discussion among all 3 pre-programs before they get started in 2017 January. Have you guys looked over their syllabus? Omg, they are so rigorous and intensive!

I will start my view first.
I founds 2 old threads which are very helpful and closest the most on talking about the pre-courses.

1. https://www.quantnet.com/threads/ucb-pre-program-review.8410/
the guy named Sky seemed to express a lot of troubles and unhappiness to the whole courses.

2. https://www.quantnet.com/threads/need-preparation-advice-for-a-mfe-program.6713/
A guy asked for the prep advice for the whole program.

I will take the course offsite so I am aware of all the technical issues and disadvantages. The homework will be asked to deliver by Latex. Even though I know Latex in fundamental level, that would be quiet troublesome if you have no familiarity with Latex at all.

My main concern is to handle the papers. There are 9 papers handed out in the math syllabus. I have looked over all of them and wow they are tough to dig in.
I think the hardest one is 4. Ross (2014) - The recovery theorem.
1. Pratt (1964) and 2. Lamont and Thaler (2003) are pretty lengthy and full of finance terms.
The easiest one can read by oneself, I think, would be 3. Litterman (1991); it is short and required not much math.
5. Nash (1952) is brutal too. I have learned some Game Theory but not non co-operative games like this. The symbols and mathematical notations in the paper are just insane in the paper.
8. Black and Scholes (1973) and 9. Cox (1979) are the two concentrated on topic of option-pricing. I haven't touched any of them.

Do all of course attendants suppose to understand all of papers by reading them thoroughly; knowing the essence of the paper, know what they are talking about in the middle of papers. They are a lot of smart folks out there can figure these things out by themselves but I doubt there is an one single person can understand all those paper by just reading them without having discussion and prod talk with others.
Guys, so nobody has any comments on the content of the syllabus.

Anyone knows what role spectral theory and stochastic matrix plays for MFE as the two topics are mentioned in the syllabus. You know, to study the whole theory is pretty broad and pure-mathematics.

Do anyone know why they mention spectral theory and stochastic matrix? for what financial applications?