Level of mathematics required for STs

[Gamma.alpha.lambda]

Hi,

What is the level of mathematics required for tackling each ST subject?

What textbooks are available to get one to the appropriate level? I'd like to use ones where there are questions and fully worked out solutions.

Does the Foundation ActEd Pack cover the mathematics for the STs?

I have only completed courses in Calculus, Advance Calculus, Linear Algebra, Real Analysis and Differential Equations. Calculus was a one year course and the rest were one semester. Besides calculus, the other courses used notes of about 80-100 pages instead of textbooks. We used Stewert Calculus: Concepts and Contexts for Calculus and AC.

I don't really feel like I understood the Analysis course when compared to how natural concepts from the CTs feel after Q&A Bank, Series X Assignments and seven or so past papers.

The mathematics in the core technical exams is all right for me.

Thanks in advance

 

[morrisja]

I assume by saying the maths in the CTs is fine that you've taken and passed these exams or at least reached a standard where you could take and pass them (through exemption courses).

If that's the case then based on my experience (currently studying ST2), you'll find the maths is on roughly the same level, just there is a lot less of it. Despite being a Specialist "Technical" subject, the emphasis is not on maths.

For ST2, if you were very comfortable with CT5 you'll find that the maths in the questions is not challenging. Calculation questions aren't even guaranteed to come up in a paper. It's much more based on the technical concepts of the specialist area. I think it's more comparable to CA1 than to a CT subject. Possibly a blend of the 2 types of exam. But not nearly as torturous as CA1.

This may not be the case for all ST subjects, but I don't believe that any of them are particularly mathematical.

What ST(s) are you planning on sitting, possibly someone can give you more specific insight?

 

[Gamma.alpha.lambda]

Hi,

I have completed CT 1,2,3,4,7 - (2 and 7) through University.

I am writing CT6 and CT8 this exam period. I have finished the notes for these and CT5 and I am currently doing exam papers for 6 and 8 and have finished Q&A 1-5 plus series X assignments as practice. I will write CT5 and CA1 next period.

As far as STs go, I really would not like to get into health, life or pensions. Thinking about mortality scares me. I worked through the latter half of CT4 and through CT5 like I was reading a Stephen King novel.

So that leaves ST5-9 to choose from, I guess. What level would be required for these?

Incidentally, did you know you can purchase a life insurance policy to get your head/body preserved upon your legal death by a Cryonics company called Alcor?

There is also Initiative 2045 which aims to make tpx = 1 for all x,t element R-plus for a human (I'm not sure if this is really how to state it precisely). Basically a Russian Billionaire named Dmitry Itskov wrote an open letter to Forbes richest people in the world saying that the world needs to research indefinite life extension.

Let's get some theory developed on hedging mortality risk!

Sorry for going off topic.

 

[morrisja]

My first instinct is that the maths for any of these subjects will not be that difficult.I've got a friend who's taking ST7 and from what I gather the maths is no more difficult than anything you'd encounter in a CT. The difference really lies in the concepts that are explored and your ability to apply them to a situation.


Are you currently working in a particular sector of insurance? That would usually decide which STs you'll sit. I'm working in a life company so I have to sit ST2, but I've got options regarding the 2nd ST that I choose.


Regarding the off topic introduced, interesting ideas.. I had a bit to say on the potential impacts of indefinite life extension, but I'm not going to clog up your thread with an extended off topic essay..

 

[Gamma.alpha.lambda]

I'll make a thread for it now. I'm not working. I'm currently studying full time.

 

[Edwin]

Visit the ST6 forum. According to what I pick up, ST6 is the only highly 'technical-rigoros' ST.

 

[learner]

To anyone interested in fiction about death and alive to dead transitions I can suggest reading the following book.

Passage by Connie Willis: a review from Goodreads

"A tunnel, a light, a door. And beyond it ... the unimaginable.

Dr. Joanna Lander is a psychologist specializing in near-death experiences. She is about to get help from a new doctor with the power to give her the chance to get as close to death as anyone can.

A brilliant young neurologist, Dr. Richard Wright has come up with a way to manufacture the near-death experience using a psychoactive drug. Joanna’s first NDE is as fascinating as she imagined — so astounding that she knows she must go back, if only to find out why that place is so hauntingly familiar.

But each time Joanna goes under, her sense of dread begins to grow, because part of her already knows why the experience is so familiar, and why she has every reason to be afraid.

Yet just when Joanna thinks she understands, she’s in for the biggest surprise of all — a shattering scenario that will keep you feverishly reading until the final climactic page.
Paperback, 780 pages"

This is a good, possibly controversial, SF book and worth reading to the end, but it is rather too long. It tackles its subject (near death experiences) in some depth, and this is partly why it is difficult to read. It also provides food for thought for CT4 students: is alive -> dead the only finite state space for this process?

Alive is a transient state and dead a recurrent state. There is a unique stationary distribution. CT4 students must have a detached approach to the subject. This can come from prior training, for example in stochastic processes, applied probability or mathematics.

As far as the ST subjects are concerned, the Foundation Acted course (in the edition of it that I have) states that it covers all the mathematics required for the CT subjects. Therefore it may not cover some of the required mathematics for the STs. This is particularly relevant where material has recently been added to the examinations.

This could include GLMS and copulas in ST8. Background knowledge of measure-theoretic probability and Lebesgue's theory of integration could be useful for ST6. More generally a mathematics degree would be a useful background for ST6, and for some of the other STs. You need a strong mathematics background if you want to be an expert in advanced areas of financial mathematics.

 

[Gamma.alpha.lambda]

So the STs which require higher level mathematics are ST6, ST8 and ST9? The rest can be tackled with more or less CT level knowledge?

In light of the previous post, could the people who have completed a 4-year pure mathematics degree post the textbooks/reference books they used after second year during their undergraduate career? I'm assuming a masters in mathematics would be overkill for Actuarial and that CTs can be tackled with 2nd year mathematics knowledge.

Or if you can get it to textbooks that have mathematics that is more relevant for Actuarial purposes.

I mention textbooks because I really hate lecture notes especially the ones that just have "Definition 1.1 ... Proposition 1.2... Corollary 1.3... Lemma 1.4... ... Definition 10815.1..." with no explanations or examples and few questions . My dream mathematics textbooks would be set out like the combined materials packs we get for the CTs. Maybe ActEd should start publishing mathematics textbooks for undergraduates.

I will check out the book you recommended Learner.

With regards to alive->dead, the transition arrow is that inbetween state. It's the state that you occupy in an o(dt) period of time where you are niether alive nor dead. Well, that's my nonsense take on it. It's really hard to think of transition as instantaneous when it comes to time as time forms a continuum so how do you define the next "instant".

Check out and comment on the indefinite life extension thread under "General". Maybe the problem of mortality is meant to be solved by Actuaries since it is our thing.

 

[John Lee]

Maybe ActEd should start publishing mathematics textbooks for undergraduates.

This has been a dream of mine as I struggled at Uni with books that assume you understand and hence don't explain and then don't have solutions, only answers...to odd numbered questions.

However, after repeatedly approaching my university and offering to write them a textbook which will (shock! horror!) help students and let them have the profits from the sales for their Uni funds - the tutors have never even acknowledged my emails

 

[td290]

I can speak from experience of ST7 and ST8. My gut feeling, based on the courses you say you've completed, is that you're most of the way there already. Nothing from these subjects reaches the level of rigour and difficulty of the Analysis courses I did at university. The one potential concern is that you don't mention having done any statistics courses. But to be honest, even that isn't going to hold you back much since the way the statistical techniques are introduced in the course notes assumes very little prior knowledge, and what they do assume could be gathered just by looking at A-Level textbooks, which are generally quite user friendly.

 

[Gamma.alpha.lambda]

Well, for Calculus, Stewert is awesome and you can buy the solutions manual.

For Linear Algebra there is Anton, Elementary Linear Algebra, which has a solutions manual.

For differential equations there is Boyce Elementary differential equations, again, with a solutions manual.

These cover up to second year maths and in my opinion, Universities should adopt them as a standard and tell students to buy the solutions. The books are quite comprehensive.

The real problem is Real Analysis. It's a hard course to understand even at an introductory level. In my course, we got 36 questions from tutorials. There were a few exercises in the printed notes and a few extra problems but alas, no solutions and no textbook. Relevent past papers were hard to come by since there was a syllabus change that year. So, I feel like I know nothing from the course even though I passed it. I did learn how to prove zero is less than one from it though.

I can only imagine higher level maths textbooks go into the realm of the obscure with very little reinforcement of concepts.

 

[John Lee]

But to be honest, even that isn't going to hold you back much since the way the statistical techniques are introduced in the course notes assumes very little prior knowledge, and what they do assume could be gathered just by looking at A-Level textbooks, which are generally quite user friendly.

You've got to mention my StatsPack

It's so much better than A level textbooks (I know I was an A level teacher and
have looked at all the textbooks) I do say so myself...