Pure or Applied maths with stats

[3.141592]

Hi all,

This post will be long, but I hope in giving more relevant information, the replies will be more helpful. Apologies for the length, and thanks for reading, given now. I'll state the question here though to avoid you having to search for it:

Does it make any real difference whether one takes either applied maths or pure maths, with statistics at undergraduate level, if there is no interest in a PhD in either?

I have a BSc and an MA in philosophy. I love it and wanted to do a PhD in it and get a uni job. This was my single-minded dream. But the state of uni employment has gotten worse, especially for lots of arts and humanities subjects, since my undergrad ended in 2008. I've decided it's not worth the sacrifice.

Studying philosophy meant mathematical logic. I enjoyed it and did well. This led me to start a part-time degree in mathematics and statistics in 2009. I had to stop for my philosophy MA but am now studying it again. My goal is to become a professional statistician. Almost certainly in medical statistics or public health as, of stat jobs, this seems to fit best with my several motivations (increase store of human knowledge; expose charlatans who peddle fear and prey on people with health problems and surplus cash; help finding effective treatments/interventions for diseases; a good work-life balance (I would never, ever, ever want some 70+hour a week, every week, with long commute, weekend working, staying away, on-call at 3am job)). Of course I will take whatever stepping-stone job I can get right now that will help down the line when I am more qualified.

(I know a master's is required for many stats jobs in this field and I have been encouraged by a top uni here to apply for a 1-year course in maths/stats for semi-numerate graduates to gain access to their MSc Statistics. But I feel I need more of my current undergrad courses to make sure I pass this access intensive crash course. Only 65% or above guarantees an MSc place. And it's all far more expensive than my current undergrad institution.)

In this undergraduate I am currently on, either track covers the same maths content up to the second year. I am completing my first 100 of 360 credits (unless I transfer elsewhere for the MSc).

Pure track then covers: formal proof, abstract structures, linear algebra, analysis, group theory.

Applied track covers: differential equations, linear algebra, vector calculus.

I can only pick one.

If it is relevant, almost the entire final year is statistics. 1/4 is applied probability. 1/4 is linear modelling. 1/4 is mathematical statistics. The last quarter would be the same on either track - I would pick a course on applied discrete mathematics.

Also covered in the second year are: multivariate statistics, time series, Bayesian inference, and medical statistics.

I include this content as it is probably relevant regarding my question. You can see all but one stats module is applied. And being 28, in massive student debt, two degrees for an aborted career, living with parents, no car (can't afford driving lessons even), no savings and working in a supermarket at night, stacking shelves, I made a deal with myself: I must study something I enjoy, but it must be a powerful aid to my CV and lead to a fulfilling and financially comfortable career. Not necessarily 6 figures, but certainly halfway there after a decade at least. This all makes me think I should pick applied maths. Statistical jobs in industry are, after all, applied. And I need the step from study to work to be as small and swift as possible.

But, for what it's worth, I do not like calculus (I know this is in both tracks but it appears there is less in the pure track), and did really enjoy mathematical logic during philosophy, so that makes me think pure.

Sorry again for such a long post. I really have no time or money now to waste on fascinating but only useful-in-periphery subjects (I know, 'unreasonable effectiveness of mathematics', 'logical thinking is always useful etc. etc.) but by the same token I do not want to slog through a track I do not enjoy so much - which is how the applied track appears to me - if it is not much more beneficial to my goal of becoming a professional statistician.

Thankyou so much in advance.

 

[MarneMath]

I feel the need to say this, but your philosophy major shows (so many needless words in this post!). Secondly, isn't it obvious? If you want to be a profession statistician, then you should go for the route that requires more stats. If you plan to go to graduate school, then take a course or two in analysis because you'll beed it for graduate level probability theory.

Honestly, there is probably more calculus in the pure course than the applied. While the applied route may use more techniques, have fun learning all about calculus again from a more 'mature' perspective.

 

[3.141592]

It's not obvious: neither track requires more stats than the other. The stats is exactly the same regardless. That's why I posted the topics listed for each track, in case one who knows more about them than me can say if stats is involved, directly related etc.

Analysis is in the pure track so that's a tick for that route; thanks.

 

[MarneMath]

If that's the case it doesn't really matter now does it? Without knowing what kind of flexibility or courses are in each track, then you're asking for some very vague opinions. At my university, the difference between applied and pure was a required abstract algebra course and a required second analysis course. Other than that you had a somewhat free reign of electives. So therefore, I could've done a complete applied track, and still take analysis.

So here's some vague advice. What matters most, if you plan for a career in stat, is NOT your ability to work with a subharmonic function on a Riemann manifold, it's about your ability to translate real world data into reasonable conclusions. This involves a lot of programing (know R and SAS) and a lot of numerical analysis.

Will you use vector calculus? Probably not. Will you set up a differential equation. Probably not. Will you use linear algebra? All the time. Will you use measure theory probability after grad school? Probably not. Will you use a hidden markov? Probably not. What you do in the real world is rather basic, especially at the entry level.

 

[3.141592]

I'm not being funny and I don't mean to seem rude, but I honestly don't know if it "doesn't really matter now does it?"; that's why I asked.

I have not worked as a medical statistician and do not know any. I have not covered mathematics beyond first-year undergraduate. I am only starting second-year statistics now.

The statistics track would be the same if I chose a joint degree with computing and not mathematics. Whether or not mathematics or computing is more or less relevant to a professional medical statistician is a question that matters to one faced with that choice of subject given said aim. Said aim is my aim and my choice is between pure or applied maths. I hope anyone with experience or knowledge can advise.

I listed the topics in my first post but here is the blurb from the course catalogue if it is of any use to anyone:

"Pure: Group Theory explores sets of mathematical objects that can be combined – such as numbers, which can be added or multiplied, or rotations and reflections of a shape, which can be performed in succession. Linear Algebra explores 2- and 3-dimensional space and systems of linear equations, and develops themes arising from the links between these topics. Analysis, the foundation of calculus, covers operations such as differentiation and integration, arising from infinite limiting processes.

Applied: This course covers classical mechanical models as well as some non-mechanical models such as population dynamics; and methods including vector algebra, differential equations, calculus (including several variables and vector calculus), matrices, methods for three-dimensional problems, and numerical methods. Teaching is supported and enhanced by use of a computer algebra package."

This is the total difference between my choices of pure and applied. The stats is identical in each track. The first year is identical in each and finished. The final year leaves one option for mathematics and I will pick the same either way. All I want to know is if there is much between the two choices I have listed for one who wishes to become a professional medical statistician down the line, and to work with data in some way before that happens.

From your posts I take it that you think not, and that real world statisics is basic, especially at entry level, so perhaps I should not worry. Thanks again for replying.

 

[chiro]

Hey 3.141592.

I would recommend doing the more applied subjects and do pure ones only that are necessary.

The reason is that the applied thinking is different from the pure thinking: two different skillsets that require different kinds of training and development.

Statisticians in a broad definition are professional advisors or advice consultants.

The mathematics is required since it is something that has been proven and is useful for a particular set of purposes, but statisticians are not mathematicians (pure) in the strictest sense: they are advisors.

People come to statisticians with questions about almost anything and the role of a statistician is to guide them through the process at all levels to help give the best answer possible to their question under uncertainty.

I would recommend you take a few programming courses as well.

 

[3.141592]

Hi Chiro,

Thanks for taking the time to reply.

That is something I had not considered re. the approach to the material. Good point. It did seem to me like applied was the natural option, but I know logic comes under pure and have enjoyed that; also, as I've said above, not knowing much maths, I don't know if it makes much difference to applied stats.

Yes I've seen a fair few adverts for statisticians citing programming skills required/desirable. Perhaps I'll have my logic cake after all!

Sadly, this (UK) university, like most UK ones, is much more restrictive in course choice than I understand e.g. US unis are, in relation to course choice. Without dropping the maths strand in favour of computing, there's no real scope for programming courses. Although it does teach use of at least 4 stats software packages so maybe that includes some programming? Failing that, I'm trying to teach myself some Python from a book.

Thanks again Chiro.

 

[chiro]

Also if you want to get into the statistical fields I'd recommend learning R which is free and is becoming one de-facto tool in statistical computation:

http://www.r-project.org/

 

[3.141592]

Brilliant - thanks!

 

[Shaun_W]

I cannot answer your question directly as it is not an area I am familiar with, however I think you are focusing too much on academics and not enough on what industry requirements might be. By that I mean: how does one actually land their first job in the career you are after? Is it via a graduate scheme or a do they go straight into a junior role?

If it is via a graduate scheme, what are the entry requirements? Many graduate schemes, even ones for highly numerical positions like actuaries, recruit from any degree discipline, and as such it might turn out that the difference between pure and applied maths in your case is purely academic. Also watch out for any UCAS points requirements, it'd be a mighty shame for you to spend thousands of pounds on a masters degree only to be automatically rejected from graduate schemes because you do not meet the required UCAS tariff points.

However if employees go straight into a junior role there might well be strict requirements on what is required academically to be considered. You'll have to find this out, and that will answer your question.

 

[3.141592]

Thankyou for replying. I am sure you are right that I should spend as much time on industry requirements as academics. To that effect, contrary as it may seem, I might switch out of my undergraduate in maths and stats, into an MSc in Medical Stats. Careers advice and many, many job searches over a couple of years suggest that to be a medical statistician one needs an MSc in Medical Stats. Almost never is a specific undergraduate degree or A-level subjects/grades specified. Good for me, because...

Most graduate schemes for numerical positions are closed to me because I do not have the requisite UCAS points. At 16, I was not serious about my education. It was only when I got into uni I worked hard. 12 years later I have a 2.1, and an MA at merit, and good grades for the first year of a maths and stats undergrad, and many years working in an office (showing I am reliable enough to hold a job and get on with colleagues) won't get them to even talk to me. Still paying for my youthful mistakes!

Thanks for your input.