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Underground > Laboratory >

(Re)learning Math(s)

  
 
Saturn's nod
21:21 / 30.04.06
I'm starting to realise it would be useful to have more math(s) and statistical methods in my brain for the research I do. It's been several years since my undergrad math(s) course, and I find that I have only hazy memories. I look at an expression in a paper, and think 'well, I know I used to know what that means.'

So anyway, I want to rejuvenate my maths brain. Preferably, I want to have as much statistics and calculus available in mind as in a typical maths undergraduate course. I have some decent textbooks, so I guess one answer here is, well, get on with it, start work: set up some regular appointment with myself, and start wading though the textbooks. But maybe there's a smarter way to go about it. What kind of research is there about relearning - or indeed about learning - stats and calculus? Anyone have experience to offer of how they regained mathematical competence after a couple of years away from formal math(s) courses, or otherwise learned advanced maths outside formal classss?
 
 
nameinuse
19:52 / 01.05.06
If you want fun, or at least more captivating than dry formulae, have a look at gambling and game theory (great for stats and interesting psycholoy), or take a reasonably cursory (as it's a deep subject and a means to an end in this context) look at quantum mechanics and group theory.

Maths can describe pretty much everything you'd want to look at, just choose something you'd like to know more about and look at it from a numerical angle. Personally I'd use gambling theory as a very good way to get into stats.

Calculus, on the other hand, is something I've not found much use for aside from deriving equations in physics (and therefore no use in the rest of my life). Find someone who speaks fluent maths and chat to them for a while - skill swap or something - and see what you pick up that way.
 
 
Quantum
18:58 / 02.05.06
Probability in Feynmann diagrams. Seriously, look into the math of Quantum Physics and after a short time calculus and trig will seem easy.

More helpfully, as you re-read old material it will all come flooding back, ancient portions of your brain will fire up, cough out dust and come out calculating. At least, that's what my Psychology lecturer said.
 
 
ngsq12
12:48 / 17.05.06
I recommend the book "Mathematics From the Birth of Numbers" by Jan Gullberg (ISBN:0-393-04002-X). A superb encyclopedia on the subject and it's the same size as the terrifying "The Road to Reality" by Roger Penrose(ISBN:0-224-04447-8). I get to about chapter six and than my brain melts. Great diagrams though, many of them look like magical sigils or something.

I am in a slightly different position. I love the subject but have had no thorough grounding in it. I suspect I may always be a layman (sob).
 
 
Lurid Archive
14:18 / 17.05.06
I feel that I should really have something to say about this, but I'm not sure I can be much help. There is a point where you really do have to buckle down and learn the stuff. That said, the point of it all can get lost in the tricky details, which can be a barrier to some people. In the end, though, the feeling of elation when you understand something is well worth it.
 
 
Red Concrete
09:10 / 18.05.06
What kind of research do you do? I imagine statistics would be more useful to you than maths - unless you really want to know maths...

I moved from wet lab-based training to a maths/stats posstdoc in the past year, and I'd say necessity was the driving force. There are probably plenty of introductory textbooks in maths/stats aimed people in your field. You'll probably find that you remember or intuitively know a lot of what you learn...

I've found it gets easier to dive into a new subject and learn it well, as I get older. There's nothing like maturity for motivation.

Also, do you program? Try writing a couple of small C, or perl, or shell scripts to simulate something you're working on. Really basic, so you don't get bogged down. You might find that mathematical or statistical questions occur to you that you can then read into, or test yourself.
 
 
Saturn's nod
12:11 / 19.05.06
Which discipline did you do your doctorate in, Red Concrete? I'm interested in those transitions, as I'm planning for my postdoc movements and might be going the same way: environmental microbiology in my case towards maths/stats.

Thanks for all the good ideas. The bits of maths I'm reading are in genetics/bioinformatics/computational biology. I'm currently interested in distance measures for nucleotide sequence comparisons, so e.g. stuff like the Gonnet matrix, and what I'd really like is to get myself into a position where I can push that kind of thing forward rather than just making use of what statisticians not trained in biology have developed. So it's more the need for refamiliarity with matrix notation than actual calculus - I guess I said calculus because I remember that notation from tensor calculus, tensors being so much fun that they stuck in my mind! (Although, I'm convinced that e.g. eigenvector/harmonic solutions stuff has more potential use in biology/ecology than just the various multivariate analysis systems for plucking signal out of noise, but that could just be me.)

Game theory is core evolutionary/ecological biology, so that would indeed be a good starting point: at the moment I'm pondering about starting with what could be called the foundational text of genetics or even of mathematical biology: R. A. Fisher's 1930 work The Genetical Theory of Natural Selection. I could let the demands of that read drive my maths relearning.

I like the suggestion about simulations: I have done some simulation programming before (a population genetics sim in Java for an undergrad project). Especially, sounds like it will be good for stats - I could write a function in Excel & then can make nice graphs when I've generated the distribution. Although maybe something other software - what's the Open Office spreadsheet app like? - since I've mainly got access to unix machines at present.

I have my copy of Riley Hobson & Bence (2002) Mathematical methods for physics and engineering, which was the core text of my second year undergrad maths course: it's a 1200+ page weight of text, but has the advantage of covering everything I already know I need to know.

I have been wondering about trying to start a maths club at work - maybe there are other researchers who want to meet up for e.g. 2 hours once a week, just to sit together in the same room and work on maths, maybe to swap notes and help each other out.

And, ngsq12: I would say don't let a lack of formal training put you off doing maths. I think maths is one of those things, unlike biology (all that hefty lab equipment slows the curve!), that it's possible to develop genuine competence in, informally. An evening class might help get you started, but if you have the desire, there's no reason not to become mathematically competent. Especially since I think it's clear that the current styles of formal maths teaching don't suit everyone's way of learning. I've heard that there are lots of people around who could be very talented with mathematical concepts but have been put off at some early stage because mathematical teaching in schools didn't suit them.
 
 
ngsq12
18:30 / 21.05.06
Thankyou for your words of encouragement.
 
 
Red Concrete
19:34 / 21.05.06
Saturn's nod, I'm also in genetics, but not bioinformatics. Started in biochemistry, then my PhD was molecular genetics: mostly gene mapping using linkage and association studies - what they used to call reverse genetics. It wasn't a lab with great (or any) stats experience or expertise, so I had to teach myself.

I wouldn't really recommend Excel for simulations - that said, I did all my simulations for my PhD in Excel... The 256-column limit can be frustrating, it's pretty slow, and the files are huge when they start filling up with data. I've never used Open Office enough to know what their spreadsheet is like. Have you ever used R? It's pretty popular, and I hear very good for plots and graphics once you get to know it. Perl of course is very popular in bioinformatics, but for real speed use C/++.
 
  
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