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You couldn’t add it up.

I have a physics degree. My definition of “bad at math” is struggling with the derivative of a function of a function. Or let’s put it more bluntly – as an undergrad I never used a calculator in exams. It was all letters – mostly Greek but in some cases Hebrew. But apparently I am unusual. 49% of UK apparently adults can’t do sums. I wouldn’t even call it mathematics. Sums is not math. This is maths. Adding-up is not. Hell! When I was 16 I got a summer job in a sweet shop and people looked at me funny because I was quicker than the till. Still am and they still look at me funny and now I know why.

I mean for fuck’s sake! What sort of arseholes are we? The nation of Newton and Wren can’t hack this:

Hasran has planned a new TV cupboard. A TV is 40cm wide and will sit in the middle of a shelf that is 900mm wide. How wide is the gap on each side of the TV?

A: 10cm; B. 25cm; C. 43cm; D. 50cm

God fuck us all! Although what I’d like to know is why Hasran has built a 900mm TV cupboard for a 400mm TV? Why has he built a cupboard in the first anyway? My TV hangs on the wall. It’s hardly a secret passion is it? I mean when the Sky man came to upgrade our box to HD and all it wasn’t like I asked him to park round the back like an illegal abortionist was it?

Now here’s the real rub. Can they see through the Monty Hall veridical paradox? Because it took me two seconds. There were pure maths post-docs in the pub that evening tearing apart beer-mats to scribble on but I clocked it in the noggin in a witch-space second. A mere astrophysics student. And keen amateur poker player. BTW if you want a really good explanation of Monty Hall then this is the best I’ve read. Not a great book overall but that bit is gold. There is also a bit on bifurcation chaos theory and period-doubling which I can’t make my mind up about. It is either a brilliant portrayal of the longs and shorts of Asperger’s Syndrome or it is utterly wrong. And if the latter then it is possibly a satire. I have considered a post about it. Paul Marks would like what I had to say.

Anyway, I guess I just wrote the last paragraph because I wear my mathematical ability with pride. Apparently a lot of my country-folk are proud of their lack in that respect. Well, various people are proud of that. Lots apparently. I do not, as various researchers do, feel for the general economy. No! I just think they have missed out on the ravishing exceptional beauty of the very Queen of Science herself. As someone who has poked under her petticoats I can tell you they are missing a right treat. Now of course you could do “Modern Studies” at the “University” of Wolverhampton. You could do that but you could also rip the Universe apart and see how it ticks. I did. Your choice.

PS. I’m not sure Wolverhampton still does “Modern Studies” but a quick Google reveals it no longer does modern European languages. That is piss-poor.


  1. Roue le Jour says:

    Well, if you can’t do sums, you can’t check the government’s. Which I think is the point, really.

  2. Red Admiral says:

    Doing a milk round (pre-calculators) helped with the mental arithmetic but what really did it was scoring for the Dairy darts team. The slightest delay or error pounced on instantly. As a result, I’m still quite good 20 years on, if a bit traumatised.

  3. Lynne says:

    Maybe this will explain why. Nine years ago I received a phone call from my son’s then maths teacher (my son was 14 at the time). She was complaining that he hadn’t taken his calculator to class on the day of a test. Now I don’t happen to believe this was any kind of disaster because my son was taught the old fashioned way and he excelled at it. It was more interesting and hands on. He considered (and still does) using a calculator as cheating.

    I asked her how my son had performed on the test. He’d performed extremely well, as expected since maths, as well as science, are his strong points. So what was the problem? Well the problem was that the “test” was to prove that the kids could use their calculators. The teacher was complaining that my son was producing correct answers without a calculator!

    You could have knocked me backwards with a wet haddock. This was supposed to be a science and technology college FFS. I didn’t consider for a minute that the technology alluded to was a replacement for using grey matter. Not until I received that ‘phone call. How poor was the teaching standards if they needed to reinforce calculator skills?

    I was unsympathetic to the teacher’s plight, much to her annoyance. My son, when asked about the episode, said he purposely left his calculator at home to prove that using the instrument for such piddling problems was completely unnecessary. Even at such a tender age he could suss bullshit and considered the use of the calculator as a direct insult to his intelligence and ability (when he digs in he goes JCB). He explained this to the teacher but she didn’t have a tick box for such a left of field response. There was a time, in days long since gone, that he would have been complimented on his ability to calculate accurately without resorting to artificial means. Instead he was criticised for his non-conformist attitude. It seems that conformity to institutional ignorance is more important than harnessing and utilising actual knowledge. Social engineering anyone? My offspring was having none of it.

    Kids are taught to rely on calculators even for the most basic sums. Solid grounding in mental arithmetic has been side-lined, probably because it interferes with achieving “targets”. Parts of the GCSE maths exam allows for the use of calculators which is a disgrace. Is it any wonder that, in the absence of an electronic crutch, they stumble and fall?

  4. NickM says:

    Fascinating! Basically my understanding here is that there are school math exams which involve calculators and those that don’t and they can’t calibrate if rapscallions like your son “break the rules” because GCSEs and such are not at all about education but about grading.

    Now, my viewpoint is that calculators aren’t cheating as such. I have taught math and the biggest problem I had was the lack of algebra. So many kids can’t comprehend the basic issue which is to get the problem down and then put the numbers in. They want numbers in from the start. They don’t learn the general. You have to have the general before the specifics. I had a girlfriend once who was failing a physics degree badly. She never got the theory. She did “drill questions”. She never played with the equations. It’s the same thing as going route one with the numbers. Now one of the trickiest things in physics and something hammered home into me at Nottingham was order of magnitude and dimensional analysis. And that comes from – well, if you are asked to calculate a current and the result isn’t in Amps then it has gone seriously Pete Tong. Similarly if you work out the mass of the Earth in an astrophysics question as 3.6kg you have seriously gone wrong. My cat weighs 3.6 kg. But all these errors start at the start. They are to do with a lack of understanding and not a cock-up in the doing as such. Anyway, you son sounds a bright lad. Good on him. Of course another thing is he probs embarrassed teacher.

    You have to be able to guesstimate and that is mental arithmetic.

  5. As I spend a lot of my time doing posts on numbers and statistics (I hesitate to call it maths), I am not surprised at all.

    Most people refuse to accept certain basic published facts and to plus minus times divide and so on, after Xmas there is article after article saying e.g. “Britain’s households threw away £600 million’s worth of uneaten food” and I think, so what, that’s about £10 each, par for the course.

    Once you start on tax you might as well give up, people refuse to accept that we pay four times as much VAT as we pay in Council Tax, for example, despite this is a known fact.

  6. NickM says:

    If I recall you have a “magic fag packet”. God alone knows the quantity of furious smoking I have done over the A4 pad or keyboard. I’ll tell you something odd. You can do math too fast. When you are in the zone you get ahead of yourself and write utter gibberish. As to VAT. Well my most recent major purchase was a computer system and El Gove (or is that Gove?) got 200 quidlings from me. So yeah, I know. Here is a little known fact. I once had a water meter. Now VAT was charged on water supplied but not on sewage drained. I couldn’t have a glass of water without the HMRC getting their 17.5% cut. I could have a piss mind so that was OK. What sort of demented state taxes water?

  7. RAB says:

    God we are so fucked arn’t we? I answered all those questions correctly in about the same time it took to read them, and I’m sure almost all of my generation could.

    I’ve said it before and I’ll say it again, it was the abolition of the 11plus what done it. Now we can go into the merits of having to pass such a crucial exam at such a tender age some other time, but what having the exam did was concentrate the minds of junior school teachers wonderfully. All 11 years olds of my generation could read write and count. They may not all have been smart enough to pass it, but at least they could friggin read and understand it. Thet’s when the rot set in, and there’s no remedy in sight that I can see.

    A couple of years ago there was one of those reality programmes on the tellybox, which took today’s 15 year olds back to a Grammar School regime. These were all reckoned to be A and B grade students by the way. Well a lot of the prog was taken up with the social things like discipline and stuff, but about two weeks in to the experiment, they were given a Maths exam. The kids assumed that it was an old O Level paper. Only 3 out of 50 passed (all from private schools, Quelle Suprise!). But the exam wasn’t an old O level paper at all, it was an old 11 plus one.

    Nope we are fuckety fuck fucked folks!

  8. Sam Duncan says:

    “Can they see through the Monty Hall veridical paradox?”

    The nation that’s glued to Deal or No Deal? You even have to ask?

    I have to say, I’m not that good at mental arithmetic myself. I can do it (and am, at least, old enough to have been taught it at school) but not nearly as quicky or easily as I’d like. Which makes me the one-eyed man in the Kingdom of the Blind most of the time.

  9. NickM says:

    Ah but RAB. (a) the pass rate for the 11+ was determined by LEAs. It was very high in South Wales. That is not a critique of you BTW. Also my Mother-in-law failed her 11+ but passed at 13+ That is two bites of the cherry so why not? That is a reasonable system that takes into account we mature at different ages. Bear in mind the idea of school/college ’til 18/21 is relatively recent so why not? Or put it another way. I was 1/1 at my secondary school. That was 1 for maths and 1 for general. It went down to 7/7. My younger brother was 1/1 but that was (due to demographics) out of 9/9. Lordy were they something else! My Dad taught at a comp too and they graded differently – they had AS1-3, TC1-3 and G. AS – arts and sciences, TC – technical and commercial and G – general. The head even reffed the Gs as “The hewers of wood and drawers of water”. Can you believe that? Seeing as that was Saltwell in Gateshead he was probably right.

    But I do wonder. I mean at 11 I’m put in the top 7th twice (oddly enough I wind up at the University with most applications per place in the country – you might have a passing acquaintance with it RAB) and that is cool but what about Lee Eddy who was 7/7? Talk about destroying someone at the age of 11. Like I said there was no 13+ in my day and I guess the system was more didactic (Christ – I once saw the lower echelon GCSE maths papers and they were about telling the time on an analogue clock – and that is what is expected after 11 years of formal education!). Christ almighty we even had PE seperately. And yeah, seriously the upper sets were expected to play Rugby or Cricket and it was football and cross-country for the lower orders. Selected at 11. Now I’m not getting bleeding heart here because whilst the setting was interesting to say the least (and let’s speak bluntly here -class-based) the lower sets were generally vile. I hate to say that but it’s true. There were some appalling cock-ups (the school re-jiggled the setting system to cope with extra intake so my mate Paul was utterly arbitrarily dropped from Set 2 to set 4 – yes, really) but by and large the thickies were chucked into the outer darkness and there were some characters there.

    One of the most awesome scenes I ever saw involved a complete chinning. Now I’d had a fight with Nick. He was generally regarded as the hardest lad in the school but neither of us came out hurt (so I get respect – not least from Nick). I mean I never landed a meaningful blow on him but neither did he on me. I wouldn’t say we became pals as such after but we’d chat and stuff and he was a decent sort and I guess he thought I was too. But back to the awesome chinning. Nick was a hard fella and a decent sort but we also had scrotes. Nick sprinted for the County. He had a sports bag. Now this reprehensible cove called Hawthorne decided once out of sheer evil to urinate into Nick’s bag. I actually learned evil at school. Deranged, demented evil – the sheer devilment of it – there is no other explanation. Well, Nick was not a happy camper with having his sport’s kit pissed on so there follows the most rapid chinning in human history. To call it kinetic would be to disgracefully not use the word ballistic. I mean it was blink and it was gone. Hawthorne wound-up sitting on his copious arse 10 meters from where he started in a state of befuddlement and having lost all bladder control (which in the context was ironic – . I thought (a) Hawthorne got what he richly deserved (b) I’d had a fight with Nick but hey that was different – I mean that was honourable, no one lost control of basic bodily functions and we wound up after the end of school having chats in the pub). I guess because we were both ultimately decent folks. Hawthorne wasn’t. Well, of course he wasn’t! Pissing in a lad’s PE kit out of sheer deviation clearly isn’t the act of a man of honour or integrity but it was more than that. Hawthorne used to prowl the corridors as a general figure of menace. It is a peculiar thing but he thought himself “cool”. He squired a brace of lasses (one under each arm) and wore fake Raybans. He was a class act all round. He was a bust flush when several hundred of us saw him on his fat arse with a spreading dark patch around the gusset of his Farah slacks. He subsequently made a truly abysmal attempt to rape my (female) biology lab partner. He then received the second hardest twatting of his life. Yes, by her. He didn’t piss himself that time but he kept the faux Raybans on religiously for a while after. No way I would have messed with Sarah because she was a good friend and tat is wrong and (unlike Hawthorne) I knew she had a vicious right hook on her. Although does any of that matter really? Yeah, I fancied her but did that mean I would behave like an oaf around her? Of course not! I wanted her to like me not submit to me by force. An oaf like Hawthorne didn’t see it that way. I just got nowhere amiably – she once gave me her heart – well when the teach was out of the room we once hurled cow hearts at each other. But she was a fun lab partner. We were the two best biology students in the school and that was cool. Trust me on this. A good lab partner is diamonds.

  10. RAB says:

    Yes the 13+ thing was the way the system was supposed to work, to assist those kids who had not developed fully by 11.

    My best mate in Cathays, the luddite Hippie of La Honda (Nigel) as I call him here, had two best mates in Junior school who failed the 11+. Well when we became friends we all used to play together in Heath Park and got along famously. I never thought they were thicker than me or anything, quite the opposite. Anyway come aged 13 there they were in our school having been transferred from their Secondary Modern. Both went on to University, Roger for Chemistry and Neil for Economics, as did Nigel of course. He got 3 As at A level in an age when that was almost unheard of. One smart cookie my still oldest best friend, even though we rarely see each other as he lives outside San Francisco. Our old school sent at least half a dozen, sometimes up to ten, pupils to Oxbridge every year when we were there, leave alone the Russell Group ones. Now I am reliably informed, it sends none.

    All down to that idiological Labour asshole Crossland, with his rational take on Education reform…”If it’s the last thing I do, I’m going to destroy every fucking grammar school in England. And Wales and Northern Ireland”.

    Well done you cunt, you didn’t only destroy the Grammar Schools, but the entire educational foundation of this country!

    I have a post coming up Nick (when I can get the fuckin scanner working) of memories of my time at our old Alma Mater in the early 70s. Some great black and white pics of the destruction of the meadows etc.

  11. Thornavis says:

    Didn’t they operate a quota system with the 11+ ? If there were too many passes in a year the bar was raised and people who would have got through another time were failed or have I imagined that ? It must be true, there’s no other obvious explanation for my failing it. That failure split me from my closest friends, not that that’s an argument against the exam in itself but it’s a hard thing to do to eleven year olds.

  12. Thornavis says:

    I’ve never heard of that 13+ thing, we certainly didn’t have it at my school. I can think of a couple who would have passed it, not me though.

  13. RAB says:

    Didn’t they operate a quota system with the 11+ ?

    Well don’t they still? You are fitting pupils to the places available, not selecting on strict academic excellence alone. Can you imagine the mayhem and outrage if an Exam Board today (or anytime) failed the entire year of A level students as being not up to snuff?

  14. Ed P says:

    The 13+ was known previously as Common Entrance.

    My brother, a professor of physics at an American university, suffered a stroke ten years ago, losing his speech entirely. What’s perhaps of interest to you is that his early maths was wiped out too – times tables & basics – but not A-level & degree+ maths. So he had to learn to talk with a different part of his brain – successfully – but also practise “5 x 7 is 35″, etc. again, like a five-year-old!

  15. Kevin B says:

    My personal problem with the eleven plus was that once I’d passed it, that was me done with this education stuff. They put me in the A-stream doing latin and stuff ‘cos I was so brilliant, and by the end of the first term I was in the B stream and after two years I was in the D stream. I don’t know if it was something about growing up, or getting the bike, (Dad promised me a bike if I passed), but once the eleven plus was over, that was me done.

    Oh, I got a few O-levels, but it wasn’t till after I’d been to work, been in the RAF, and got a proper job that I finally wised up to the fact that I didn’t have as much education as I needed. Then it was day release, night school and an HND, (a qualification they could do with bringing back – and the way of achieving it), but at least when I was making my way, a degree wasn’t the be all and end all.

    Not that I’m dissing the eleven plus, just my reaction to it. That whole grammar school / secondary modern thing worked a lot better than the current comprehensive crap does.

  16. APL says:

    Just been for a job interview for a minimum wage position.

    Me 51 everyone else there, barely 25, I felt a right prat actually.

    Since this was a position in a bank call center, there were a few literacy and numeracy tests. Nothing too difficult, a few sentences giving one an opportunity to identify the difference between ‘there’ and ‘their’, that sort of thing, four sums testing the ability to add, subtract, multiply and divide (calculator provided) and one that asked the solution to 33% of a hundred, the female university student sitting next to me wrote 30.(She was quite fit actually, so could be forgiven much.)

    Well, I’ve never been much good at spelling and my arithmetic isn’t much cop either.

    The results of the tests, only one person got full marks.

  17. Stonyground says:

    I found the question to be piss easy but you do have to understand the metric system to work it out.

    There is an interesting comparison to be made between calculators and Sat-Navs. Old gits like me have had to find their way around using a road atlas. One method is to plan your route in advance and stick a list of road numbers and junction numbers to your dashboard. The last part of the journey is often the most difficult, involving the perusal of street maps and the interrogation of passing pedestrians.

    Sat-Navs are a totally superior way of finding your way around. My device directed me from a house near Hornsea to the front door of the Kings Hall in Ilkley totally without fuss (to see an ELP tribute if you must know). The thing calculates your journey time and gives an ETA which is always spot on. The problem of course is that future generations will be incapable of finding their way around without one.

  18. NickM says:

    I think metric. Now I’m not saying it is the vitals but it is how we measure. But I really think SI. I’m currently at 300K. Yes, I think in Kelvins.

  19. RAB says:

    Sat-Navs are a totally superior way of finding your way around.

    Um debatable Stoney, especially if they haven’t been updated properly. They can also be hilarious. The one we were using in Brittany last year, Ne Parle Francais. The mistranslations kept us chuckling for many a tedious mile. And there seemed to be an inordinate amount of roundabouts at crossroads that didn’t register on our Sat Nav (Got the whole quota for EU freebee road improvements in one short year obviously), and the ones that did, tediously kept saying ” Take second exit on right” which basically meant carry straight on.

  20. Nick M: “VAT was charged on water supplied but not on sewage drained. I couldn’t have a glass of water without the HMRC getting their 17.5% cut. I could have a piss mind so that was OK. What sort of demented state taxes water?”

    The volume of sewage they charge you for is exactly the same as the volume of fresh water they charge you for, so whether they apply VAT to the former or the latter makes no difference. And yes, you could piss without VAT, until it gets smelly and you flush.

    Actually, it doesn’t even make sense to charge separately for water supplied and sewage drained, does it?

    The VAT is meaningless, the main impact on water prices is OFWAT putting a cap on prices, so the government gives with one hand and takes with the other.

  21. Thornavis says:

    On the maths/arithmetic thing I was never any good at maths, just didn’t get it at all, which is something I’ve always regretted. OKish at arithmetic but what really taught me to add up and subtract was working as a bus conductor, although that missing 30 bob I had to pay back still rankles, I swear it wasn’t my error. Anyway this was pre-decimal and adding up pounds shillings and pence was a feat which I should imagine would be well beyond most school leavers today, I love the look of total incomprehension on the face of youngsters when I explain how the old money worked.

  22. macheath says:

    Remember the fuss over look-say versus phonics? Essentially the progressives had it that if you showed children whole words and sentences they would work out the basic phonic system for themselves.

    The same thing was applied to maths teaching in the early stages; instead of teaching the basic skills, then applying them to problems, the courses introduced problems from the start, assuming that children would deduce the basic principles from the way they arrived at the answer.

    In both cases, the brightest and most literate pupils will cope, while the rest need much careful explanation, interpretation and guidance to reach the desired conclusion. Unfortunately, at least where maths is concerned, this guidance is often provided by teachers and assistants whose own knowledge of the subject goes no further than the rudimentary requrements of a C at GCSE.

    Add to that the obligatory propaganda elements that over-elaborate the questions – healthy eating, public transport, gender equality and multiculturalism – and you have a recipe for confusion, compounded by the fact those people you describe as proud of their lack of mathematical ability ceaselessly proclaim it to all and sundry, including their impressionable offspring, perpetuating low expectations in the population as a whole.

  23. CJ Nerd says:

    While there’s a discussion in this general area, may I chuck in a request for advice?

    Can anyone recommend a suitable textbook/website with which to study maths for astronomy?

    I’m interested in taking a part-time astronomy course. It’s taught at undergraduate level, and carries half the credit of the first year of an undergraduate degree.

    Maths was my weakest subject at school. I ended up with O level grade Bs in Maths and Additional Maths, and A level Grade C in Physical Science (ie Physics and Chemistry). I then went on to a good language-based degree at an ancient university. All this was about 30 years ago.

    I fully recognise that astronomy is largely physics, and you can’t do physics without maths. I’m not asking for the course to be dumbed down for me; I’m keen to haul myself up to the level required. I’ve got about six months before the course starts.

    Any ideas where I could start? I’m already aware of this and plan to start working through it.


  24. bloke in spain says:

    Mmmmm. Mental arithmetic, or arithmetic for the mental.
    First job, before I saw the light & got a life, was on the Stock Exchange. That was in the pre-decimal days & when a desktop calculator was a box of cogs with a handle to turn. The firm’s newfangled computer occupied half an office block floor & could churn out portfolio valuations at a speed they could have used a monumental mason instead of a print head. Hence, most of the calculation was done in that region between the ears & below the hair. Did we really cope with 217 shares @ 176s9d? Or even worse, 3287@6s3 3/4d. Or gilts @ £99 17/64? Must have done because it was done & we were the people doing it.
    Later, in a more sensible life, served behind the bar in a busy village pub. Till was just a wooden thing with a lot of buttons & a big lever. Serious rounds as well. Half a dozen assorted beers & shorts & mixers for the wenches. Sometimes ordered all in one go. Othertimes as you served ‘em. Heaven help the barman who was a couple of pence out in the total though.
    Mental arithmetic’s as much memory as anything. I still know 100-n=? for every n between 1>99. Probably every addition of any two numbers between 1>99. Don’t actually have to calculate. I rarely get the decimal point in the wrong place, but then I know roughly what the answer is before I start.
    Gets problematic out in the real world, though. Sticking stuff on the belt at the supermarket checkout I probably know the price of each item to within a few cents & can total 40 of them, to within a couple of €uros, quicker than they can swipe them. Gets a little awkward when the total’s queried & the look of puzzlement when a recheck throws up the pack of coffee got run through twice. Like one’s a bit odd or something.
    But for maths, I’m hopeless. Didn’t even get to do the O-level, my mark on the mock was so poor. Just do what has to be done.

  25. Kevin B says:

    bis, I always prefered the guys who would order “three pints of Directors, a Brown and Mild, a pint of Harp for the weirdo and a G&T, a V&T, a Bacardi and coke and an Oranges and Lemons for the wife whose unhappy duty it is to drive us home”, rather than the “Pint of Bitter please.” “That’ll be one and eleven sir.” “Oh, and a pint of mild.” “That’ll be three and six”. “Oh and a half of lager”, “Oh and …”, “Oh and …”, “Oh and …”. For some reason I found that a pain in the arse.

    Mind you, they were better than the beardie weirdie declaiming “A pint of your best ale my good fellow!” who then spent the rest of the evening sipping said pint whilst loudly complaining that “You can’t get real ale any more”, and whingeing about the breweries.

  26. David Gillies says:

    Derivative of a function of a function, Nick. D’ye mean chain rule, dear boy? As in d/dx f(g(x) = f’(g(x))g’(x)?

    I reach my limit with things like algebraic geometry and the group-theoretic aspects of topology. I have a vague inkling of what a Lie algebra is but I get lost among all the homomorphisms and diffeomorphisms and fibrations and wedge products.

    CJ Nerd: it’s hard to recommend a textbook. You really need to know spherical trigonometry and things get complicated quite fast. If you can get visitor’s access to your local university library they will have a section.

  27. Roue le Jour says:

    For the record, the 11+ was merely the grammar school entrance exam. The more grammar school places in an education district, the lower the necessary pass mark. If I recall correctly, the range was something like the top 7% in deprived areas, but 17% in the leafy suburbs.

  28. NickM says:

    CJ Nerd,
    The first rule of astronomy club is to know that it’s hard. You seem to have got that one. O-Level B for undergrad level… OK, fine. Beyond that this is my advice. Get a buddy on the course. If poss one you can actually meet. I have met more students who failed (or did badly) due to not grokking what the course was really about than for any other reason. If you have a study partner on the same course you can more easily avoid going down blind alleys. I have known – and it’s truly tragic – loads of folks who spent enormous effort studying the wrong thing. The put the time in, just not wisely. That is why it is tragic. A for effort, D for results still means a D. Specifically maths for astronomy… I’d really need to see the syllabus but without that I can make some very broad (note that) recommendations. Get friendly with the Calculus. Learn it as a technique and don’t bother with the pure math stuff of limits etc. You can learn it “hot-wired”. Yes, it will cost you post-facto if you do postgrad stuff but for undergrad not knowing how it works in the engine room isn’t a problem. My Solar Systems Dynamics Lecturer told me something incredibly important about newtonian mech but that can wait. It could for me. Basically I’d answered a question wrong in my homework and I asked him about it. I wasn’t having a go or anything. I wanted to know. Why else was I doing an MSc at QMC if not to know? Anyway, how’s your algebra? That is like #2 after not grokking what the course is really about for fails from my experience. Don’t think numbers. Think concepts – think how they mesh and what they actually mean without the numbers applied. If you can understand you can calculate but it doesn’t go the other way round. As to a specific book or course… No idea. Broadly speaking astronomy is very classical unlike say Q-Mech or Solid State. I aced my last exams in those because the math is weird but a lot of my course-mates struggled. Astro is not like that. The math is not “sophisticated” – it’s just difficult. I mean you don’t get stuff in angle brackets – just nails calculus and algebra. I would suggest a book on engineering math. There are a lot available. Now a final thing. They are very thick tomes. Frequently this is because they are “programmed learning” so don’t let that intimidate you. They may have a lot of pages but it’s a lot of quickly worked through pages. It’s the slim volumes that state things like, “After some simple algebra we have equation 9.135″ that ought to scare. “Some simple algebra” means a bright student spends three hours and possibly hurls things out the window in frustration. The longer books take you more completely through the process. The thinner volumes might look easier but are much more of an exercise in saying, “I’m very clever, catch me if you can!” by the author.

    So an engineering math book should see you right. Worked for me!

  29. CountingCats says:

    CJ old fruit….

    Have a poke around this site:

    Swinburne University offers an online course, no physical presence necessary, in Astronomy leading to Certificate/Diploma/Masters. You can go to Phd if your fancy takes you. So just doing the half year you mentioned would result in a formal postgrad qualification, the Certificate.

    If your maths is a bit shakey, they recommend the following online catch up course:

    The courses may be based in the wonderful world of Oz, but who cares?

    James Cook University in Townsville also offer Astronomy Online.

    Then there is this, just down the road from me but in the hinterland:

    They actually let you take over some of their equipment remotely. Cool.

  30. RAB says:

    BIS, do you ever get what I do with youngsters behind check outs these days, if your purchase comes to £5.10p and the smallest note you have is £10, but you have change, and you say to them, I’ll give you the 10p shall I? And invariably they reply “Nah it’s ok the tenner is plenty sir”, and give you a funny look. They just do not understand that you are trying to help them, and without the computerised till telling them, they would have no chance of giving you the right change.

    A quick note on Private schools too. When we still had the 11+ and Grammars, there were a lot more small private schools about. They were usually 4th rate educationally and thrived because the parents of the kids who sent them to them, knew they would never pass the 11+ and so to avoid the stigma of going to a Secondary Modern, they went private. Consequently us Grammar school kiddies, far from thinking that Private school kids were rich and privileged, we thought they were obviously a bit thick, because why would you pay to educate your kids when you could get a first class one for free if you were smart enough to pass an exam?

    We used Pounds Shillings and Pence back then too, it’s complexity sharpened up your mental arithmetic no end. Will Ian B (yes that one) be along in a minute I wonder? ;-)

  31. CJ Nerd says:

    Hi Nick,
    Thank you very very much for this.

    The strategy advice makes a lot of sense- I wouldn’t have worked it out myself, but I can see the sense of it and it will save me a lot of wasted time. The bit about big step-by-step tomes versus slim ones with stuff left as “an exercise for the reader” will save me many hours of banging my head!

    I’m going to spend some time digging into the Swinburn and Unilearn sites, which looks very much like the sort to thing I need.

    The best idea I had before today was to go though a biography of Halley that I’m reading, pick out all the maths topics that were beyond me, and study them. Crude, and maybe not effective.

    Your responses have now given me a good idea of where to go and what steps to use to get there- much better!

    The course I’m planning is next year’s offering of this:

    I’ve had an email from the course administrator suggesting that I don’t need to worry too much about the mathematical content, but I think I’d be doing it with one hand behind my back if I want in with no preparation. I have six months before it starts, so I might as well do something that will help.

    Again, many many thanks

    Hi David,
    Good idea- I visit Cambridge’s Institute of Astronomy for public lectures every week, so I’ll ask them if I can access the library. Thanks for the idea. And yes, I do foresee some spherical trigonometry coming my way…

  32. Paul Marks says:

    It was not a maths question (even in the school definition of mathematics) – it was an observation question (English language comprehension style). The question really was “will you spot that we have switched from cm to mm?”

    The fact that they consider this a “maths” question speaks volumes.

  33. NickM says:

    CJ Nerd,
    Spherical trig will come your way with a vengeance. The Halley idea I don’t recommend. Simply speaking the reason geniuses were needed like Halley, Hooke, Newton and yet their works can be comprehended by the likes of me is the mathematical formalism has been simplified over the years so it has gone from being something that looks like a grimoire from Hogwarts to being something an UG like me can get a handle on. An example of this is Maxwell’s equations. As originally written down they are appalling and there are 30 odd of them. As used now they are four vector equations or one tensor equation. Now if you get the more sophisticated math involved it’s much easier to work with. My point here (and it remains that the majority of the math you will need to know is very classical) is that math is much easier these days. It has to be. We go farther than our forebears but we ain’t smarter. We can go further because it is simplified in the sense of worked out better over the years – or to quote Newton, we stand on the shoulders of giants. For example Richard Feynman didn’t win the Nobel for discovering anything per-se but for rebuilding Paul Dirac’s QED in a way that made it much easier to work with. So, my point is whilst the source texts might seem the obvious ones they really are digging up the Dead Sea Scrolls compared and trying to understand C1st AD compared to reading the NIV.

  34. Paul Marks says:

    By the way it is not a “two cultures” (arts and humanities versus mathematics and the physical sciences divide).

    For example, the powers that be tried to use multiple choice examinations for history.

    It is a subject that is wildly unsuitable for multiple choice based questions (for various reasons), but they did it anyway.

    It is not “just” a matter of the establishment not understanding mathematics – they do not understand any other subject either.

  35. RAB says:

    Hands up all of you who, like me, think Nick should write a Maths Textbook?

    Ok, Nick being Nick he’ll probably call it …. The Cuntulation of Counting, or something, but I bet it would become the biggest selling textbook of all time. ;-)

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