Mathematical Studies

This is a letter to a blogger called Stewart Griffin who send me a link to his blog in which he denigrated Maths Studies degree programmes at Irish universities:

Dear Stewart,
Thank you for your message.
I looked at your blog.  It does not appear to
take comments, so I am writing to you.
You are seriously misinformed about Maths Studies,
if you think that this order is reasonable:

Mathematics, Applied Mathematics, Physics, Engineering (with significant maths content), Computer Science, Mathematical Studies, Chemistry, Biology

as a ranking of fitness of degrees to prepare maths teachers.
I suggest that you start by getting the facts about the maths
content of these various kinds of degree programmes, before
you lay about you in this way.  You will find that you have put
ahead of maths studies a number of programme-types that typically
involve the study of some rather small (typically well less than 50%)
subset of a maths studies programme, and certainly at no higher
level of rigour, to say the least.  Maths studies programmes entail
between 80 and 110 ECTS credits in Maths courses, depending on
whether the student takes a double-hons or single-hons degree. You
make fun of the occurrence of a 5-credit module on History of Maths
in our programme. But this is an entirely appropriate module for a
prospective maths teacher, and it was not in put there  to make the
programme easier.  A maths teacher should have an understanding
of the origins and development of the discipline, and a broad and
sufficiently deep exposure to all the mainstream areas of maths.
Fifty years ago, the standard training for a maths teacher involved
the 3-subject general degree, with maths as one of the three.  This
translates, in modern terms into 55 ECTS credits (15+20+20) in
maths, involving so-called general-level,  (pass-level) courses.  An
engineering graduate from UCD would have had a greater level
of exposure to maths, over the four years, except that they would
have been light on areas such as groups, rings, fields, and
number theory.  Many people were, and
are teaching maths with much less exposure than this, such as
Arts, Science, and Commerce graduates with as little as
one year of maths (15 ECTS credits).  With the elimination of
general degrees, the maths studies programmes were created by
adding to the general maths programmes.  The additions, typically,
involve more exposure to proof, to modern geometries, and to
subjects that have become more important in the modern world,
such as symbolic computation, combinatorics, coding theory,
cryptography, as well as history and philosophy of maths. 
In the meantime, most S+T programmes have gone
in the opposite direction, reducing exposure to maths to the
absolute minimum required for the later courses in the
application, usually confining it to the first two years,
emphasising drill at the expense of concept,
paying no attention to rigour, in short giving a narrower
and shallower maths education.
As a consequence, your school principal should on no account
send in recent graduates in any of the S+T areas you list,
except Maths, Applied Maths and Maths Studies, to teach
maths to his students, unless they have taken steps to
deepen and broaden their mathematical education.

Best regards,
Tony O'Farrell.

Sabbatical over

Too much life for blogging, since July. Freud is supposed to have said  that all that really matters is Love and Work.  If that be so, then I live as one should, because all I do is love, and work.  Term began on the 20th, and I enjoy the contact with bright, hopeful youngsters again.
In the tail end of the Summer, I read through some engaging stuff: (the English and Irish text of) a parallel-text anthology of  Irish poetry with Czech translations (ISBN 80-86055-80-9), a collection of essays about Ireland, by a German journalist (Ralph Sotscheck, Saint Patrick in der Bingohalle, Irische Einblicke, ISBN 3-85452-718-7), Collected Stories by V.S. Pritchett (ISBN 0-7011-2305-2), a collection by Isaac Bashevis Singer (A Crown of Feathers  and other stories, ISBN 0-224-00986-9),
a translation of The Analects of Confucius (ISBN 978-1853-26462-7), a biography of the poet Attila Josef, by Thomas Kabdebo (ISBN 1-89792202-7), a couple of rather dated books on cosmology:
G.J. Whitrow, the Structure and Evolution of the Universe, Hutchinson, 1959; and G.C. McVittie, Fact and Theory in Cosmology, Eyre and Spottiswoode, 1961, and I reread a translation of J.L. Borges collection Ficciones, Grove Press 1962 and Feynman's sparkling and provocative memoir, Surely You're Joking, Mr. Feynman!    Pritchett and Singer are just brilliant, but  I can't imagine what I saw in Borges. 
Now I'm just reading Maths, apart from occasional dips into the Tale of Genji.  It looks as though this novel will take me a long, long time.
I'm teaching introductory mathematical computing, with Maple, and basic real analysis.
I'm currently investigating the distribution of cubic residues to composite moduli, with an application in view to Diophantine approximation.  I like number theory, but have a lot to learn.

Phil Hickey's Blog

I went to school with Phil Hickey, who blogs at:

http://behaviorismandmentalhealth.com/

What he has to say is very interesting, and rather shocking.  It appears that there is no scientific evidence of specific chemical imbalance in most people suffering from depression, and so no scientific basis for the treatment of depression by antidepressive drugs.  The same applies to other disorders, such as attention-deficit hyperactivity disorder.  He cites specific  sources for this finding. I had no idea.  I've encountered many depressed students in my time, almost all on medicine, and never dreamed of suggesting they come off the medicine.   In fact, I assumed that if they did so, they would be at increased risk of suicide, which is, along with road traffic accidents,  one of the two main causes of death among our students.   And everything I'd heard before this, including comments by professionals, was to the effect that "the drugs work", and in fact that  "there has been no progress in psychiatry apart from the development of useful drugs."

I still won't advise people to stop taking the pills, but I won't encourage them to continue, either.  Not my job, or competence.   Patients should be able to trust their doctors.

You Tube

The recorded music business is finished. And, I need never again be stuck for a word, a phrase, or a bar of any song. Everything is there.

Jessica

Back Home

Much peregrination since the start of May: Scotland, to hike up Ben Nevis; Madison, WI, to work on the biholomorphic group; conference in Edwardsville, IL; day in Chicago, mostly at the Art Institute; Helsinki; holiday in the Ebro delta; Valencia; Connemara, to hike the Maamturk mountains. Entertained visitors in between. Met many old friends, and perhaps some new. Now looking forward to some stability.

Recently read, or reread:

J.M. Castellano Gil and F.J. Macias Martin. History of the Canary Islands.
84-7926-114-5. English a bit broken. Interesting (and sad) story of the conquest. Some data on references in antiquity (Homer?, Hesiod, Pindar, Herodotus, Diodorus of Sicily, Strabo, Plutarch, Sallust, Pomponius Mela and Pliny the Elder. Also some folklore, including a story about Brendan the Navigator. Short chapters on links with America, the literature, and art.

S. Vere Benson. The Observer's Book of Birds. Ferederick Warne. Rev. ed. 1960. My old bird book, a very useful field guide.

Eric Dempsey and Michael Casey. Finding Birds in Ireland. The Complete Guide. 978-07171-3916-3. About places where birds may be found. It is very hard to use it to locate info about the location of a particular species, as the index is unhelpful in this regard. Has many maps, and has a glossary of Irish names for most species.

Colm O Lochlainn. Irish Street Ballads. Three Candles. Dublin. 1939. This and More Irish Street Ballads, 1965, are indispensible.

Henry James. The Wings of the Dove. Slow build-up to a classic disaster. After the first few hundred pages, I couldn't put it down, and stayed up far too late in Helsinki to finish it. Great book.

Tom Brown's School Days, by An Old Boy. Rev. ed. 1889, repr. 1890. (f.p. 1857). Not at all what I expected, and much more interesting. I expected something like a propotype of Frank Richards' books, but this is a far more sober affair, much concerned with moral matters, such as the duty to study honestly. In relation to the famous fight with Flashman, the author has a disquisition about the place of fighting in a boy's life. I was struck by: "After all, what would life be, without fighting?"

Ray Monk. Wittgenstein. The Duty of Genius. Vintage. 1991. 0-09-988370-8. Very good read, but every time I begin to think I understand W's point of view, he does something that proves me wrong. In the end, I am torn between the desire to read it again from the start (and spend serious time studying W's work) and the rather attractive idea that I should take W's advice to his various friends, and give up philosophy altogether to do something useful.

E.E. Cummings

Selected Poems 1923-1958. Faber and Faber. ISBN 987-0-571-08986-4
(Selected by the poet)
I'd neglected this man, hitherto, for no better reason than my aversion to gimmickry: he uses idiosyncratic punctuation (frequently none) and rarely uses a capital letter. Then, a few weeks ago we watched a movie in which the always watchable Cameron Diaz played an almost illiterate girl, who slowly read one of EEC's love poems to a blind patient, and I was amazed by its beauty. Now I'm a convert.
Some are political, some humorous, some erotic, a few religious, but most are about love, and life, and light. In form, quite a few are sonnets, the style strongly reminiscent of Shakespeare. For instance:

true lovers in each happening of their hearts
live longer than all which and every who;
despite what fear denies,what hope asserts,
what falsest both disprove by proving true
....

But he uses all sorts of standard metrical and rhyming structures, with just an occasional innovation, in which the layout on the page suggests the intended phrasing, and pauses. Such as this:

...
so world is a leaf so tree is a bough
(and birds sing sweeter
than books
tell how)
so here is away and so your is a my
(with a down
up
around again fly)
forever was never till now

His word-order sometimes recalls Horace:

anyone lived in a pretty how town
(with up so floating many bells down)

(-- the use of parentheses is a characteristic. Sometimes, there is just one short sentence outside the parenteses, and a whole world inside.)
So much, so beautiful -- read it!