The book is "Arithmetic for Sixth and Higher Standards", by The Christian Brothers. Gill and Son. Dublin. Bears no date, but internal evidence puts a lower bound of 1949 on the date.
The Christian Brothers never signed their books, individually. All were treated as the work of the community.
This copy seemed to belong to a James Hall, from Inchicore.
I'll blog a problem, perhaps regularly. The authors appear to have taken some care to use realistic numbers, so the volume has much to tell about wages, commercial practice, and even priorities and attitudes.
107(7) (Page 107, number 7): A man with two sons in a day-school and 2 in boarding school, can just pay the total school fees from the yearly interest he receives from a certain investment. If the half-yearly fee in the day-school is 8 guineas per pupil and the yearly fee in the boarding school is 93 guineas per pupil, find the amount of the investment at a rate of 4 and a half percent.
(For younger readers, wishing to understand these prices, a guinea is 21 shillings, 20 shillings make a pound, and the pound became 1.27 euro in 1999. To be precise, the pound became (1/0.787564) euro. Of course, this information is unnecessary for the solution of the problem. On the other hand, the solution may be puzzling if you don't know that a shilling is 12 pence.)
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4 comments:
I found a neat monograph at a used book sale many years ago. It is titled Functional Operators Volume I: Measures and Integrals by John Von Neumann, Princeton University Press 1950. It's orange with paperback binding. It looks like a first edition though. I've yet to read it. It's frightening.
I haven't seen this book of VN's. It's a first-rate series, those orange paperbacks. I would not imagine they ever did second editions; the monographs provided rapid publication of up-to-the-minute ideas. Typically, the material would find its way into standard textbooks a few years later.
The ideas around measure and integral, which originated earlier in the 20th century with people like Lebesgue, Caratheodory, Lusin, Hausdorff, Suslin were reworked from various points of view in the 50's and 60's. One of these, originating with F. Riesz, I think, regards measures as elements of a dual space, and I guess that is where VN takes it up. I learned the stuff from Hewitt & Stromberg (who present the Loomis approach, contructing measures from functionals on simple spaces), and Federer (who starts with measures on arbitrary sets). The most popular book when I was a kid was Rudin.
That's interesting background on the monograph. I've had big Rudin in my amazon shopping cart for the better part of a year now. Today's payday so perhaps I'll go ahead and complete the purchase. I sometimes wish I had JvN at my beck and call. There's a problem in an actuarial paper I'd been writing that I cannot solve. It's in the last section and uses function iteration to solve a least squares problem. The algorithm appears to work, but I can only assert that my algorithm coverges to a local minimum, when it in fact converges. I mused that I might need some sort of topological equivalence to an easier problem in the preceding section.
Anyway here's a little word problem that I'd love to torment students with, if I were a teacher:
Suppose you have two sheets of paper, and the width of first sheet is the same as length of the second sheet, and that the ratio of length to width of both sheets is the same. Suppose the area of the second sheet is one half the area of the first sheet. What is the ratio of length to width?
The paper-sheet question is a good problem for, say, 13-year-olds. It is real-world, in the sense that the standard series A0, A1, A2,A3, A4, A5,.. of paper sizes follow this rule.
I'll have to think about the question in your paper.
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