申論題

II. Blank Filling Read the following article carefully and fill in each blank with an appropriate option from the box below. Each option can be used
only ONCE.
第 11 至 18 題為題組
    Mathematics can be said to have begun with the invention of numbers and arithmetic, which is believed to have occurred around ten thousand years ago, with the introduction of money.
    Time passed. Over the    11    centuries, the ancient Egyptians and Babylonians expanded the subject to include geometry and trigonometry. In those civilizations, mathematics was largely    12    , and very much of a “cookbook” variety. (“Do such and such to a number or a geometric figure, and you will get the answer.”)
    The period from around 500 BCE to 300 CE was the era of Greek mathematics. The mathematicians of ancient Greece had a particularly high regard for geometry. Indeed, they treated numbers geometrically, as measurements of length, and when they discovered that there were lengths to which their numbers did not    13   (essentially the discovery of irrational numbers), their study of number largely came to a halt.
    In fact, it was the Greeks who made mathematics into an area of study, not merely a collection of techniques for measuring, counting, and accounting. Around 500 BCE, Thales of Miletus (Miletus is now part of Turkey) introduced the idea that the precisely stated assertions of mathematics could be logically proved by formal arguments. This innovation marked the birth of the theorem, now the bedrock of
mathematics. This formal approach by the Greeks    14    in the publication of Euclid’s Elements, reputedly the most widely circulated book of all time after the Bible.
    By and large, school mathematics is based on all the developments listed above, together with just two further    15    , both from the seventeenth century: calculus and probability theory.
    Is school mathematics tantamount to mathematics? Anyone whose view of mathematics is    16    to what is typically taught in schools is unlikely to appreciate that research in mathematics is a thriving, worldwide activity, or to accept that mathematics does    17    , often to a considerable extent, most walks of present-day life and society. For example, they are unlikely to know which organization in the United States employs the greatest number of Ph.Ds. in mathematics. (The answer is almost certainly the National Security Agency, though the exact number is an official secret. Most of those mathematicians work on code breaking, to enable the agency to read    18    messages that are intercepted by monitoring systems—at least, that is what is generally assumed, though again the Agency won’t say. Though most Americans probably know that the NSA engages in code breaking, many do not realize it requires mathematics, and hence do not think of the NSA as an organization that employs a large number of advanced mathematicians.)
(A) correspond (B) ensuing (C) purloined (D) advances (E) permeate (AB) utilitarian
(AC) sophisms (AD) confined (AE) erudite (BC) culminated (BD) foregoing (BE) encrypted

11.