The math here is surprisingly weak. I'm not sure about where you guys went to school, but this is fifth grade stuff. Sure, there's a lot of memorization, more classics. But wowzers. No math.
The SAT math questions are easier than these.
Harvard 1869 entrance exam
21–30 of 141 posts
Re: Harvard 1869 entrance exam
#22In a way, this reinforces my hypothesis that Latin in traditional Western higher education was never quite so much about Latin itself as it was about gaining a deeper understanding and greater praxis of your native tongue by reading its source code.
Re: Harvard 1869 entrance exam
#23The math here is surprisingly weak. I'm not sure about where you guys went to school, but this is fifth grade stuff. Sure, there's a lot of memorization, more classics. But wowzers. No math.
You're exaggerating more than a little bit.
There's 2 trigonometric proofs, and a number of less than obvious geometric proofs, especially the latter ones pertaining to the circle. The rational equation in #8 on algebra going to involve solving a cubic. And although #7 in arithmetic wouldn't be too hard if you worked entirely in pence, it is still a trickier problem in the days before decimalization.
Granted, it's weird in this day of students taking 5+ AP classes to see no calculus, but the math isn't weak at all. Remember, there's no calculators here. Maybe a slide rule and a table of trig values/logarithms. But that's still a lot of work by hand.
Re: Harvard 1869 entrance exam
#24The math here is surprisingly weak. I'm not sure about where you guys went to school, but this is fifth grade stuff. Sure, there's a lot of memorization, more classics. But wowzers. No math.
I very much doubt that most college students today, even in technical majors, could work out the geometry proofs. I was a calculus TA for two years in college (at an engineering school), and students don't know geometry anymore. Nor can they prove anything at all.
Not sure why this is, or was, getting downvoted. For most high school students, geometry consists of 1 semester in their entire high school career, and it mostly involves learning about triangles and polygons and learning the (n-2)/180 formula and a few, trivial proofs. The depth of Geometry on the Harvard test is not very deep per se, but it's easily out of reach for most high schoolers.
Now the students who do math contests and are AIME/USAMO level could probably do the geometry section here without a lot of trouble, but they are the exception.
Re: Harvard 1869 entrance exam
#25I'm surprised there's no calculus. Not even a basic derivative. The rest of the exam is certainly difficult to warrant a calculus question.
I think that at that point calculus was a grad-school-level thing. At the very least, it wasn't being taught in high schools. In fact, I'm pretty sure it's only taught in high schools today under the aegis of Advanced Placement classes, which give you college credit.
Many, many schools today offer "College Prep" calculus, which is far less rigorous than AP Calc. It covers most of the same topics, but with less depth. It's unlikely a College Prep Calc class would spend much time, if any, memorizing Trig Identities for integration. Generally very little epsilon-delta work, etc.
Re: Harvard 1869 entrance exam
#26Re: Harvard 1869 entrance exam
#27The math here is surprisingly weak. I'm not sure about where you guys went to school, but this is fifth grade stuff. Sure, there's a lot of memorization, more classics. But wowzers. No math.
This math is much harder than the math on the current SAT test. There are no geometry proofs or trig/logarithms on the SAT. However, most admits into Harvard nowadays have either a solid AP Test score in Calculus and/or a SAT2 Math score, so that's sort of an unfair comparison.
Re: Harvard 1869 entrance exam
#28In a way, this reinforces my hypothesis that Latin in traditional Western higher education was never quite so much about Latin itself as it was about gaining a deeper understanding and greater praxis of your native tongue by reading its source code.
Uhm, what? You couldn't be more off. Traditionally, any liberal arts education would include extensive familiarity with the classics. That means Plato & Dante, at the minimum, whether a BA or BS. You were expected to know Latin and Greek because you were expected to read Latin and Greek. If you were pursuing a BS, then perhaps you would read Euclid's "Elements" instead of Thucydides' "The History of the Peloponnesian War". (&c., It's not like those were the only texts one would encounter.) But languages were a prerequisite because they lacked the chronological hubris of our age. Hence the tight coupling with Geography: notice the ties between Xenophon in translation & the role of the Ten Thousand in Geography.
Re: Harvard 1869 entrance exam
#29Earlier quoted context omitted.
I very much doubt that most college students today, even in technical majors, could work out the geometry proofs. I was a calculus TA for two years in college (at an engineering school), and students don't know geometry anymore. Nor can they prove anything at all.
Not sure why this is, or was, getting downvoted. For most high school students, geometry consists of 1 semester in their entire high school career, and it mostly involves learning about triangles and polygons and learning the (n-2)/180 formula and a few, trivial proofs. The depth of Geometry on the Harvard test is not very deep per se, but it's easily out of reach for most high schoolers. Now the students who do math…
If things continue as they are, expect this to change a bit. In particular, proofs like #4 on Geometry is going to be a requirement in 45 of the 50 states.
Check G-SRT.4 at http://www.corestandards.org/the-standards/mathematics/high-...
Re: Harvard 1869 entrance exam
#30Curious to hear about the 'General Supposition' (in the Greek question for sophomores). Seems like it's really only found in New Testament Greek. Makes the test rather biased towards a particular religion. But perhaps that started to change right around that time with Eliot. Charles W. Eliot, president 1869–1909, eliminated the favored position of Christianity from the curriculum while opening it to student self-dire…
I am Greek and had to do six years of Ancient Greek. I don't understand how you got to that conclusion. The test is asking questions on ancient Greek grammar and only. It has nothing to do with religion or what so ever, New Testament Greek is very close but also very different from Ancient Greek -it has some idiosyncrasies of it's own. I really want to know how you concluded that this has something to do with religio…
You're right. I spoke too quickly. Thanks.
I studied ancient Greek too for several years. I hadn't heard of this 'General Supposition' as a way to describe conditional clauses. Apparently -- just looked it up some -- it was an older way of describing the categories we use now (which are mostly temporal based -- future less-vivid, etc.). So there are two spheres for classifying conditional clauses.
If you look up the Goodwin grammar reference for 'General Suppositions', the vast majority are from NT Greek. So that's what made think it was mostly used in NT Greek.
So in a way, thinking about conditionals as 'General Suppositions' is sort of biased in that direction.
But you're right, could apply to Classical Greek too. I should've remembered that Classical Greek is mostly a superset of NT Greek, so there would be examples there too, etc.
But it's actually a rather deep question. Classifying conditions as 'general' asks for a kind of aphoristic understanding of things (talking only about the very general case). I would hazard a guess that the majority of this is in NT Greek. But I suppose some historians and philosophers also generalized (Thucydides, Plato) in this way and could have their protases classified as such. But it is sort of a different way of thinking. Bad to generalize ;-) -- but it may go quite to the heart of certain differences between aspects of NT and ancient Greek.