In 1969 Lang wrote an article for the Columbia Daily Spectator, Don't
Blame Us if You Flunk Math (Volume III, Number 4, December 8, 1969). The phrasing of the subline illustrates how much the times have changed:"A fifteen minute quiz raises questions what kind of people should be taught what kinds of math at Columbia".
He provides a basic introductory test for calculus courses and argues for its adequacy to decide who should or should not take them. The amazing predictive success is not mentioned, though. It seems it was used as a placement test for sections with three different levels of difficulty, but the prediction story is more fun, I guess.
"During the last few years there have been some complaints concerning the
calculus courses. The situation was particularly tense last year when I
was away, and the math department got a lot of flak. Since I am departmental
representative this year I have tried to pin point some of the causes for the
difficulties. We separate our first and second year calculus students into three groups, A, B, C, of which A is supposed to be the more computational and easiest,
B more theoretical and harder, and C for the very interested and the talented
[...] Following complaints which Mr. Wyer regarded as comjng from unqualified students, the course was watered down and became less rewarding to the more responsible students. Mr. Wyer vouches for the opinions of at least ten others who agree with him. Mr. Wyer questions the insight of students criticizing math courses as
being too "theoretical". As he says: "It is not an infrequent occurrence in
the fields of physics and engineering for a student to do very well in his
introductory mathematics courses and subsequently to run into difficulties".
After receiving Mr. Wyer's letter, I decided to give a short test to check
Mr. Wyer's opinions. The test consisted of five problems, and was given to the
1A sections. One can draw some conclusions: a) The test is very easy and students
unable to do reasonably well on such a test should not be taking a calculus course."
You have fifteen minutes to do the following problems:
Solve the system of equations: $3x - 2y = 1;$
$4x + 7y = 15$
Solve the system of equations: $3x - y + 2z = 1;$
$x - y - z = 0;$
$2x - 2y + 3z = 3$
Solve the following equations:
a) $2x^2 - 4x + 5 = 0;$
b) $3x^2 + 2x - 8 = 0$
What is the sine of an angle of:
a) 45 degrees b) 30 degrees c) 90 degrees
$1/(x+y) - 1/(x-y) = -2y/(x^2 - y^2)$