What would Math Lecturers score on the Putnam?

[Wi_N]

Main Question or Discussion Point

Would they ace it? For those of you who don't know The Putnam is the hardest math test for undergrad students. The test has 120 points but most only score a few.

 

[jedishrfu]

While I can't answer your question, I realize it would probably depend on the math lecturer and what he taught regularly. As we progress in our math studies, the math we learn in grade school is child's play to us now. Following that extension if your job is to teach higher level math then that math will be child's play to you and you should easily be able to do the problems you routinely assign to your students. I'm sure this would be true of the Putnam.

I had a geometry teacher who once scolded us for our poor performance on his tests. He told us that it took him 5 minutes to work out and write down the answers in full to any of his tests and from that he would give us 45 minutes to complete the test. He showed us how we answered his questions in frivolous roundabout ways that wasted precious time because we didn't know exactly how or in what manner we could present our answer to him.

The big takeaway for me was its okay to plot a line solution to y=mx+b by simply drawing and labeling the axes x,y with tick marks to y-intercept (no numbered labels for each tick mark) and similarly for the other point using tick marks on the x-axis for the x-value and a vertical bar with more tick marks for the y-value and then simply labeling the point.

We students had been trying to reproduce the books plots in gory detail with 10 numbered tick marks in each direction on each axis before we even started the problem. We didn't realize that we could've used the same notational shortcuts that the teacher used when drawing answers on the black board. Duh...

The second thing I learned was how to reduce trig notation to brief cryptic diagrams that I would write at the top of my paper so I didn't have to keep remembering it during the test. It was a kind of visual cue that allowed me to speed through the test with confidence.

Some example mnemonic devices I used were:

s2+c2=1                    // for   sin^2(a) + cos^2(a) = 1           
1+t2=s2                     // for    1 + tan^2(a) = sec^2(a)
sab=sacb+casb        // for sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
cab=cacb-sasb         // cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

https://www.liverpool.ac.uk/~maryrees/homepagemath191/trigid.pdf

 

[f95toli]

While I can't answer your question, I realize it would probably depend on the math lecturer and what he taught regularly. As we progress in our math studies, the math we learn in grade school is child's play to us now. Following that extension if your job is to teach higher level math then that math will be child's play to you and you should easily be able to do the problems you routinely assign to your students. I'm sure this would be true of the Putnam.

Whereas I agree with the bit I put in bold I don't think the part it italics follows. You can be very good a "standard" math without being great at the type of math you sometimes find in the types of tests the OP is referring to; the reason is simply that these tests do not necessarily test knowledge but problem solving skills and whereas the former is something can learn by studying most of us will never be great at solving the kind of rather obscure problems you would e.g. find in the math Olympiad.

 

[jedishrfu]

There exists an instructor who designs and teaches Putnam-like problems and thus would be able to score well in it which means they might even ace it. However, we could also argue that there does not exist an instructor who designs and teaches Putnam-like problems but then who writes the test. (Proof left to the student)

Here's a writeup from Bruce Reznick who wrote and chaired the Putnam exam in the 1980's:

https://faculty.math.illinois.edu/~reznick/putnam.pdf