I can't agree with the "mathematics used to weed out" terminology, the weeding out may be an incidental part, but I've never encountered a place where mathematics was used to diminish the number of people following a pursuit. Certainly not the way that Organic Chemistry is used to weed out premed students.
And certainly not in Computer Science, as mathematics is avoided in many cases where it would greatly aid in reasoning about systems, due to the quantity of people who dislike it.
And in Physics, mathematics isn't used to weed out people, but to train them on the theories that underpin the entire field.
I'd be interested in hearing where this happens, because it's certainly not been my experience.
"... as mathematics is avoided in many cases where it would greatly aid in reasoning about systems, due to the quantity of people who dislike it."
Computer science at Penn has been doing this especially. In the overview of mathematics course at Penn, any mention of algebra has been removed. They used to have a section on toy RSA--deleted. It seems like they want to remove all mathematical rigor here, just to turn out more people with a CS degree. People can hardly walk away doing a proof, like the showing how a greedy algorithm such as Kruschkal's can work. To see this for me is frustrating to say the least. So I must concur.
Side story. The other thing is, CS has nearly doubled since I attended, 4 years ago, and they have NOT hired faculty to keep up. Class sizes are getting ridiculous.
Calculus is a requirement for all undergrad science degrees in most places, and a biologist has about as much use for integral calculus as a fish does with a bicycle. They're much better served by statistics, which is not, a majority of the time, an undegrad requirement for all majors.
There are large areas biology that depend crucially on calculus and other math. Genetics as a field is extremely quantitative. Ecology and evolution also rely heavily on mathematical models. You can get by in some parts of molecular biology and field biology without a great understanding of calculus, but even in those subfields its important to have an undergraduate-level understanding of genetics, ecology, and evolution.
At my university in germany, students had 3 semesters to prove themself. They had to pass certain exams. Otherwise they get kicked out. They gave you 2 maths courses, of which you have to pass at least 1 exam. Math was the game changer for most students, who did not make it.
It's been used for exactly that purpose at one particular university I'm highly familiar with. Certain departments (e.g. Psychology) didn't want to deal with the hassle of flunking their students out, so they outsourced the job to us (math) by requiring calc 1.
"Weed out" is a euphemism. The purpose isn't to diminish the number of people following a pursuit, it's to ensure they have the analytical aptitude to be successful at it.
Quite a few competitive major programs where I got my degree required students to complete 1st year calculus (differential, integral, multivariate) and some or all of 1st year physics (mechanics, electromagnetism, waves, optics) before applying.
I know at my Alma Mater, University of Maryland, all the comp. sci majors had to pass calc 2. I knew of some people retaking one of those courses 2 or 3 times trying to pass. UMD is generally considered a top 10 comp. sci. school. Just anecdotal evidence though, I'm not trying to argue against you.
It was pretty well-known, and it was really obvious because at most schools, calculus is three semesters, while UTD condensed it down to two without reducing the material at all.
And certainly not in Computer Science, as mathematics is avoided in many cases where it would greatly aid in reasoning about systems, due to the quantity of people who dislike it.
And in Physics, mathematics isn't used to weed out people, but to train them on the theories that underpin the entire field.
I'd be interested in hearing where this happens, because it's certainly not been my experience.