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Stanford, Harvard data science no more

stanforddaily.com

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Re: Stanford, Harvard data science no more

#41

Post by comte7092 »

simplotek wrote: post #36
comte7092 wrote: post #31

Earlier quoted context omitted.

High schools often teach physics and without calculus as a prerequisite. It definitely makes it more challenging, but you can still communicate the concepts at a different level of detail.

> High schools often teach physics and without calculus as a prerequisite. Does it though? For example, you simply cannot teach Newton's laws of motion without knowing what a derivative is.

> For example, you simply cannot teach Newton's laws of motion without knowing what a derivative is.

You absolutely can do that. You might now want to, but you can, and people do.

Re: Stanford, Harvard data science no more

#42

Post by tzs »

simplotek wrote: post #28
roddylindsay wrote: post #25

A high school "data science" course, if designed properly, will be far more useful to students and beneficial to society than calculus. Every high school student should learn how to grapple with uncertainty, how to evaluate statistical claims and experiments, how to interpret graphs and charts, understand how machine learning models work (at a high level), and internalize concepts like "significance", "error bars", a…

> A high school "data science" course, if designed properly, will be far more useful to students and beneficial to society than calculus. How do you expect students to understand what they are doing with "data science" without learning probability and statistics, and how do you expect students to get probability and statistics without learning calculus? I mean, Bayes' theorem. How do you get people to get it if they…

I don't recall Bayes' theorem involving calculus. Are you sure you aren't thinking of some other theorem?

Bayes' theorem follows straightforwardly from P(A & B) = P(A|B) P(B) and P(A & B) = P(B & A). The latter tells us that we can swap A and B in the former without changing the value, giving us P(A|B) P(B) = P(B|A) P(A).

Rearranging gives P(A|B) = P(B|A) P(A) / P(B), which is Bayes' theorem.

Re: Stanford, Harvard data science no more

#43

Post by hollandheese »

roddylindsay wrote: post #25

A high school "data science" course, if designed properly, will be far more useful to students and beneficial to society than calculus. Every high school student should learn how to grapple with uncertainty, how to evaluate statistical claims and experiments, how to interpret graphs and charts, understand how machine learning models work (at a high level), and internalize concepts like "significance", "error bars", a…

>understand how machine learning models work (at a high level)

>Calculus, on the other hand, will be used by very few students,

These two statements do not mesh. Understanding how machine learning models work requires Calculus.

Re: Stanford, Harvard data science no more

#44

Post by hollandheese »

kenjackson wrote: post #5

While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig. Not to say there aren’t useful aspects, but the curriculum is so inefficient. And maybe it’s because everyone needs some part of it, but that part is different for each person. Math is interesting in that th…

>While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig.

Statements like this are a big part of the reason statisticians never trust anyone who works in "data science". The whole field is basically applied statistics/calculus and you're saying none of that is useful.

Re: Stanford, Harvard data science no more

#45

Post by mlyle »

kenjackson wrote: post #27
mlyle wrote: post #23

Earlier quoted context omitted.

I think a lot of things use calculus concepts, even if calculus isn't explicitly invoked. A whole lot of finance and pharmacology are about exponential functions and their derivatives and integrals, for instance. A whole lot of fields use optimization, even if "just asking the computer to do it", etc. I admit I am weaker now in calculus and linear algebra because I lean on CAS and simulation a lot... but at least I k…

To be clear, I'm not referring to the concepts as they exist in the universe. But rather the actual material taught in the courses. For example, there's a lot topology that we use in the real world, but the material in the class is only of use to a small percentage of people in the world. I spent a chunk of my career optimizing FDMs and FEMs, but above and beyond that I haven't had a great need for Calculus until I s…

> but above and beyond that I haven't had a great need for Calculus until I started doing some deep learning.

I think a whole lot of what we talk about in compsci... calculus is table stakes. Sure, it's not differential equations, but how do we talk about behavior at the limit or nonlinear scaling without it.

Even just making up functions that are smooth in their derivative and cross though a few points is something I've had to do a lot for decent heuristics.

> And I suspect the work that you're talking about is exactly what I was thinking about when I wrote that even if Calculus is needed, it's the stuff taught in the first semester.

What's taught in the first semester varies a lot. I'm familiar with AP Calc BC, and sure-- a little bit of the stuff in the last half of the course (differential equations, vector-valued functions) is a little more esoteric for many careers. But a lot of stuff isn't so much (polar coordinates, the "practical integration" stuff that uses basic mechanics, calculator skills, etc)

Re: Stanford, Harvard data science no more

#46

Post by rawgabbit »

The article is written poorly with a click bait title.

This is the Stanford guidance. Mathematics: four years of rigorous mathematics incorporating a solid grounding in fundamental skills (algebra, geometry, trigonometry). We also welcome additional mathematical preparation, including calculus and statistics.

This is the Harvard guidance. Update to math curricular guidance: There is no single academic path we expect all students to follow, but the strongest applicants take the most rigorous secondary school curricula available to them. We receive many questions specifically about what type of math courses students should take. Applicants to Harvard should excel in a challenging high school math sequence corresponding to their educational interests and aspirations. Rigorous and relevant data science, computer science, statistics, mathematical modeling, calculus, and other advanced math classes are given equal consideration in the application process.

Re: Stanford, Harvard data science no more

#47

Post by comte7092 »

simplotek wrote: post #40
mturmon wrote: post #38

Earlier quoted context omitted.

You can sidestep calculus by just using the discrete setting rather than a continuous one. If you want to introduce continuous distributions like the Gaussian one, you can just say "area under the curve" if you need to connect the density to a numerical probability. They don't have to know how to do the integral, in the case of a Gaussian, it's just tabulated anyway. I'd argue that you could teach a perfectly reasona…

> If you want to introduce continuous distributions like the Gaussian one, you can just say "area under the curve" if you need to connect the density to a numerical probability. What name do you give to this "area under the curve", or the "rate of change" of this area? They are pretty fundamental concepts with important and basic properties, which affect things like local optima and minimization, and expected value a…

You call “area under the curve”… area under the curve. Expected values, least squares, linear model, etc can all be explained in the discrete case without calculus.

High school math isn’t and doesn’t need to be rigorously proofed based, if you lack some do the tooling necessary to demonstrate a proof, you can tell a student, “the proof requires calculus” and boom, you’ve given them a reason to take an interest in the subject.

Re: Stanford, Harvard data science no more

#48

Post by tinglymintyfrsh »

Seems like a mischaracterization because I don't see a problem.

UC CS undergrads had to take statistics for engineers and scientists.

UC CS undergrad majors in particular could end within 2 courses from a math undergrad degree. Is this not the case that squishier applied courses are possible?

EE/CS undergrads had to take the entire upper-division physics track for scientists and engineers, including modern physics.

So has something changed since then and is something changing back?

Re: Stanford, Harvard data science no more

#49

Post by kenjackson »

hollandheese wrote: post #44
kenjackson wrote: post #5

While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig. Not to say there aren’t useful aspects, but the curriculum is so inefficient. And maybe it’s because everyone needs some part of it, but that part is different for each person. Math is interesting in that th…

>While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig. Statements like this are a big part of the reason statisticians never trust anyone who works in "data science". The whole field is basically applied statistics/calculus and you're saying none of that is use…

Sorry, the statement I made wasn't intended to be connected that way. Data science uses a bunch of math beyond trig. I meant that in general math beyond trig becomes much less useful. I was talking about the general usefulness of different levels/types of taught math for white collar jobs/living. Not what is of use for data science.

Re: Stanford, Harvard data science no more

#50

Post by theGnuMe »

vineyardmike wrote: post #21
theGnuMe wrote: post #18

Earlier quoted context omitted.

It's rote learning though as ChatGPT proves by its scores on AP calculus exams. This is just a way to maintain elite admissions.

Just because ChatGPT can do it, doesn’t mean that it isn’t valuable for a human to learn. This is especially true for foundational courses.

Its valuable if you wrap it up in an applied problem solving course like physics. That’s the point of the new curriculum reform anyway. Other countries that exceed us in test scores do this.

So it really begs the question as to what is the point? The only thing I can think of is college admissions. A specific selection of rigorous memorization for elite admission.

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