Lol. I know how to custom sort in Excel. That puts me in pretty rarified air attorney-wise.
I can do formulas, too, and can even read a profit loss statement! But that’s showing off.
Seriously, how appalling is it that professionals who have to keep billable hours can’t do basic math?
Some attorneys use both Word and Excel (at least this one does). May help that I was a CPA before I was an attorney (two bad career choices, maybe third ones the charm?). Wihout question I use Word a lot more but I still don’t know but a small fraction of what Word can do (and even less of what Excel can do). But I can do what I need with both tools.
I think the bigger issue for many attorneys isn’t Excel itself but that it involves math. There is a certain anxiety level there which isn’t limited to attorneys. There just seems to be some type of block. Even though often what is required isn’t very complicated or sophisticated. I deal mainly with c-suite folks with a lean towards the treasury/finance side. In my experience, being comfortable with numbers is very helpful. Can help bridge gaps between business and legal functions.
This is way off topic but all I can conclude is that attorneys have money to burn on proprietary software. Everywhere I have worked in years uses the Google suite. It’s true that many features are missing, and that’s an annoyance, but having documents and spreadsheets immediately shareable is a big plus, aside from not having to pay for a license. (I occasionally miss Excel, but I forget why now and will only remember the next time I want to do something that’s missing.)
Way way way off topic, but I suspect the preference for the proprietary software has its origin in concern for attorney client privilege, which gives rise to a desire to have complete control over files, which makes sharing in the cloud suspect re: data breaches.
Plus, we are control freaks who don’t adapt to change well. I know plenty of people who still use Word Perfect. They have their templates and they aren’t about to change what has worked for 30 years.
"So, pardon my cynicism. I do not believe that calculus is fundamental, except in math analysis, physics, some other physical sciences, and specific engineering disciplines.:
At the risk of pouring on, it’s also used in more advanced econ classes and can be used in intro classes but the professor doesn’t want to scare the class by bringing Calculus in.
Also if you’re questioning the need for calculus for non-stem, why not question the need to take foreign language or literature for stem students? For stem students, about as useless as Calculus is for non-stem students right? Not really using the stuff I learned reading Shakespeare.
Well now that you mention it, foreign language seems like more of a nice to have than a requirement. If (as is typical in the US, at least in non-elite schools) you never develop fluency, it’s unclear what’s the point.
As for literature, history, arts requirements, etc., it is good to have a well-rounded education, but the tangible benefits might be oversold. Usually these are introductory breadth requirements for non-majors. Well, if calculus is to be considered an introductory breadth requirement, then why limit it to STEM students? Newton’s contribution is just as important as Shakespeare’s, right?
Sure. Though it is actually less useful in computer science, which at its core concerns discrete and not continuous systems. Why don’t people learn inductive proof at least as early as they learn the mathematics that leads to calculus? In my domain, it has been much more useful.
I enjoyed calculus, and that’s one reason I’m reluctant to inflict it on those who will not, but if we’re going to, I don’t want to add insult to injury with the false promise that they’re actually going to apply it outside of a particular subset of fields.
Proof by induction is just one (and a relatively simple) method of mathematical proof. There isn’t enough material to build a course on. It could be incorporated in an algebra or trignometry course, but nearly all US HS’s currently shy away from proof-based math. It’s also not viewed as useful or foundational (as calculus, for example, even though you may disagree, from the perspective of a subgroup of CS students).
I agree that some proof-based math is useful, and method of inductive proof could be part of it. IMO, the best math course in HS should be a proof-based geometry course. It measures much more accurately (than calculus, or some other math class in HS) a student’s aptitude in math.
Ironically the long standing first term intro course at Cambridge (Numbers and Sets) takes precisely the opposite perspective, treating induction as the foundational aspect of math analysis (though it certainly isn’t likely to be adaptable to a high school level course):
“This course is concerned not so much with teaching you new parts of mathematics as with explaining how the language of mathematical arguments is used. We will use simple mathematics to develop an understanding of how results are established.
Because you will be exploring a broader and more intricate range of mathematical ideas at university, you will need to develop greater skills in understanding arguments and in formulating your own. These arguments are usually constructed in a careful, logical way as proofs of propositions. We begin with clearly stated and plausible assumptions or axioms and then develop a more and more complex theory from them. The course, and the lecturer, will have succeeded if you finish the course able to construct valid arguments of your own and to examine critically those that are presented to you. Example sheets and supervisions will play a key role in achieving this. These skills will form the basis for the later courses, particularly those devoted to Pure Mathematics.
In order to give examples of arguments, we will take two topics: sets and numbers. Set theory provides a basic vocabulary for much of mathematics. We can use it to express in a convenient and precise shorthand the relationships between different objects. Numbers have always been a fascinating and fundamental part of Mathematics. We will use them to provide examples of proofs, algorithms and counter-examples.
Initially we will study the natural numbers 1,2,3,… and especially mathematical induction. Then we expand to consider integers and arithmetic leading to codes like the RSA code used on the internet. Finally we move to rational, real and complex numbers where we lay the logical foundations for analysis. (Analysis is the name given to the study of, for example, the precise meaning of differentiation and integration and the sorts of functions to which these processes can be applied.)”
"I look at it more as a term that identifies a missing area in K-12 and a call to action to figure out the curriculum. "
There’s a lot more pressing problems in K-12 than adding data science to the curriculum to think the implementation could happen soon, even if you could figure out what that implementation is. Things like schools in lower SES districts, technology access, post-covid plans among a host of other things are going to be worked on. Even if you got something to happen, there’s no way you could get it adopted nationally, common core maybe but that’s another set of issues. So maybe local districts mandate it, but then you need teachers who know data science and why wouldn’t they do it at a college or maybe, consult.
I think practically you could make the stats course more of a data science course, but that would favor private, higher SES-public schools that have the teachers, tools etc…
The “Numbers and Sets” course would be an excellent additional math course in high school. I think it would make much more sense than the Linear Algebra courses that some high schools have.
I 'm going to go out on a limb and and say there might be ten high schools in the US that can teach a class taught at Cambridge. Linear Algebra maybe taught at 100 or so, most kids take it at a local community college/DE.
In theory, high school math teachers should have been college math majors who also earned whatever teaching credential is required by the state or high school. So they should in theory be able to teach a rigorous proof-based numbers and sets course. Of course, whether there will be much student interest in a high school (even one with large numbers of advanced-in-math students) is another matter.
Note that a course that focuses on instruction in various proof techniques and methods is offered by some college math departments as a sophomore level course for math majors to prepare for upper level courses like abstract algebra, real analysis, etc… Presumably, that is the same reason why Cambridge has that course early in its math major curriculum.
And yet, it is probably not much harder than calculus or linear algebra. And definitely much more interesting than linear algebra, which IMO is the most boring math possible.
Hmm, strange. My bachelor’s degree is not from a US college, and my major wasn’t math (CS), but I studied real analysis and abstract algebra in my freshman year.
Hmm, try the problem sheets:
Not sure I can solve any of these off the top of my head nowadays…
I can’t either, but I know how to start. 
For example, for the first one, assume that two of the numbers ARE prime, and prove that the third can’t be.
EDIT: Ah, it is actually even easier. If n is even, it is not prime. If it is odd, one of n or n+2 or n+4 will be divisible by 5.
Perhaps you mean divisible by 3? For example, none of 7, 9, and 11 are divisible by 5. But exactly one least one of n, n+2, and n+4 will be divisible by 3 for odd n since odd multiples of 3 are spaced 3*2 apart – if n is multiple of 3, n+6 is also multiple of 3.
This isn’t quite right. For example, none of the integers in the sequence 9, 11, 13 is divisible by 5.
Assume the three integers n, n+2, n+4 were all prime that are greater than 3. One of the integers in the consecutive integer sequence n, n+1, n+2 must be divisible by 3. Since n, n+2 were prime (and neither can be 3), n+1 must be divisible by 3. Similarly, n+3 must also be divisible by 3. So we can write n+1 = 3k and n+3 = 3m. Subtracting the two, we have (n+3)-(n+1) = 3m-3k = 3(m-k), a multiple of 3, which leads to a contradiction that the difference between the two adjacent even integers (n+3, n+1) must be 2. Therefore, the sequence n, n+2, n+4 can’t be all prime, unless one of them (the smallest one, meaning n) is 3.
Perhaps you all can share a Google doc to solve the problem sets instead of doing so here.