This site uses cookies to improve your experience. To help us insure we adhere to various privacy regulations, please select your country/region of residence. If you do not select a country, we will assume you are from the United States. Select your Cookie Settings or view our Privacy Policy and Terms of Use.
Cookie Settings
Cookies and similar technologies are used on this website for proper function of the website, for tracking performance analytics and for marketing purposes. We and some of our third-party providers may use cookie data for various purposes. Please review the cookie settings below and choose your preference.
Used for the proper function of the website
Used for monitoring website traffic and interactions
Cookie Settings
Cookies and similar technologies are used on this website for proper function of the website, for tracking performance analytics and for marketing purposes. We and some of our third-party providers may use cookie data for various purposes. Please review the cookie settings below and choose your preference.
Strictly Necessary: Used for the proper function of the website
Performance/Analytics: Used for monitoring website traffic and interactions
Reflecting on my own self-identification, I had a vague sense it had something to do with Holifield’s Algebra II class, which I took in ninth grade. It’s important to ensure messages or opportunities to engage in math are equal for everyone they teach, she says. But a case of “senioritis” caused her to drop out of high school calculus.
In its current form, school algebra serves as a gatekeeper to higher-level mathematics. Researchers and policy makers have pushed to open that gate—providing more students access to algebra, focusing in particular on those students historically denied access to higher-level mathematics. Let’s Not Be So Quick to Give Up on Algebra.
For instance, only 38% of schools serving predominantly Black and Latinx students offer calculus, compared to 50% of all high schools. In middle schools offering algebra, white students make up 50% of the attendees, but 58% of those enrolled in algebra classes. Economic disparities are just as stark. Changing placement policies.
It’s equally, if not more, important for human-like AIs as well—immediately giving them what we can think of as computational knowledge superpowers, that leverage the non-human-like power of structured computation and structured knowledge. It’s a tremendously powerful way of working.
Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”
In more explicit form we could write this as Equal [f[x_, y_], f[f[y_, x_],y_]] —where Equal ( ) has the “known meaning” of representing equality. and at t steps gives a total number of rules equal to: ✕. So how about logic, or, more specifically Boolean algebra ? ✕. ✕.
Here's the one from Winter 2021 for calculus and here's the one for modern algebra. I only have a preliminary tabulation of the course grades right now, but it's the most striking bimodal distribution I have ever seen, with a large number of D grades and an almost equally large number of A's.
In general, the number of edges that come out of a single node in a evaluation graph will be equal to the number of instances of the function f that appear on the right-hand side of the recursive definition we’re using (i.e. in computer algebra systems I’d used. 2 in the case of the standard Fibonacci definition).
For integers, the obvious notion of equivalence is numerical equality. For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it.
Any integral of an algebraic function can in principle be done in terms of our general DifferentialRoot objects. When you do operations on Around numbers the “errors” are combined using a certain calculus of errors that’s effectively based on Gaussian distributions—and the results you get are always in some sense statistical.
We organize all of the trending information in your field so you don't have to. Join 28,000+ users and stay up to date on the latest articles your peers are reading.
You know about us, now we want to get to know you!
Let's personalize your content
Let's get even more personalized
We recognize your account from another site in our network, please click 'Send Email' below to continue with verifying your account and setting a password.
Let's personalize your content