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> A broad base of at least some of stats, linear algebra Stats is a non-starter without calculus. You'd just be doing the "ram a bunch of rules for derivation

> A broad base of at least some of stats, linear algebra Stats is a non-starter without calculus. You'd just be doing the "ram a bunch of rules for derivation and integration into your head." method since first principles require calculus. Linear algebra is less reliant on calculus, but the fun stuff still requires calculus. I learned basic linear algebra in high school for what it's worth, just enough to solve systems of linear equations.

majormajor 4y ago
No, you could focus on the applications of those rules, of which there are more in day to day life. If I see a car's speedometer moving, I don't need to be able to figure out how long it would take to travel a certain distance. But dealing with infrequent events in a smarter way? Super useful. Teach it the way you suggest and it would just be another useless math class that people would tune out of instead of grounding it in their everyday life experiences. ("Deriving from first principles" isn't the interesting stuff about calculus, either. And we're not requiring quantum physics to derive gravity from first principles in high school...)
Agentlien 4y ago
Tangentially related to this discussion but I'm curious what you consider "the fun stuff"? I use linear algebra every day in my work as a graphics programmer. A huge portion of what I do depends on it. While I frequently need calculus it's still a minority of the time. Derivates obviously show up everywhere: velocity, acceleration, gradients, ... But it seems to me only the narrow portion relating to physically-based rendering or simulation requires an understanding of integrals. At the moment I can mainly think of how it's used to define continuous functions before introducing the discretization used to actually compute them.
zoolily 4y ago
The use of calculus in introductory statistics is a historical artifact. Before computers, it was easier to use mathematical models like probability distributions than to do resampling. With computers, it's easy and more intuitive to use a resampling approach and textbooks that use such approaches are becoming more common. OpenIntro's Introduction to Modern Statistics is a free textbook of that type. You can find it at https://openintro-ims.netlify.app/ https://openintro-ims.netlify.app/

majormajor 4y ago

No, you could focus on the applications of those rules, of which there are more in day to day life. If I see a car's speedometer moving, I don't need to be able to figure out how long it would take to travel a certain distance. But dealing with infrequent events in a smarter way? Super useful. Teach it the way you suggest and it would just be another useless math class that people would tune out of instead of grounding it in their everyday life experiences. ("Deriving from first principles" isn't the interesting stuff about calculus, either. And we're not requiring quantum physics to derive gravity from first principles in high school...)

Agentlien 4y ago

Tangentially related to this discussion but I'm curious what you consider "the fun stuff"? I use linear algebra every day in my work as a graphics programmer. A huge portion of what I do depends on it. While I frequently need calculus it's still a minority of the time. Derivates obviously show up everywhere: velocity, acceleration, gradients, ... But it seems to me only the narrow portion relating to physically-based rendering or simulation requires an understanding of integrals. At the moment I can mainly think of how it's used to define continuous functions before introducing the discretization used to actually compute them.

zoolily 4y ago

The use of calculus in introductory statistics is a historical artifact. Before computers, it was easier to use mathematical models like probability distributions than to do resampling. With computers, it's easy and more intuitive to use a resampling approach and textbooks that use such approaches are becoming more common. OpenIntro's Introduction to Modern Statistics is a free textbook of that type. You can find it at https://openintro-ims.netlify.app/ https://openintro-ims.netlify.app/