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I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I stru

I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning calculus (I also never took any "prealgebra" and managed algebra just fine). I can't even imagine what a pre{calculus,algebra} course would possibly teach.

maxerickson 12y ago
They introduce some of the fundamental concepts of the later courses (and try to tie them into previous knowledge). In the U.S. system, they also serve as a review, I guess with the hope of shoring up knowledge that students were missing (but I think such an approach for math education is pretty optimistic; figuring out what they don't know and fixing that must be more valuable than just showing them things again).
hga 12y ago
Precalculus as I'm using it is a level of math, not a particular course (although there are of course courses with that title). In addition to what you learned in high school, assuming your Algebra II was like mine, plenty of analytic geometry, it would also include trigonometry. To do as well as you did, you obviously picked that up on your own, as did I. (While in theory I took a trig and further analytic geometry course in high school, followed by a semester of the calculus, the teacher flatly refused to teach anything, and trig at that level in that textbook was absolutely boring and unmotivated (e.g. didn't mention you needed it to do calculus on rotation including AC electricity); I only stayed in these automatic A courses so I'd have them on my transcript (I'd already taken my first go at the calculus in a summer course taught at a university before this, but focused most of my attention on a PDP-11/70 running UNIX(TM) Version 6, which ended up being infinitely more valuable (as it turned out, perhaps lifesaving; the introductory programming class that was my excuse for using it was easy, so I focused on UNIX(TM), Adventure and other games, wandering around the filesystem (very much like Adventure :-), software engineering, helping others debug their final class project, and using nroff for my class project which had more exposition on software engineering than code; included that in my college applications)). Expanding on maxerickson's comment, I gather formal precalculus courses also start teaching you about limits and stuff like that; since basic differentiation, especially speed and acceleration, is relatively simple, I'd hope it would teach an intro to that, which goes along nicely with the limits. It could also be a fancy name for a (further) analytic geometry course, and/or include trig motivated by the calculus vs., oh, surveying.
- groovy2shoes 12y ago
  Thanks for the clarification. I changed schools a few times growing up and "missed out" on some actual courses called "prealgebra" and "precalculus", which lead to my assumption. I think what really helped me pick up different branches of math was actually getting the motivation from somewhere. My learning of Discrete Math was fueled by my interest in programming; for Calculus it was the neat applications in Physics. Calculating for calculation's sake was always pretty boring, and I'd tune out without some other kind of applicable motivation. By the sounds of it, I'm much younger than you (having attended high school in the mid-2000s), but it's interesting that I did pretty similar stuff when I was bored in school. I wrote more than a couple of essays using groff just for the hell of it. Good times :)
  - hga 12y ago
    You're very welcome, and indeed, back in my days, late '70s for high school, not only did we have to walk uphill both ways in snow to get there, but the computer programming course was taught in conjunction with the local college, probably the same course they used. It was punched card FORTRAN "IV" on an IBM 1130 (scare quotes because IBM's definition of FORTRAN IV was so permissive this compiler only have numeric ifs; that is, an if statement evaluated an expression and it had three lines it would goto if negative, 0 or positive). It wasn't as bad as it might sound; sure, punched cards were a bit of a pain, and we all knew they were obsolescent (1978-9), but then again it was a chance to learn how they did things when dinosaurs roamed the earth. But the neatest thing was no computer priesthood for this class: the main computer for the school was an 370/115 (360 series: revolutionary '60s architecture using discrete silicon transistors and core memory, the 370 series used ICs including for main memory (!), the -115 model was the lowest end/slowest, but it ran BASIC fine :-), and they leased the obsolescent 1130 and just put it in a corner. We'd put our cards in the card reader, hit go, hit the right buttons or whatever to break it out of an infinite loop if necessary, feed in a boot card if it got really confused, all under essentially no supervision, but good help, of the priesthood in the other corner of the room tending the mainframe. It also had a console, and an interactive program was one of the projects. Lots of people older than me also cut their teeth on the 1130, Wikipedia has a partial list: https://en.wikipedia.org/wiki/IBM_1130#Influence_of_the_1130 https://en.wikipedia.org/wiki/IBM_1130#Influence_of_the_1130 I wonder, if only the university library had a book on LISP; instead it had lots of good books on software engineering, which along with the programming taught me the basics. Like don't mix up '0' and 'O' in your variable names, especially if the first cut of the card deck is being produced by students learning how to do date entry from a coding form you filled out (http://www.atkielski.com/PDF/data/fortran.pdf http://www.atkielski.com/PDF/data/fortran.pdf). Whereas the DEC PDP-11/70 running UNIX(TM) I used was at a big university's summer school following that. And fortunately not at all loaded down then, and it was a very fast system, even had a fixed head disk for swapping. So in my case I was semi-bored with the introductory programming course (at the end the professor privately but nicely called me out for being a ringer), and wrote up the final project using nroff and a XEROX Daisywheel to counter that. Just because even primitive word processing that was extremely neat, and a lot better than typing out a paper in the previous summer on a Selectric typewriter with auto-erase, the best there was at the time.

maxerickson 12y ago

They introduce some of the fundamental concepts of the later courses (and try to tie them into previous knowledge). In the U.S. system, they also serve as a review, I guess with the hope of shoring up knowledge that students were missing (but I think such an approach for math education is pretty optimistic; figuring out what they don't know and fixing that must be more valuable than just showing them things again).

hga 12y ago

Precalculus as I'm using it is a level of math, not a particular course (although there are of course courses with that title). In addition to what you learned in high school, assuming your Algebra II was like mine, plenty of analytic geometry, it would also include trigonometry. To do as well as you did, you obviously picked that up on your own, as did I. (While in theory I took a trig and further analytic geometry course in high school, followed by a semester of the calculus, the teacher flatly refused to teach anything, and trig at that level in that textbook was absolutely boring and unmotivated (e.g. didn't mention you needed it to do calculus on rotation including AC electricity); I only stayed in these automatic A courses so I'd have them on my transcript (I'd already taken my first go at the calculus in a summer course taught at a university before this, but focused most of my attention on a PDP-11/70 running UNIX(TM) Version 6, which ended up being infinitely more valuable (as it turned out, perhaps lifesaving; the introductory programming class that was my excuse for using it was easy, so I focused on UNIX(TM), Adventure and other games, wandering around the filesystem (very much like Adventure :-), software engineering, helping others debug their final class project, and using nroff for my class project which had more exposition on software engineering than code; included that in my college applications)). Expanding on maxerickson's comment, I gather formal precalculus courses also start teaching you about limits and stuff like that; since basic differentiation, especially speed and acceleration, is relatively simple, I'd hope it would teach an intro to that, which goes along nicely with the limits. It could also be a fancy name for a (further) analytic geometry course, and/or include trig motivated by the calculus vs., oh, surveying.

groovy2shoes 12y ago
Thanks for the clarification. I changed schools a few times growing up and "missed out" on some actual courses called "prealgebra" and "precalculus", which lead to my assumption. I think what really helped me pick up different branches of math was actually getting the motivation from somewhere. My learning of Discrete Math was fueled by my interest in programming; for Calculus it was the neat applications in Physics. Calculating for calculation's sake was always pretty boring, and I'd tune out without some other kind of applicable motivation. By the sounds of it, I'm much younger than you (having attended high school in the mid-2000s), but it's interesting that I did pretty similar stuff when I was bored in school. I wrote more than a couple of essays using groff just for the hell of it. Good times :)
- hga 12y ago
  You're very welcome, and indeed, back in my days, late '70s for high school, not only did we have to walk uphill both ways in snow to get there, but the computer programming course was taught in conjunction with the local college, probably the same course they used. It was punched card FORTRAN "IV" on an IBM 1130 (scare quotes because IBM's definition of FORTRAN IV was so permissive this compiler only have numeric ifs; that is, an if statement evaluated an expression and it had three lines it would goto if negative, 0 or positive). It wasn't as bad as it might sound; sure, punched cards were a bit of a pain, and we all knew they were obsolescent (1978-9), but then again it was a chance to learn how they did things when dinosaurs roamed the earth. But the neatest thing was no computer priesthood for this class: the main computer for the school was an 370/115 (360 series: revolutionary '60s architecture using discrete silicon transistors and core memory, the 370 series used ICs including for main memory (!), the -115 model was the lowest end/slowest, but it ran BASIC fine :-), and they leased the obsolescent 1130 and just put it in a corner. We'd put our cards in the card reader, hit go, hit the right buttons or whatever to break it out of an infinite loop if necessary, feed in a boot card if it got really confused, all under essentially no supervision, but good help, of the priesthood in the other corner of the room tending the mainframe. It also had a console, and an interactive program was one of the projects. Lots of people older than me also cut their teeth on the 1130, Wikipedia has a partial list: https://en.wikipedia.org/wiki/IBM_1130#Influence_of_the_1130 https://en.wikipedia.org/wiki/IBM_1130#Influence_of_the_1130 I wonder, if only the university library had a book on LISP; instead it had lots of good books on software engineering, which along with the programming taught me the basics. Like don't mix up '0' and 'O' in your variable names, especially if the first cut of the card deck is being produced by students learning how to do date entry from a coding form you filled out (http://www.atkielski.com/PDF/data/fortran.pdf http://www.atkielski.com/PDF/data/fortran.pdf). Whereas the DEC PDP-11/70 running UNIX(TM) I used was at a big university's summer school following that. And fortunately not at all loaded down then, and it was a very fast system, even had a fixed head disk for swapping. So in my case I was semi-bored with the introductory programming course (at the end the professor privately but nicely called me out for being a ringer), and wrote up the final project using nroff and a XEROX Daisywheel to counter that. Just because even primitive word processing that was extremely neat, and a lot better than typing out a paper in the previous summer on a Selectric typewriter with auto-erase, the best there was at the time.