3 ms·

When do you people in the US start to learn about integrals? Is it expected that a first-year undergraduate student already has the knowledge to understand the

When do you people in the US start to learn about integrals? Is it expected that a first-year undergraduate student already has the knowledge to understand the book? I don't have the required "prerequisites" as the GP puts it to understand the book, but I should :( and it might shame me into studying a bit :) (then again, I probably won't)

deleted 16y ago
[deleted]
acangiano 16y ago
I started doing integrals on my own when I was 14 (grade 9), but my classmates didn't learn about integrals until grade 13. This was in Italy however, and I'm not sure about when they're introduced to students in the States. I can tell you though, that a first year undergraduate student at a scientific faculty shouldn't be overly worried about approaching a book like this.
golwengaud 16y ago
(Single) integrals are freshman calculus, which is nominally taught in the first year of university. In reality, my experience is that many students (and, I would guess most science/engineering/math majors) take AP calculus during their last year of high school (17-18 years old), and proceed to differential equations, multivariable calculus, or whatever is next in their major's sequence during the first year of university.
- GFischer 16y ago
  Thanks for the answers. For all the flak US education receives, the option of taking AP classes sounds good (and it gives college credits, which is even better!). From your post I could find http://en.wikipedia.org/wiki/Advanced_Placement_Calculus http://en.wikipedia.org/wiki/Advanced_Placement_Calculus which shows that AP Calculus does indeed include integrals.
  - jgg 16y ago
    Thanks for the answers. For all the flak US education receives, the option of taking AP classes sounds good (and it gives college credits, which is even better!). This is utterly derailing the main topic of conversation, but... I know that a lot of mathematicians dislike AP Calculus. The original thinking was that Calculus couldn't be taught to highschoolers, so you waited until University to take it. Aspiring mathematicians would take a rigorous, proof-based Caclulus course, which would prepare them to tackle harder subjects in the future. Everyone else (engineers, chemists, physicists, etc.) would take a more general/applied course. Now, all but a handful of universities offer such courses, under the assumption that anyone who wants to be a mathematician has surely taken AP Caclulus. So the idea of proof-based Calc. for future mathematicians has been lost in transition, and the end result is that you have kids hitting Multivariate Calculus and Differential Equations who haven't seen a proof in their lives. The current AP Calculus courses are 99% computation. I was challenged while working through Spviak's book with no teacher guidance in highschool, but I scored a perfect 5 on the AP test with little effort.
    - mturmon 16y ago
      In short, the lack of a proof-based class renders students Calc-clueless. (groan) This happened to me. I went straight from high school calc into college differential equations because the AP score allowed me. It took a Rudin-based analysis course, much later, for me to appreciate proofs of convergence or epsilon-delta arguments, because my H.S. calc did not have them, and the college diff-eq assumed you knew them already. The shock was painful. Eventually though, you learn what you need to know.
      - jgg 16y ago
        It took a Rudin-based analysis course, much later, for me to appreciate proofs of convergence or epsilon-delta arguments, because my H.S. calc did not have them, and the college diff-eq assumed you knew them already. The shock was painful. I have yet to take a course that uses the so-called "terse little blue book from hell". (: Eventually though, you learn what you need to know. Indeed, although I wonder about people becoming discouraged about being mathematicians simply because they've been misled for so long about what's on the "other side" of college math.
mhd 16y ago
I think for most of us the better question is: How soon do you start forgetting all the required details about integrals...

deleted 16y ago

[deleted]

acangiano 16y ago

I started doing integrals on my own when I was 14 (grade 9), but my classmates didn't learn about integrals until grade 13. This was in Italy however, and I'm not sure about when they're introduced to students in the States. I can tell you though, that a first year undergraduate student at a scientific faculty shouldn't be overly worried about approaching a book like this.

golwengaud 16y ago

(Single) integrals are freshman calculus, which is nominally taught in the first year of university. In reality, my experience is that many students (and, I would guess most science/engineering/math majors) take AP calculus during their last year of high school (17-18 years old), and proceed to differential equations, multivariable calculus, or whatever is next in their major's sequence during the first year of university.

GFischer 16y ago
Thanks for the answers. For all the flak US education receives, the option of taking AP classes sounds good (and it gives college credits, which is even better!). From your post I could find http://en.wikipedia.org/wiki/Advanced_Placement_Calculus http://en.wikipedia.org/wiki/Advanced_Placement_Calculus which shows that AP Calculus does indeed include integrals.
- jgg 16y ago
  Thanks for the answers. For all the flak US education receives, the option of taking AP classes sounds good (and it gives college credits, which is even better!). This is utterly derailing the main topic of conversation, but... I know that a lot of mathematicians dislike AP Calculus. The original thinking was that Calculus couldn't be taught to highschoolers, so you waited until University to take it. Aspiring mathematicians would take a rigorous, proof-based Caclulus course, which would prepare them to tackle harder subjects in the future. Everyone else (engineers, chemists, physicists, etc.) would take a more general/applied course. Now, all but a handful of universities offer such courses, under the assumption that anyone who wants to be a mathematician has surely taken AP Caclulus. So the idea of proof-based Calc. for future mathematicians has been lost in transition, and the end result is that you have kids hitting Multivariate Calculus and Differential Equations who haven't seen a proof in their lives. The current AP Calculus courses are 99% computation. I was challenged while working through Spviak's book with no teacher guidance in highschool, but I scored a perfect 5 on the AP test with little effort.
  - mturmon 16y ago
    In short, the lack of a proof-based class renders students Calc-clueless. (groan) This happened to me. I went straight from high school calc into college differential equations because the AP score allowed me. It took a Rudin-based analysis course, much later, for me to appreciate proofs of convergence or epsilon-delta arguments, because my H.S. calc did not have them, and the college diff-eq assumed you knew them already. The shock was painful. Eventually though, you learn what you need to know.
    - jgg 16y ago
      It took a Rudin-based analysis course, much later, for me to appreciate proofs of convergence or epsilon-delta arguments, because my H.S. calc did not have them, and the college diff-eq assumed you knew them already. The shock was painful. I have yet to take a course that uses the so-called "terse little blue book from hell". (: Eventually though, you learn what you need to know. Indeed, although I wonder about people becoming discouraged about being mathematicians simply because they've been misled for so long about what's on the "other side" of college math.

mhd 16y ago

I think for most of us the better question is: How soon do you start forgetting all the required details about integrals...