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mathwonk

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Well i don't know you and it is of course quite possible that everything you say is correct, DR13. If so however, then you are very different from almost all the students I have met in my professional career lasting over 40 years. In all that time i have seldom met any students at all, who understand even a modicum of calculus, no matter what score they obtained on BC/AP tests and classes.

They were often deceived into thinking they understood college level calculus however because most colleges have had to dumb down their courses to accommodate these AP students. Hence although high school AP students do not understand calculus at what used to be a college level, colleges have lowered the level of their classes so as to prevent all these students from failing.

In the present day curriculum, we now offer three or four different college classes in calculus, at different levels. For the most gifted students, the best advice I can give them is to take calculus again from the beginning in college, but take it in a high level honors class, so as to get the deepest experience of it. I.e. to take a "Spivak style" class.

The reason a student should not take college credit for AP calculus and then begin in sophomore calculus is that he will have moved himself from an honors level high school course to a non honors level college course. I.e. there are almost no (you could of course be another of the one or two exceptions I have met in 30 years) graduating high school AP students who are qualified to begin college in a second honors level calculus class, i.e. a course from say Apostol volume 2, or from Loomis and Sternberg.

The few exceptions tend to wind up at Harvard or MIT, and have prepared by taking genuine college level classes in high school from real colleges, or from super high schools like Exeter and Andover, or the Bronx high school of science.

Hence NOT starting in a first year honors level college calculus class in college is usually doing yourself a disfavor, and lowering the level of your education. I.e. if you take the regular second year course you are likely qualified for, you will never again be able to enter the honors level work and you will never learn it, and you will likely never achieve the level of preparation needed to become a professional mathematician, if that is one of your possible goals.

Here is a little test for you: did you learn to prove that a continuous function on a closed bounded interval has a maximum in your high school AP class? This was covered in the first semester of my college class when I was a student, and I taught it in my first semester honors class at an average state university, not the higher level first semester Spivak class, just the class for people who had done well in AP courses.

Easier: can you state and prove the fundamental theorem of calculus? I teach this even in my non honors classes in college. Of course if you can really do these things, then indeed you have learned a lot in your high school classes and your preparation is unusual. But very few students at my university have this preparation from high school. It is certainly not included in the usual AP syllabus or tests I have seen.

They were often deceived into thinking they understood college level calculus however because most colleges have had to dumb down their courses to accommodate these AP students. Hence although high school AP students do not understand calculus at what used to be a college level, colleges have lowered the level of their classes so as to prevent all these students from failing.

In the present day curriculum, we now offer three or four different college classes in calculus, at different levels. For the most gifted students, the best advice I can give them is to take calculus again from the beginning in college, but take it in a high level honors class, so as to get the deepest experience of it. I.e. to take a "Spivak style" class.

The reason a student should not take college credit for AP calculus and then begin in sophomore calculus is that he will have moved himself from an honors level high school course to a non honors level college course. I.e. there are almost no (you could of course be another of the one or two exceptions I have met in 30 years) graduating high school AP students who are qualified to begin college in a second honors level calculus class, i.e. a course from say Apostol volume 2, or from Loomis and Sternberg.

The few exceptions tend to wind up at Harvard or MIT, and have prepared by taking genuine college level classes in high school from real colleges, or from super high schools like Exeter and Andover, or the Bronx high school of science.

Hence NOT starting in a first year honors level college calculus class in college is usually doing yourself a disfavor, and lowering the level of your education. I.e. if you take the regular second year course you are likely qualified for, you will never again be able to enter the honors level work and you will never learn it, and you will likely never achieve the level of preparation needed to become a professional mathematician, if that is one of your possible goals.

Here is a little test for you: did you learn to prove that a continuous function on a closed bounded interval has a maximum in your high school AP class? This was covered in the first semester of my college class when I was a student, and I taught it in my first semester honors class at an average state university, not the higher level first semester Spivak class, just the class for people who had done well in AP courses.

Easier: can you state and prove the fundamental theorem of calculus? I teach this even in my non honors classes in college. Of course if you can really do these things, then indeed you have learned a lot in your high school classes and your preparation is unusual. But very few students at my university have this preparation from high school. It is certainly not included in the usual AP syllabus or tests I have seen.

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