One semester down - Which class was the "nightmare" class?

[BCEagle91]

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<p>I think there may be a confusion in understanding here. Introductory
Calculus at the college level is typically either geared towards
engineering/physics/hard sciences, or towards others/business/soft
sciences. The non-science calculus (I termed it Calculus Lite when I
taught these courses) has virtually zero theory. No proofs to speak
of. You lay out the basic concepts, get the techniques down, and work
on applying them to various problems. Sometimes a school has a special
sequence “Calculus for Business Majors” which focuses the applications
on Revenue - cost - profit type applications.</p>

<p>The calculus for engineering and science majors has quite a bit of
theory and proofs, and is much more in depth across the spectrum of
functions (trig, logs, etc.). In my courses we used Leithold for 3
semesters.</p>

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<p>I don’t think that we have much disagreement here but there are
colleges that use Anton, Osterbee, and other for calculus for science
and engineering and those books don’t cover much theory. We could even
take a look at Gilbert Strangs’s calulus textbook where we find this:</p>

<p>“I want to say clearly: Mathematics is not formulas, or computations,
or even proofs, but ideas. The symbols and pictures are the language.
The book and the professor and the computer can join in teaching it.
The computer should be non-threatening (like this book and your
professor) - you can work at your own pace. Your part is to learn by
doing.”</p>

<p>I’m not familiar with Leithold - is it like Apostol or Spivak? I have
about 13 calculus texts at home dating back to the 1940s so I have a
little variety to look at.</p>

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<p>Virtually every college teaching this stuffs will have a similar
Lite/Not breakdown, although the non-science path typically is 1
course or maybe 2, while the engineer/science path is at least 4
courses. Neither of these sequences gets anywhere near real analysis,
which is at a whole 'nuther level, being solely theories and
proofs. You have to have had the intro courses before you can even get
near the real analysis level.</p>

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<p>What do you think of teaching the first chapter of Spivak to high-school
or even middle-school kids?</p>