<p>What “formula for average value” is there other than the integral divided by the length of the interval? </p>
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<p>MiamiDAP, colleges offer degrees in statistics. The first course in statistics will not be the formula-based, plug-and-chug statistics course that social science students take, but a course called Theory of Probability or some such, where students learn where the formulas came from. Students will need to compute average values of some fairly hairy functions. Students who can’t integrate an exponential need not apply.</p>
<p>There is a famous quote “A question that sometimes drives me hazy: am I or are the others crazy? – Albert Einstein”.
I don’t know but it seems people forget that Newton’s laws of motions are explained by calculus and they are the back bone of everyday actions/reactions.
From any mathematical modeling used in stock market to medical equipment producing the mapping of human bodies stem from applications of Calculus.
The computers that render graphics for you to look at the digital photographs to anything visual stunning has its basis in calculus.
Please it is true not everyone can understand Calculus and not everyone need to do it also. But if it was not there most of the things you are able to do and use won’t exists.</p>
<p>Yea, that’s what I thought. So why is the argument then Calculus versus Statistics then? What is so important about Calculus and Statistics that this is what the argument is over, and not like Calculus versus Algebra?</p>
<p>Some basic notions of algebra are covered in typical high school courses like Algebra I and Algebra II, which are taken by more students than Calculus courses.</p>
<p>The initial course to the field of algebra would be something like “Introduction to Algebraic Structures” or the like. This class is usually a bit difficult and abstract, and high school students would mostly struggle with it. IME, it’s a pretty common course for undergraduate math majors.</p>
<p>I don’t think it’d be a big disaster if such a class replaced Calculus for the advanced 12th grade seniors. It’s certainly an interesting area, and it’s a more “beautiful” subject than introductory calculus. The major downside is that it’s a lot less practical. All those future science and engineering majors have to learn calculus, but the overwhelming majority won’t ever touch abstract algebra again.</p>
<p>My family comes from Romania, and I know a little bit about the high school math curriculums there from my parents (at least the ones that were common in the 1970s and 1980s.) Math courses did not focus on one subject for an entire year - they integrated several different areas every year. Calculus was introduced in 11th grade and continued in 12th grade, but 12th grade math also introduced algebraic structures. I think this type of approach could be useful in the US as well - but it’s a pretty radical change. Additionally, Romania followed the European approach of having “focused” high schools. So the high schools with these math curricula were technical high schools geared toward future math, science, and engineering majors.</p>
<p>Another interesting compromise might be linear algebra. Linear algebra has many more practical applications than introductory abstract algebra, and many students do end up having to learn it. Introductory linear algebra courses are more or less matrix algebra, and a lot of the subject currently comes up in Algebra II, which is why I suppose that very few high schools bother offering a separate linear algebra course.</p>
<p>As abstract algebra is almost never offered in high school, most people really have no idea what it is. And since statistics is the main reason Social Studies can call themselves Social Sciences, it tends to be what a lot of people see as the most applicable “math subject.” Calculus is also an important part of the backbone of most physical sciences, so it is important for students in those areas.</p>