The Glade 4.0

Indeed. And even if it was with respect to x, it should be

(1/3)*x^3 + 3*x + C

Alternatively, since x wasn't specified, it could be

(x^2+3)*a + C.

_________________
"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

If you hold x constant.

If you had:

y=x^2 +3

If z is a function of x or y and you are integrating wrt to z, then it becomes much more complicated. Otherwise, yes, you can hold x and y constant and integrate wrt a third variable. The solution, I believe would be:

yz = z(x^2 + 3) + C (where the constants of integration are grouped into C).

But only if z is constant (not a function) of x and y.

_________________
"It's real, grew up in trife life, the times of white lines
The hype vice, murderous nighttimes and knife fights invite crimes" - Nasir Jones

Khross is not a mathematician. It is very likely he had not considered that the variable of integration is left unspecified.

Xeq, both of your introductory statements are categorically false. Science and math are not more difficult than they were a hundred years ago. The math topics that are covered in algebra are, for the most part, the same. The difference is that now there are more topics - something which is totally irrelevant to the algebra student. We now have tensor analysis, which did not exist in the 1800s (but did in the 1900s). This means nothing to an algebra student. You do not learn about tensors in algebra. Likewise, it means nothing to the calculus student because you do not learn about tensors in calculus. Science is the same way. Quantum mechanics does not make physics 1 harder. We do not teach quantum mechanics in physics 1. We teach classical Newtonian mechanics, and Newton's laws have not changed.

_________________
Buckle your pants or they might fall down.

In fairness, it's very possible he may have meant "more complex" instead of "more difficult," as many people hold those to be synonymous (whether they are or aren't).

_________________
“The duty of a patriot is to protect his country from its government.” - Thomas Paine

Yes, but those developments in those fields aren't anything that affect 95+% of the undergraduate population. Everything I've learned has been around for hundreds of years.

_________________
"It's real, grew up in trife life, the times of white lines
The hype vice, murderous nighttimes and knife fights invite crimes" - Nasir Jones

I'm not refuting that. I'm simply saying that Xeq may have "mis-spoke."

_________________
“The duty of a patriot is to protect his country from its government.” - Thomas Paine

Ok, maybe the straight introductory classes haven't changed much, but even that's not absolute. I definitely learned about time dilation and relativity in Intro to Physics, and that's not 100 years old yet.

But when I said "math and science aren't easier now than they were 100 years ago," I didn't just mean the introductory classes. Someone with an undergrad degree in biology, chemistry, math, or physics has to learn a lot more about those subjects than someone with one of those degrees did 100 years ago. It's harder. I mean, PCR isn't even 25 years old yet and I certainly learned about that for my bio degree, as it obsoleted a large number of standard biology techniques when it was introduced.

The main change between now and then was that back then if you wanted a degree, you had to learn the quadrivium, the fine arts, and Latin, and far more in depth than the intro to chemistry class they make math majors take now. Colleges are just cutting back on courses that don't have practical application. I imagine this makes degrees a lot easier to get, as learning things outside of your area of interest is far harder than learning in your chosen field. The hardest classes for me in college by far were the English classes, there is no comparison.

PCR is a specific technique that allows you to increase sample sizes of specific DNA sequences right?

_________________

To the contrary, I suspect most colleges are extending the "freshman" introductory classes to standardize the undergraduate learning experience at the expense of field specific classes, and those field specific classes are getting shifted in "professional" degree programs, such as Masters programs.

Undergraduate degrees have filled the gap left by high school education when HS became remedial years for what should have been learned in middle schools.

I find it very difficult to believe that the majority of eighth graders can conceivably master Calculus I. There's no way to do this without resorting to an extreme version of the German or Japanese educational system where successful students are expected to make school their entire lives and starts tracking the "failures" who can't handle this extreme load towards menial jobs as early as age 13.

Also, the German economic system makes me think this chain of events is unlikely. If you think an undergraduate degree is too necessary in the US, then, well, you've never been to Germany. There is a massive glass ceiling in virtually every line of employment for those who do not have one. In the US, you might get hired on the basis of experience with no degree. In Germany, this does not happen, ever. No degree, no job. If your papers are not in order you are ****, sorry. That's why German schools drive the kids so hard, everyone KNOWS that if you fail to get that college degree, it's a dead end for your life there.

Yes, basically the DNA strand you want to replicate is put in a test tube with DNA polymerase and free nucleotides. You heat the solution to seperate the DNA strands, and then upon cooling the DNA polymerase adds a complement strand to each free strand, doubling the amount of DNA every cycle.

This has been known to be theoretically possible for decades, the major breakthrough was discovering heat-resistant DNA polymerase in thermophilic bacteria that could survive the temperature needed to seperate the DNA strands, so the entire process could be automated. Before that, you had to manually add more DNA polymerase in between every cycle, which made it very tedious and expensive.

At no point in my post did I suggest any such thing, so I don't see the point behind this post of yours.

You said "high school became remedial years for what should have been learned in middle school." Since calculus IS taught in American high schools, you're arguing that it should be (or would have been, if our system worked like it "used to") taught in middle schools instead.

I don't think he meant all four years of high school education should be compressed into middle school.

_________________
The Dude abides.

Calculus is taught in high school, but its generally an AP/IB class and certainly not part of the core curriculum for graduation in public schools, unlike Algebra/Geometry. Primarily because Calculus isn't required or used on the standardized tests for graduation/school evaluations.

I think this is accurate. There is much more specialization today than there was years ago. I think there is an argument to be made that in some ways our education today has become more broad but less deep on certain topics.