Quantitative and Qualitative Study Design Examples

Recent questions in Study design
High school statisticsAnswered question
Goundoubuf Goundoubuf 2022-11-23

i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?
historical past/issues:
My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.
i have taught this magnificence three times earlier than. (a part of the purpose that i'm posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik's dice.
the students' math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren't. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed "pre-calculus": trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.
So, any ideas? preferably, i'd like to find some thing a bit "sexy" (like the Rubik's cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of "see" institution idea on the cube became pretty popular.
(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)

High school statisticsAnswered question
clealtAfforcewug clealtAfforcewug 2022-11-06

What kind of mathematical "discoveries" have enabled mankind to build modern computers?
After studying the very thrilling Examples of mathematical discoveries which had been saved as a mystery I got here to think of something: maximum math discoveries appear to had been made centuries ago, and with Pascal and Leibniz we already had machines that would add and multiply (a few don't forget them as the first computer systems). Of direction modern computer systems needed energy and electric signals that can be transformed to at least one's and zero's, but those we've since the 19th century. First computer systems were also built with transistors, however we've the ones since the 1940's.
current computers are, at their center, not so extraordinary from the primary computer systems that followed the Von Neumann structure (with its arithmetic-logic unit). this is: they understand how move information from one place to any other, the way to upload and a way to multiply, in addition to perform logical operations (and, or, xor, now not), and from that they get all of the other operations (some can substract, divide and do some different stuff, however it is all very primitive in that sense). Of path, current computers paintings at a miles better level than their predecessors: while inside the beginning programming needed to be accomplished the use of commands composed of zero's and 1's or, in the event that they were lucky, the usage of meeting language, now we have high stage programming languages that (to say it kind of) enclose a group of these single commands into one high stage command.
And when I see pretty graphics in video-games, programs like photoshop, 3D rendering, CAD programs and such, I always think of all the calculus stuff I learned and how it must be applied to achieve those wonderful results.
And this is where my question arises: all of this mathematical knowledge has been available to us for way longer than computers existed. So, are there any modern mathematical discoveries that enabled the giant leap we took from the first computers we had in the 40's to what we have now? Or maybe old math started being applied in a different way at some point in time?

High school statisticsAnswered question
Jorge Schmitt Jorge Schmitt 2022-11-02

Probability question. Find the probability that the data set falls within 45% to 52% of the data set
one of your employees has cautioned that your enterprise expand a brand new product. A survey is designed to have a look at whether or not or not there may be hobby inside the new product. The reaction is on a 1 to five scale with 1 indicating without a doubt could no longer buy, · · ·, and 5 indicating absolutely could purchase. For an preliminary analysis, you will document the responses 1, 2, and 3 as No, and 4 and 5 as yes.
a. five people are surveyed. what is the opportunity that as a minimum three of them replied sure?
b. 100 people are surveyed. what's the approximate possibility that between 45% to fifty two% of people answered sure?
For component a) There are 5 choices that human beings can respond by way of 1, 2 ,three ,4 and five. when you consider that 1, 2 and three are considered "No", the possibility of a person answering "No" is three/five. For choices four and 4, the probability of a person responding with this is 2/5.
This seems like it fallows a binomial distribution so I calculated the chance of P(three) + P(four) + P(five).
but for component b), i'm stressed. i will calculate the chance of a person pronouncing sure but I do not know how to calculate the chance that a percentage of people announcing sure. Does absolutely everyone recognize how to technique this question? I though approximately the use of the Z table, however that already calculates region.

High school statisticsAnswered question
Marlene Brooks Marlene Brooks 2022-10-31

Finding the function of a parabolic curve between two tangents
Alright folks, first question here so let me make the situation and background clear.
I'm attempting to start studying for aerospace engineering, so I'm working on improving on my math skills as we speak, but couldn't help "jumping in" to some of the design and starting to look at it. I'm not adverse to algebra, although my calculus legs haven't been walked on in awhile, which is why I haven't been able to get farther myself on my own question.
Another side reason is that I'm attempting to get the gist of equation-based curves in CAD, so rocket engine nozzle curves are perfect for learning that...if I can figure out the equations!
If the format or my thoughts seem a bit off, I have an idea of the concepts in play here, my math skills have just atrophied a little too much for my own comfort.
What I'm working with is the G.V.R. Rao approximation of a bell nozzle curve; essentially,
f c = { 0.382 R t For divergent throat curve f p Main body
Where f p starts from a point with a tangent of angle θ n and ends at a point with a tangent of angle θ e . f p also has to fit in a region equal to L f 0.382 R t , where L f is the complete distance between the throat and exit plane, so the displacement in the x- or y-axis, depending on how you view the rocket (orientation-wise).
I do know how to differentiate the curve f p to get f p and then find the angle of the slope at a point, but this is backsolving from two slopes to find the region in between.
If it's any help, ideally I'd be constructing the nozzle in CAD vertically, that is, y n > y e
What I'm looking for is help toward the derivation of a formula that allows me to construct a curve that is smooth between the two points. One of the reasons I've had a hard time figuring out the exact parameters is because it feels a lot like curve-fitting, which I haven't had much experience with.
If anyone can help break it down for me, it'd be much appreciated but if the question turns out to be too vague, references to places where I can get the requisite learning would be also appreciated.

High school statisticsAnswered question
Tessa Peters Tessa Peters 2022-10-30

What Are R-Modules Used For?
Kind of a simple question, but what exactly are R-modules used for? Do they have any engineering applications?
I am a graduate student researcher in computer architecture, a subfield of computer engineering. Specifically, I do research on the best way to build future general purpose processors
One thing I am looking into is if it is possible to apply mathematics to improve the design of CPUs. That is, can we use concepts from mathematics to improve the execution of general purpose programs on hardware. CPUs are a massive engineering design problem, and where exactly we could improve the design by applying math isn't entirely clear.
What I don't have is a very deep mathematical background. I have taken an introductory abstract algebra course and one in coding theory. I've also read a number of coding theory papers...
I know that other electrical engineering subfields like communications and compressed sensing have successfully applied elements of linear algebra and abstract algebra and have gotten very good results.
The fact that this particular question spans both engineering and mathematics makes it both hard to formulate and to discuss with people. I'd be happy to talk about it in more detail, but I'm not entirely sure what the best forum would be for that.
At least for now, I figured a good place to start would be to see if other people have successfully used some of the more abstract math concepts in engineering systems. One of the few I am aware of are R-modules, so I figured I'd ask if anyone knows of some engineering uses of them...

When you are dealing with statistics and probability as a college student or need to solve some questions for your school class, the study design is an interesting concept to consider. The most important is to design and structure your statistical data. Start with the study design questions that must be answered by taking notes and explaining why you have taken a specific methodology. It will help you to narrow things down and avoid serving several statistical methods that can either make things simpler or even more complex. The study design example that you choose should serve as the template only as you should keep things unique! For example, when you need finding Y intercept