What are some applications of sets & relations in science/business/tech that a highschooler can understand? To kindle a young mind, what examples can be given?

Tia English
2022-10-02
Answered

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Jaylyn George

Answered 2022-10-03
Author has **6** answers

Well, I would not say there are none, but it is understandably naive to expect that there are going to be direct applications which the «young mind» will be able to understand. From such a basic notion as «sets and relations» to an actual real life application there are layers and layers of abstraction, of concrete application of abstract ideas, and what not. To pick a random example from an answer below, it is rather silly to say that digital electronics is an application of sets and relations—like saying that the Golden Gate bridge is an example of the applications of water, which was though surely involved in many ways in the construction of the bridge.

Sets and relations are part of the background on which modern mathematics is built, and as such takes part in essentially everything we do. So if you want examples point to your cellular phone, to the traffic lights, to the search box in eBay, to the stock market, to a satellite, &c.

Sets and relations are part of the background on which modern mathematics is built, and as such takes part in essentially everything we do. So if you want examples point to your cellular phone, to the traffic lights, to the search box in eBay, to the stock market, to a satellite, &c.

asked 2021-01-31

The centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and Questions Navigation Menu preliminary estimate of the proportion who smoke of .26.

a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02?(to the nearest whole number) Use 95% confidence.

b) Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c) What is the 95% confidence interval for the proportion of smokers in the population?(to 4 decimals)?

a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02?(to the nearest whole number) Use 95% confidence.

b) Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c) What is the 95% confidence interval for the proportion of smokers in the population?(to 4 decimals)?

asked 2022-11-03

Initial-value problem for non-linear partial differential equation ${y}_{x}^{2}=k/{y}_{t}^{2}-1$

For this problem, y is a function of two variables: one space variable x and one time variable t.

k>0 is some constant.

And x takes is value in the interval [0,1] and $t\ge 0$

At the initial time, y follows a parabolic profile, like $y(x,0)=1-(x-\frac{1}{2}{)}^{2}$

Finally, y satisfies this PDE:

$${\left(\frac{\mathrm{\partial}y}{\mathrm{\partial}x}\right)}^{2}=\frac{k}{{\left(\frac{\mathrm{\partial}y}{\mathrm{\partial}t}\right)}^{2}}-1.$$

Does anyone have an idea how to solve this problem (and find the expression of y(x,t)) ?

About: The problem arise in physics, when studying the temporal shift of a front of iron particles in a magnetic field.

For this problem, y is a function of two variables: one space variable x and one time variable t.

k>0 is some constant.

And x takes is value in the interval [0,1] and $t\ge 0$

At the initial time, y follows a parabolic profile, like $y(x,0)=1-(x-\frac{1}{2}{)}^{2}$

Finally, y satisfies this PDE:

$${\left(\frac{\mathrm{\partial}y}{\mathrm{\partial}x}\right)}^{2}=\frac{k}{{\left(\frac{\mathrm{\partial}y}{\mathrm{\partial}t}\right)}^{2}}-1.$$

Does anyone have an idea how to solve this problem (and find the expression of y(x,t)) ?

About: The problem arise in physics, when studying the temporal shift of a front of iron particles in a magnetic field.

asked 2020-12-30

Whether the given study is observational or designed experiment and the reason.

asked 2022-11-10

Should I go back and start with a more "proof" based approach?

I should go to a book like the one by Spivak which is entirely different from the book used for my course, and learn or in a way re-learn it the way it's presented in that book?

Would a more proof based approach help me in this understanding? Will I always lack some aspect of understanding if I don't know how to prove these problems?

To quote one of the comments on this question, the question can also be put

"will studying calculus in a proof based manner help in understanding the techniques I've already learned"

I should go to a book like the one by Spivak which is entirely different from the book used for my course, and learn or in a way re-learn it the way it's presented in that book?

Would a more proof based approach help me in this understanding? Will I always lack some aspect of understanding if I don't know how to prove these problems?

To quote one of the comments on this question, the question can also be put

"will studying calculus in a proof based manner help in understanding the techniques I've already learned"

asked 2022-10-30

What can we conclude from correlation?

I just got my statistics test back and I am totally confused about one of the questions!

A study was done that took a simple random sample of 40 people and measured whether the subjects were right-handed or left-handed, as well as their ages. The study showed that the proportion of left-handed people and the ages had a strong negative correlation. What can we conclude?

Explain your answer.

I know that we can't conclude that getting older causes people to become right-handed. Something else might be causing it, not the age. If two things are correlated, we can only conclude association, not causation. So I wrote:

We can conclude that many people become right-handed as they grow older, but we cannot tell why.

That's exactly what association means, but my teacher marked me wrong! What mistake did I make? Is 40 too small of a sample size to make any conclusions?

I just got my statistics test back and I am totally confused about one of the questions!

A study was done that took a simple random sample of 40 people and measured whether the subjects were right-handed or left-handed, as well as their ages. The study showed that the proportion of left-handed people and the ages had a strong negative correlation. What can we conclude?

Explain your answer.

I know that we can't conclude that getting older causes people to become right-handed. Something else might be causing it, not the age. If two things are correlated, we can only conclude association, not causation. So I wrote:

We can conclude that many people become right-handed as they grow older, but we cannot tell why.

That's exactly what association means, but my teacher marked me wrong! What mistake did I make? Is 40 too small of a sample size to make any conclusions?

asked 2020-11-30

Which graphic display can be key in communicating complex study protocols?

A) CONSORT charts

B) Bubble map

C) Stem plots

D) Study outline

A) CONSORT charts

B) Bubble map

C) Stem plots

D) Study outline

asked 2022-09-07

Multiple Choice: What is the design for this experiment?

The prompt is the following: A biology student wants to determine if using a fertilizer would help promote the growth of new babies in spider plants. The student has access to 90 baby spider plants of three varieties: green, variegated, and curly. There are 30 plants of each variety. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. The numbers 1–30 are written on slips of paper, placed in a hat, and mixed thoroughly. A plant is selected and a slip of paper is drawn. If the slip has the numbers 1–15, then the plant will receive fertilizer. If the slip has the numbers 16–30, the plant will not receive fertilizer. A green spider plant is selected and a slip of paper is drawn. This plant is placed in the treatment group indicated by the number, and the slip is not put back in the bag. The slips are mixed again, the next green spider plant is selected, and a slip is drawn. The plant is placed in the treatment group indicated by the number. This procedure is repeated until all 30 green spider plants are assigned to treatments. The numbered slips are placed back in the bag and this procedure is repeated for the remaining types of spider plants. After one year, the shoots will be counted for each plant.

The answer choices are as follows:

A. observational study

B. matched pairs design

C. randomized block design

D. completely randomized design

My solution: My guess is C. In this case, the matched pair is when each experimental unit receives both treatments in random order, and the participants were separated into the yoga or meditation group by a flip of the coin. In A, I do not think that it is a matched pair because each person was asked their stress level. I rule out D as well, because I do think this is a matched pairs design.

The prompt is the following: A biology student wants to determine if using a fertilizer would help promote the growth of new babies in spider plants. The student has access to 90 baby spider plants of three varieties: green, variegated, and curly. There are 30 plants of each variety. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. The numbers 1–30 are written on slips of paper, placed in a hat, and mixed thoroughly. A plant is selected and a slip of paper is drawn. If the slip has the numbers 1–15, then the plant will receive fertilizer. If the slip has the numbers 16–30, the plant will not receive fertilizer. A green spider plant is selected and a slip of paper is drawn. This plant is placed in the treatment group indicated by the number, and the slip is not put back in the bag. The slips are mixed again, the next green spider plant is selected, and a slip is drawn. The plant is placed in the treatment group indicated by the number. This procedure is repeated until all 30 green spider plants are assigned to treatments. The numbered slips are placed back in the bag and this procedure is repeated for the remaining types of spider plants. After one year, the shoots will be counted for each plant.

The answer choices are as follows:

A. observational study

B. matched pairs design

C. randomized block design

D. completely randomized design

My solution: My guess is C. In this case, the matched pair is when each experimental unit receives both treatments in random order, and the participants were separated into the yoga or meditation group by a flip of the coin. In A, I do not think that it is a matched pair because each person was asked their stress level. I rule out D as well, because I do think this is a matched pairs design.