Questions tagged [education]

For math questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

Filter by
Sorted by
Tagged with
0
votes
1answer
20 views

How to find Cramer-Rao inequality

I trying to do this function. $$f(x\mid\theta)=\theta x^{\theta-1}, \;\;0<x<1,\,\,0<\theta<\infty.$$ I have finished finding my MLE. $$L(x,\theta) = \prod_{i=1}^n \theta x_i^{\theta-1} = \...
-1
votes
0answers
18 views

Help find cosine [closed]

I don’t quite understand how to solve this. $\cos \left(\frac{\pi}{3}+\alpha\right)$ given $\sin \alpha = \frac{1}{\sqrt 3}$ and $0 < \alpha < \frac{\pi}{2}$
0
votes
1answer
50 views

How can I find a linear transformation $\mathcal{T}$ that maps an ellipse to a circle?

Let $\mathcal{T}(x,y)=(x',y')$ be a linear transformation. The image of the ellipse $4x^2-4\sqrt{2}xy+11y^2=12$ under the transformation $\mathcal{T}$ is the circle $x'^2+y'^2=4$.
0
votes
0answers
23 views

Young's Modulus problem (Check my Answer)

I am trying to calculate Young's Modulus on the graph below. I have run the test through some software, now want to calculate Young's Modulus to ensure my analysis can be relied upon to be ...
5
votes
0answers
65 views

Should we teach congruences from the start rather than normal subgroups in group theory? [closed]

Many students have difficulty initially with the idea of a quotient group, and why a normal subgroup is defined as it is. I think this is potentially made worse by the slightly obscure logic of the ...
1
vote
0answers
17 views

Can we interpret the determinant of a $2×2$ Hessian matrix in terms of the area of a parallelogram?

As we known, the determinant of a $2×2$ matrix is the area of a parallelogram? In this case, can we interpret the determinant of a $2×2$ Hessian matrix in terms of the area of a parallelogram? If so, ...
0
votes
0answers
14 views

Is there a math textbook full of real-life problems which a student is supposed to model by a function which he or she creates on its own?

To motivate students in school to learn math functions, I wonder if there is some textbook full of problems which student is supposed to find a function which model this problem. Ideally, the textbook ...
0
votes
0answers
14 views

Are there any online questions that students can use for formative assessment?

I know Dr. Martin Greenhow and his team of Brunel University London have developed online questions and I have used some of these at the following url: http://maths-for-all.co.uk/engineering-...
0
votes
1answer
25 views

Could you please explain me the first term of second equation and third equation in the following model?

I have attached the image of the model. Could you please explain me the first term of second equation and third equation in the following model. (I didn't get the meaning of terms in bracket.) ...
0
votes
0answers
17 views

one forms in the null space of a distribution

Consider a manifold M and a distribution D, a collection of linear subspaces : $D_ p $ of $ T _p M,$ for p belongs to M . Let ${ f ^ a }, (a = 1 , .. , k ),$ be independent one forms ...
0
votes
0answers
43 views

basic calculus problem [closed]

Staff is paid $\$6$ per hour. If the hotel is understaffed, the lost profit is $\$\dfrac{216}x$ where $x$ is the number of employees. What staffing level will minimize cost per hour?
0
votes
1answer
57 views

How to Cramer-Rao inequality?

I am trying to do this function: $$f(x\mid\theta)=\theta x^{\theta-1}, \;\;0<x<1,\,\,0<\theta<\infty.$$ I have finished finding my MLE. $$L(x,\theta) = \prod_{i=1}^n \theta x_i^{\theta-1} ...
0
votes
1answer
33 views

What branch of mathematics solves the problem of calculating position and distance in a space?

I'm a software engineer with very little real world math experience. I'm studying computer vision and interested in learning how to calculate the exact distance and position of an object A from an ...
0
votes
0answers
14 views

labelling vertices of a polyhedron with letters

Maybe a stupid question, but I have not met yet a clear answer. Say that the label of a cube is ABCDEFGH: does it mean that there are faces ABCD and EFGH so that E, F, G and H are respectively the ...
0
votes
2answers
54 views

What is the unknown number in this puzzle?

I am going through some simple math problems in these quarantine days. Some of them are solved by me and some of them aren't solved by me. one of the unsolvable problems is given here: Can you help ...
4
votes
2answers
130 views

Question about rigor when it comes to proof by induction

I have a general question concerning "rigor" when it comes to proof by induction. I make instructional videos about math, and I was in the process of planning a video on this topic. So I did what I ...
3
votes
1answer
81 views

Submersion or not?

How can I prove that $$ f : \mathbb R \rightarrow \mathbb R, f(x) = e^x$$ is a submersion? I know that I must prove that $$f’= e^x$$ is everywhere surjective. But how can I write it? Thank you in ...
-2
votes
0answers
44 views

Kids Homework - Getting odd numbers from even

This is probably my lowest point on S-E/S-O. A friend has some kid's maths homework (Her kids, she is not a child herself), and we just can't make any sense of it. Surely even numbers can't become ...
0
votes
0answers
20 views

Does Stewart's calculus consider endpoints of the domain of a (nice) function to be critical numbers?

This is a question of convention - specifically the convention used in Stewart's Calculus. In Stewart's calculus (the latest version), in chapter 4.1, definition 6 defines a critical number of a ...
0
votes
1answer
35 views

Suggest book(s) for Algebra I, Algebra II, Geometry and Trigonometry that goes in great details and explains all sides of the problems [closed]

I am currently reading for Dummies series of those math books and they are quite good as introduction and I really like them. But I have feeling that there can be much more extensive coverage of ...
0
votes
2answers
19 views

how to convert one expression to another

I equated them to each other, and they were equal, but .. how to make another from one
-2
votes
0answers
25 views

What are the feas ([-2,2] , -2)?

A vector d ∈ R^n is called a feasible direction at x ∈ Ω if there exists an α ̄ > 0 such that x + αd ∈ Ω for all α ∈ [0, α ̄]. The set of all feasible directions at x will be denoted feas(Ω, x). How ...
0
votes
1answer
11 views

Is a communication restriction necessary in a Prisoner's dilemma verbal formulation?

To my understanding, a prisoner's dilemma is any symmetrical game with 2 players where the payoff matrix holds the following relations: A/B> B/B > A/A > B/A and (B/B)*2 > A/B + B/A thereby making A ...
1
vote
0answers
60 views

Recommendations For Using Frankel's “The Geometry of Physics” As A Course For Both Pure Mathematics And Physics Students? [closed]

Locked up in my self-distancing isolation in NYC, I'm reminded of how much I really like Frankel's book, which contains a wealth of beautiful geometry and topology from the standpoint of a ...
0
votes
0answers
9 views

Related to doing a bibliography analysis

When doing a Literature review on a mathematics topic (same for other subjects too), I found that the articles can be searched through "document search" option in scopus or web of science, and the ...
0
votes
0answers
39 views

what does math symbol [ x ]+ mean? [duplicate]

I saw a math symbol looks like this, anyone know what does it stands for? $$-V^t + G[D^T]^+$$
-4
votes
2answers
39 views

How to get rid of maths? [closed]

Some formulas and their proofs just keep rotating in my mind. I derive it in my mind but the moment later, I feel that I don't know it. What should I do?
0
votes
2answers
49 views

Find an equation of a line tangent to $y=x^4-6x$ and perpendicular to the line $x-2y+6 = 0$. How to solve?

This is all I got at the moment: $y=x^4-6x$ $y'=4x^3-6$ $x-2y+6=0$ $y=x/2+3$
1
vote
1answer
43 views

Mathematician's analog of multiverse

I've heard a lot about multiverse from pop science TV shows and lectures. Somehow, physicists are very good at philosophizing their own theories and coming up with catchy terms that stem imagination ...
0
votes
2answers
41 views

How to isolate r in the formula of calculating compound interest with savings

How can we isolate the $r$ in the following formula? $$A = P\left(1 + \frac rn\right)^{nt} + \frac{PMT\left(\left(1 + \frac rn\right)^{nt} - 1\right)}{\frac rn}$$ I went through multiple tutorials ...
0
votes
0answers
13 views

Q statistic and Chi square tests

Let matrix $X = \{x_{ij}\}, 1\le i \le n, 1\le j \le m$ represent data of $m$ variables over $n$ instances. (Assume all variables have been normalized, i.e., $\mu_j = 0, \sigma_j = 1$) Let vector $Q ...
0
votes
0answers
23 views

How to calculate correlation between number of characters in a string and its length?

Compared to what I'm seeing here on the forum I am a total mathematical noob. I'm solving an algorithmic problem which I know how to solve but there has to be a better and much simpler solution using ...
0
votes
1answer
28 views

why are manhole covers round? does the square manhole cover really will fall if its put diagonally?

This is an interview question and its answers say that if the cover is a square then it will fall inside when put diagonally? But how will it fall if the filling area is a smaller square? Is the ...
0
votes
3answers
33 views

how many unique $3$ digit numbers can be formed using digits $1,1,1,1,2$? Explain the logic too.

Only numbers $111,112,121,211$ can be formed through these. How to get this mathematically because for $1,1,1,1,1,2$ also the answer is same $111,112,121,211$ and so on as $1$'s increases answer ...
0
votes
0answers
37 views

What would you recommend for the math thinking course?

We're going to make a new math course for kids as intermediary between middle and high school with math profile (for preparation to entrance exams to high school), and before the main part (arithmetic,...
1
vote
0answers
59 views

Studying from class notes first year at university

I am studying pure math for first year at university. In the first semester, I would only read notes from class and would refer to books or online sources that I could find(but I would only read). I ...
1
vote
1answer
166 views

Are there any relatively easy problems that make use of the Intersecting Chord Theorem? And same question for Intersecting Secants Theorem

I'm talking about the theorems as laid out here: https://www.mathopenref.com/chordsintersecting.html https://www.mathopenref.com/secantsintersecting.html They require you to know these for iGCSE ...
1
vote
1answer
56 views

Area bounded by a hyperbola

Find the area "A" of the given graph Answers should be in terms of a, b and h My attempt: (1) Look for an equation in terms of y (or maybe in terms of x since the region is bounded between $y=0$ ...
3
votes
2answers
57 views

What are the pros/cons of the Natural numbers including 0?

This question is posed to those primarily in Pre-Calculus / Secondary education, but if you have anything interesting relating to your area of mathematics that'd be awesome to hear. Note, I'm a ...
-1
votes
1answer
36 views

How to Assign a Value 1-10 Over Thousands of Entries??

First, I am not a mathematician. So, have patience with me please. I want to be able to assign a number (1-10) to n-amount of people, based on a given action. If that person does less of that action, ...
0
votes
2answers
37 views

Proofing this math pattern [closed]

I have this proof/pattern I am trying to solve: 2 + 3 = 8 3 + 7 = 27 4 + 5 = 32 5 + 8 = 60 6 + 7 = 72 7 + 8 = ? I have to find what the question (?) represents, until now I have tried a few ...
0
votes
0answers
16 views

Relationship between sequence limit ($N \rightarrow R$) and corresponding function limit ($R \rightarrow R$)

I have the sequence ($N \rightarrow R$): $$ n \, \left( 2^{1/n} \, - \, 1 \right) $$ If I consider the limit: $$ \lim_{n \rightarrow + \infty} {n \, \left( 2^{1/n} \, - \, 1 \right)} $$ and the ...
0
votes
1answer
22 views

Domain and codomain of a sequence

I'm wondering if it is correct to say that: the domain of a sequence is a discrete domain made by positive integer (the zero is included); the domain of a sequence is a continuous domain made by ...
0
votes
2answers
53 views

Minimizing a function which contains the floor function

I've the function ($A>1$ is a real positive variable; $F= \lfloor A \rfloor$ and $F \ge 1$ because $A>1$): $$ U = \frac {F + (A - F)^2 } {A} $$ How can I minimize that function? In my old ...
3
votes
0answers
30 views

Handbook for Spoken mathematics Italian

I'm looking for something similar to the book Handbook for spoken mathematics to have all the rules to precisely dictate math formulas, but for the italian language. Unfortunately I didn't find ...
0
votes
0answers
14 views

Planes, lines and distances: looking for interesting use cases

In a week from now, I am going to teach a one-time class to first-year engineering students about 3D geometry, more specifically: distances between points and lines/planes, and the common ...
3
votes
3answers
138 views

Intuition behind $\sin(\theta)$ when introducing this to high school students

When first introducing trigonometry to students, the traditional setup is to start with a right-angled triangle with reference angle $\theta$ and we label the sides with "Hypotenuse, Opposite and ...
2
votes
1answer
23 views

How do I apply horizontal stretches to logarithmic functions?

I have a question about logarithmic functions. First, I am given the following function $f(x)$: $f(x) = log_4(x)$ The question asks to apply the following series of transformations to the function ...
0
votes
1answer
30 views

2 odd degree vertices - G admits a trail that visits all nodes

I failed a graph theory exam last week and I would like to know how to solve some of the problems I got because I don't have any idea. One of the problems is: Prove that if a connected graph G has 2 ...
0
votes
0answers
63 views

3SAT satisfiable so bipartite graph is hamiltonian in polynomial time

I failed a graph theory exam last week and I would like to know how to solve some of the problems I got because I don't have any idea. One of the problems is: Prove that, if for every instance of ...

1
2 3 4 5
54