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.

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32 views

Looking for reference for quote [closed]

In graduate school, I remember hearing or seeing the rough quote: "Good mathematicians know one branch of math. Great mathematicians know two branches." I'm sure I am somewhat misquoting ...
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Number of partitions (subsets with 2 elements) of a set composed by an even number of elements

Given a set containing an even number $n$ of elements, I'd like to know the number of partitions (each subset containing 2 elements) without counting the duplicates. For example, given $A=\lbrace 1,2,...
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Proving perpendicular lines. [closed]

Prove that the line joining the center of a circle to the point of intersection of two tangents bisects the chord joining the points of tangency. I need to know how the line bisects the chord? I know ...
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Find a relation between x,y and z [closed]

Y 2 5 10 5 2 X 2 3 4 -2 Z 1 2 3 2 1 There are 3 variables x,y and z When y has a value of 2,x has a value of 2 and z has a value of 1 Similarly,When y has a value of 5, x has a value of 3 and z has a ...
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Interactive math theorem proving system with policed restrictions on the steps allowed [closed]

Let me provide you first with since background, and then my question: I am looking for a voice or text math interface to a theorem proving system. In this system, you are trying to prove something (...
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2answers
55 views

Name of the formula used to get the moments of a random vector

I'm lloking for the name of the following formula used to get the moments of a random vector ($j \in \lbrace 1,...,n \rbrace$; $ k_1,...,k_j \in \lbrace 1,...,n \rbrace $; $r_1,...r_j \in \mathbb{N}$)....
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Representing multidimensional matrix on a plane [closed]

I'd like to know if, given a multidimensional matrix, it is possible to draw it on a plane. Maybe there is a convention to do that.
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Benefits of learning subjects "classically"? [closed]

This is a bit of softer question: I'll give an example of what I'm talking about, then ask for opinions and experience. It is a well-known result that given a field $F$, the set of elements algebraic ...
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Max Volume out of a square with a open rectangular box(can you confirm my proof?)

I have a simply proof to do, but just want to get your thoughts on it if i haven't forgot something: I have a squared piece of metal with the side length of $ a $ and i need to cut out a open ...
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Linear algebra through applications for engineering kids

I am going to teach Linear algebra-I to first-year engineering students of all disciplines. The syllabus is typical: starting from what is a vector, linear span, linearly independent, $\dots$ , ...
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Please find the value of theta. [closed]

Please give the solution to the value of theta with proof in the image link attached.
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Ground Sample Distance (GSD) calculation for non-aerial images

I am working on a project for which I need to find GSD for non-aerial images. GSD is normally measured for areal images. GSD Formula for images taken vertically from a nadir view. Let's say, I am on ...
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Time work problem help needed [closed]

Is this a time work problem? hope someone could help. Peter sew 40 pants an hour. It takes John twice as long to sew the same number of pants. How long will it take them to sew 25 pants if they are ...
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How to get a solution of the inequality $5 \sin (\theta)-\frac{1}{2} \sin \left(\frac{5 \theta}{2}\right) \geq 0$ using sympy?

I'm trying my best figuring out what is going wrong with my code. So I'm trying to solve the inequality: $$5 \sin (\theta)-\frac{1}{2} \sin \left(\frac{5 \theta}{2}\right) \geq 0$$ with sympy, but I ...
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29 views

Which method would be best fit in solving this polynomial equation [closed]

For context: I'm trying to create step-by-step solutions for some high school textbook problems; the solutions are intended to be a helpful/informative guide for high-school students who will be ...
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How do I visualization generalized Pythagorean theory?

maybe the Pythagorean equation is not alone. can't this equation be just one element of an array like this for example. exponents must be prime numbers (otherwise it's just a combination of other ...
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How should I integrate this?

Could someone help integrate the following integral please: $$ \int\biggr(1+u+\frac{u^2}{2}+\frac{u^3}{6}+\frac{u^4}{24}+\frac{u^5}{120}\biggr)^{-1/2} \mathrm{d}x $$ Where, $$ u = \left(\frac{x-35.8}{...
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What is an example simillar with $\#A+\#B=\#(A\cup B) + \#(A\cap B)$?

I already know simillar form of $\#A+\#B=\#(A\cup B) + \#(A\cap B)$ holds with finite dimensional $F$-vector spaces(not clear with infinite dimensional) like this form... $$ \dim V+\dim W=\dim(V+W)+\...
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(When) do students typically learn about limit superior and inferior?

I've been taking the Khan AP Calculus BC course, and I also have been following through with pretty extensive calculus notes found here. In neither of these (or when I learned Calc in high school) ...
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29 views

Is any direct Adams Moulton formula or how to related those two formula which i am mention.

Are those formulas the same? When I am programming for Adams Moulton fourth order methods I use the 2nd formula which I mentioned in the 2nd image. Is it correct? If correct, please explain me. This ...
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1answer
43 views

Volume of Trapezoidal Prism

For a plot of land of 100 m × 80 m, the level is to be raised by spreading the earth from a stack of a rectangular base 10 m × 8 m with vertical section being a trapezium of height 2 m. The top of the ...
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Limit without De L'Hospital: $\lim_{x\to \pi/2}\frac{\sin x-1}{2x-\pi}$

We must to calculate $$\lim_{x\to \pi/2}\frac{\sin x-1}{2x-\pi}.$$ It is very simple with l'Hospital's rule that the limit is zero. But what would happen if I didn't use l'Hospital's rule? In fact if $...
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55 views

How to check if a circle lies in a certain range

I've a problem where I need to calculate the score on this board. I was able to detect the ranges, and detect the bullets. I would like to make a loop to check whether the bullet holes that are marked ...
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Calculate similarity in time and duration of two people?

I have an example problem Person A starts playing soccer at 01:00 and plays for 40mins Person B starts playing soccer at 01:20 and plays for 80mins Person C starts playing soccer at 05:00 and plays ...
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Formula of the probability of two dependent events

I'm wondering if there is a formula for the probability of two dependent events $A$ and $B$. I know that if they are independent, the formula is: $$ P(A \cap B) = P(A) \, P(B) $$ maybe if they are ...
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5answers
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Nice examples of limits to infinity in real life

I have to teach limits to infinity of real functions of one variable. I would like to start my course with a beautiful example, not simply a basic function like $1/x.$ For instance, I thought of using ...
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How to define applied mathematics? [duplicate]

In engineering, we use the term applied mathematics a lot. However, I've noticed that the exposure for proof is scarce. When I was an undergrad, even though the textbooks provided some details about ...
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Name for a basic equation where $x$ appears only once. (E.g. after collecting terms)

I'm a high school maths teacher. I was wondering if there is a name for all equations where a variable appears only once e.g. $$\frac{(x+3)^2}{4}=5\qquad {\rm{or}} \qquad \frac{1}{2}+x=\frac{3}{4}$$ I ...
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Proving that a given set is a group under function composition

Given a vector space $V$, we will observe the linear map $T:V\to V$ such that $$T_{A,v}(x) := Ax+v$$ for $A:V\to V$ a reversible linear map, and $v \in V$. We will call this set $Aff(V)$. Prove that $...
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55 views

Let $f: R \to R$ be a map of class $C^1$. Show the set P = $\left\{x \in R : f'(x) \neq 0\right\}$ is open.

I've been trying to answer this question, but I have no clue. I'd accept any hints. Let $f: R \to R$ be a map of class $C^1$. Show the set P = $\left\{x \in R : f'(x) \neq 0\right\}$ is open.
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How should one study Graduate Mathematics with a weaker background?

My question is: how should one go about studying graduate level mathematics when they have a weaker background? This is probably a weird question since most of the people go in to graduate mathematics ...
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Leading principal minors VS Leading minors

Are "leading principal minors" and "leading minors" the same thing? If not, what is the difference?
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1answer
48 views

More advanced (free) alternatives to Math3D or Geogebra [closed]

I teach vector calculus. I love both Math3D and Geogebra. But I have reached a limit in terms of what these programs can do. Some examples of features that I wish Math3D had: Draw vector fields with ...
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What are differences and the examples of syntactic knowlede and substantive knowledge in mathematics?

I am sorry if the question is not quite related to post in this forum. There is a distinction between substantive and syntactic knowledge particularly in mathematics. There are several definitions for ...
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Are ‘constant difference’ and ‘common difference’ synonymous?

I’ve seen at least two phrases to describe a fixed difference between two numbers, i.e., “constant difference” and “common difference.” For example, if Sibling A is 10 years older than Sibling B today,...
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Questions about proofs

To prove, e.g., the identity $(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$, I remembered working, in high school, in the following way. Expanding the LHS gives \begin{equation} (a^2+b^2)(c^2+d^2)=a^2c^2+a^...
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Let $U$ be a vector hyperplane. Why does this calculation not find a basis for U?

Consider the vector space $\mathbb{R}^4$ and a generic hyperplane $U = \{(a, b,c,d)\in\mathbb{R}^4: \lambda_2b + \lambda_3c + \lambda_4d = 0, \lambda_i\in\mathbb{R}_{\neq 0} \}$. The task is to find ...
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converting Two-tailed to One-tailed test

lets imagine we have a two tailed distribiution for a bunch of data. right now we want to convert it into one tailed study;our P-value at the first is: P-value= 0.44 what our p-value is going to be??? ...
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Absolute Value equations in 2 variables ($|x-y|+|x+y|=\sqrt5$) [duplicate]

I'm struggling a lot figuring out how to sketch the following $$|x-y|+|x+y|=\sqrt5$$ This is what I know for$|x-y|$ $x-y \geq 0$ then $y \leq x$ so $|x-y|= x-y$ $x-y < 0$ then $y >x$ so $|x-y|= ...
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1answer
55 views

How to modulo this formula?

I would like to write this formula in C++ language: $$\tiny{element_{k} (n-1)!(\frac{n(n-1)}{2} + \frac{(n-1)(n-2)}{4}) }$$ (2<=n<=1e5), ...
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1answer
21 views

Problems with the sets using the cardinality and the operations

A survey shows that $63\%$ of kids like brand $A$ shoes and $76\%$ like brand $B$ shoes. brand $B$. Each boy in the group surveyed expresses at least one preference. Calculate the percentage of the ...
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1answer
22 views

How to devise a formula for lower to higher?

I have to calculate a combined score based on other scores i.e. s1, s2, s3, and s4. For s1 and s2 the higher the number the better. But for s3, it could be 0,1,2,3,4,5. But for s3 the higher the ...
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56 views

Is the K(x,z) = (xz-1) ^2 a valid Mercer kernel function?

I am trying to prove that K(x,z) = (xz-1) ^2 is not a valid mercer kernel function. I think it is not a valid kernel and it doesn't meet this condition: k(x,z)=∅(x).∅(z) because of a negative value: -...
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28 views

Textbook Suggestions for Teaching Senior Level Geometry

I will be teaching a senior-level class on geometry next semester. The class consists of both Euclidean and non-Euclidean geometry with an axiomatic approach. Right now, it appears I have the liberty ...
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2answers
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Strategies to solve a limit $\lim_{x\to \pi/4} \frac{\cos(2x)}{2\cos(x)-\sqrt 2}$

This morning a colleague asked me how I would solve quickly this limit, $$\lim_{x\to \frac{\pi}{4}} \frac{\cos(2x)}{2\cos(x)-\sqrt 2}$$ Probably because I am a member of this community but I have ...
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1answer
108 views

Would you replace the usage of pi with just tau? [closed]

This is actually a technical question about what kind of mathematical practices and notation lead to a more energy-efficient society, and the expertise required to authoritatively answer this question ...
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56 views

Book recommendation of specific images of the convergence of a function and of asynthotics

I have created these images with an external tool. The first image it is done for the definition of limit, $ \lim_{x \to c} f(x)=L$, using the epsilon-delta $(\epsilon-\delta)$, to indicate that in ...
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1answer
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Popular mistakes in probability

Question: What not-trivial mistakes do students often make when solving problems in probability theory, mathematical statistics and random processes? Some examples of wrong solutions: Problem 1: Find ...
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3answers
58 views

Methods and knowledge needed for the conversion of $\sum$ and $\prod$ into non-iterative expressions

I think this might be a very broad question, but here it goes. I have made a formula, using a sigma function, to give the $n$th number in a recursive sequence. I'm trying to make it into a non-...
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2answers
45 views

An intuitive approach to solving a question of geometry

In the square $ABCD$ of side $6$, points $P$ and $Q$ move along sides $AB$ and $CB$ so that $\overline{PB}=\overline{BQ}=x$. Consider the segment $OQ$ parallel to $AB$. Which of the following ...

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