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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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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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 ...
26 views

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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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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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 ...
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 ...
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: -...
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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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 ...
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 ...
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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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 ...
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-...
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 ...