# Questions tagged [education]

For 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.

2,508 questions
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### By mathematical induction prove that? [duplicate]

$\frac{1}{n + 1} + \frac{1}{n + 2} + \frac{1}{n + 3} + ..... +\frac{1}{3(n) + 1} > 1$; Here in this sequence after checking the basis for n = 1 , i.e $\frac{1}{4} > 1$, Which cannot be true; ...
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### What does a vertical line through the top and middle portion of an equals sign mean?

I came across a new symbol in the paper Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach by Stefan P. Domino. What does this symbol mean? It looks like it's being ...
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### Find an equation in standard form of the line having slope m and y intercept b

What form is this? It's not $ax + by = c$ The given slope, $m$, and intercept, $B$, is $m=-1$, $b=2$
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### Operations with oriented angles

If I have the figure below, how can I get the angle $a_2$ (the angle is >0 in counterclockwise direction)? $$a_2 = \frac{\pi}{2} + a_1$$ or $$a_2 = \frac{\pi}{2} - a_1$$ ? Thank you for your help.
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### How to solve this problem by induction method, and derive neumann formula?

Some explaination would be helpful if$\quad$ $a^n = a(a - h)....[a - (n - 1)h ]$ $\quad$ and $\quad$ $a^0=1$ $\quad$ then $\qquad$ prove $\quad$ $(a + b)^n = \sum_{m=0}^n C_n^m a^{n - m} b^{m}$,...
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### How to prove L.H.S = R.H.S further by induction method? [duplicate]

Some solution I have done is ...
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### How to write a Optimization-Problem with independent variable und constraints correctly?

I want to write a simple Optimization-Problem in mathematics way. for example: a function $f(x) = ax + b$ has independent variable $x$ and unknow parameter $a$ and $b$. The Parameter $a$ and $b$ ...
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### Using $E[S]=E[Y]E[X_1]$ where $S=\sum_{i=1}^Y X_i$ where Y is also a random variable.

I had some trouble working on some problems and I would appreciate some help. 1), Let $\sum_{i=1}^{N}X_i=S$ where each X are iid and N is a random variable independent from all Xs. My goal is to ...
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### Find a vector that will make the set linearly independent

I have a set of vectors in $\mathbb{R}^{3}$: $\Biggl{\{}$$\begin{bmatrix}1\\2\\3\end{bmatrix},\begin{bmatrix}-2\\2\\-3\end{bmatrix},\mathbf{\vec{v}}$$\Biggl{\}}$ I want to be able to find the ...
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### Showing a sub-sequence ($r_{n_{k}}$) converges to $x$

There exists a bijection that $f : N → Q, x \in R$ *$r_{n}$:=$f(n)$ I am asked to show that there exists a sub-sequence ($r_{n_{k}}$) of ($r_{n}$) so that the limit of the sequence ($r_{n_{k}}$...
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### Convert $\sum_{k=1}^n k^2(k+1)!$ to closed form

Convert the following to closed form. $$\sum_{k=1}^n k^2(k+1)!$$ I've been trying to solve this .. no luck. You don't have to solve the whole thing, just point me in the right direction. Thank you!
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### How do i show n + k is a integral multiple of 11

(the digits of a positive two digit integer N are interchanged to form a integer)I don't know what this question means so I'm clueless and what do i do to solve? please in steps so i can understand it ...
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### How to create math ( Geometry , Analytic Geometry ) worksheets

I apologize if this is not the site for such questions. But I need a software that can create math worksheets in geometry and also adding axes with viewing important points in the plane, basically I ...
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### How is it possible to teach probability theory without sigma fields?

In introductory undergraduate probability courses, even those with a focus on set theory, I've often seen the definition of a sigma field entirely skipped over. Indeed, I've often seen the definition ...
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### Explain random variables in analog derterministic terms

I struggle to explain discrete and continuous random variable, what it mean to integrate in terms of Ito, covariance as a measure for how much two variables jointly vary, and the like. It would be ...
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### An algorithm to check if two polygons have the same area

With Euclid's propositions I.45 (constructing a rectangle equal to a given polygon) and II.14 (constructing a square equal to a given rectangle) one can reduce the comparison of areas of polygons (...
128 views

### How can I develop “mathematical thinking” as a student? [closed]

In my humble opinion as a math student and considering that my main area of interest is computer science, I see that one of the most important skills required to solve problems is the mathematic ...
98 views

### Teaching a differential equations course to computer science majors

I am currently teaching an undergraduate course on elementary differential equations in a mixed class of natural science (physics, chemistry, biology, etc) and computer science majors. Since none of ...
105 views

### Find a solution of $t\frac{dy}{dt}=t^2−t$ and determine a function $y(t)$ that passes through the given coordinates $(t, y)$ [closed]

Find a solution of $t\frac{dy}{dt}=t^2−t$ that passes through the points: i) $(0, 1)$ ii) $(0, 0)$ iii) $(1/2, 1/2)$ iv) $(2, 1/4)$ SOS: I don't know where to start and my professor is no help.
148 views

### Why are AM-GM inequality related exercises so popular

Everyday I visit this site I come across plenty AM-GM inequality related exercises. Where I went to high school (Switzerland) we were never taught this inequality. I thus fail to see the need to talk ...
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### I want to write an algorithm for two circles intersection and touching cases . How can I do it with a quadtratic equation? [duplicate]

Given that two circles with coordinates (x1, y1) and (x2, y2) and radius r1 and r2 respectively . I need to find an equation , which can be used in code to to find the coordinates and the presence of ...
518 views

### Is undergraduate “complex analysis” actually kind of “complex calculus”? Please provide references. [closed]

As far as I know: After Calculus I, II and III, math majors have basic real analysis that covers topics including uniform continuity, Riemann-Stieltjes, Bolzano-Weierstrass and is mainly proving ...
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### Interesting example of linear congruence

I am about to give a talk on linear congruence to high school students. Can you suggest an example of linear congruence that will immediately make students fall in love with linear congruence?
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### Name of a matrix with one column and row removed

I am looking for the exact name of a matrix where the i-th column and rows have been removed. I cannot remember how it is named in linear algebra, does anyone got an idea? Thanks!
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### how to calculate volume in(liters) for a specific height in horizontal cylinder

I have horizontal cylinder with diameter = 193.04 inches and length = 548.64 inches I want to find the volume of an oil at specific height with the help of some formula. I came across below formula ...
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### Is the speed at which someone does math inborn, or can it be increased through practice?

Is there scientific evidence (or at least personal experience) that shows that daily practice of math problems increases the speed at which those problems are solved? Mind you I am not talking about ...
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### The convenient approach to a calculus problem in two variables

A student came to me with the following problem. Construct a function $g \colon {\Bbb R}\to {\Bbb R}$ such that the function $f \colon {\Bbb R}^2 \to {\Bbb R}$ defined by  f(x,y)= \begin{cases} \...
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### How to create educational linear algebra animations?

I'm looking to create animations for a linear algebra course. I need things like writing and changing equations, including matrices, plotting of 2- and 3-dimensional axes with points, vectors, lines ...
3k views

### Is there a sufficiently reachable plausibility argument that $\pi$ is irrational?

I was teaching someone earlier today (precisely, a twelve-year-old) and we came upon a problem on circles. Little did I know in what direction it would lead. I was able to give a quick plausibility ...
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### Is there much benefit in memorising proofs outside of an exam setting? [closed]

This is a question I have been thinking about for a while, which seems especially important as I hope to transition from undergraduate to graduate study in the next year, where studying for an exam ...
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### Learning math while visually impaired

My eyes are destroyed. I have been unable to learn math beyond decimal division in school due to laziness and unhelpful teachers. I am now trying to mitigate this mistake by learning math from the ...
92 views

### Fermat's Last Theorem Resources

Are there any resources which describe FLT in a very tangible way which will motivate students to be interested in this subject?
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### How would you explain commutativity of multiplication of naturals to kids?

I would do it like this, and you? Put in a rectangular basket apples in such a way that you have three rows and in every row 4 apples, then you have 3x4 apples in the basket. Stay where you are and ...
This is from The Way of Analysis by Strichartz, chapter $7$, section $7.4$, page $276$. He writes "In discussing power series it is good to recall a nursery rhyme:" "There was a little girl ...