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.

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1answer
51 views

How are elements in a matrix ordered? [on hold]

I have four binary morphological characters (i.e., four variables with the possible values 1 and 0) and I want to investigate the extent to which their rates are correlated. To do this, I need to ...
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7answers
4k views
+100

Graphs for which a calculus student can reasonably compute the arclength

Given a differentiable real-valued function $f$, the arclength of its graph on $[a,b]$ is given by $$\int_a^b\sqrt{1+\left(f'(x)\right)^2}\,\mathrm{d}x$$ For many choices of $f$ this can be a ...
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9answers
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Is Calculus necessary for computer science student? [closed]

I'm a freshman in university and I'm studying Computer science and engineering. This will be my second year of studying. We don't have Calculus as a mandatory class but I can take it from elective ...
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1answer
30 views

$\frac1{b^{2/7}}$ as $b^n$ [closed]

What is $\frac1{b^{2/7}}$ Rewrite the expression in the form $b^n$.
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0answers
29 views

Is it correct to obtain a probability from actual and very small dataset. when teaching [closed]

and thanks in advance to anyone trying to answer this. I must explain I am a total novice regarding maths and statistics. Background to this question: I am doing a very basic maths course but feel an ...
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1answer
47 views

Undergraduate level numerical linear algebra course without dependency on linear algebra?

Is it possible to create an undergraduate level course on numerical/applied linear algebra without having linear algebra prerequisite? Is there any examples of syllabus?
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4answers
184 views

How has mathematics been done historically? [Book Reference Request]

I know the original question title "what is the foundation of mathematics really?" seems pretty bad, or extremely bad, since it's really a huge question to answer. And I totally accept the fact that ...
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0answers
59 views

Why does the calculation formula for 8 / 2 (2+2) have changed? [duplicate]

What is your opinion on 8 / 2 (2+2) = ? it is going viral on social networks right now the correct answer in modern math is 16 The phone calculator also shows 16 but it wans't 16 always some time ago ...
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1answer
36 views

Interesting explicit convergent subsequence for not converging bounded sequence

To illustrate the (power of) Bolzano-Weierstrass theorem I am searching for an example of a bounded but not convergent sequence and an explicit convergent subsequence. I would like it to be non ...
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3answers
19 views

Solving inequalities number line

So I am currently doing inequality problems and i have the answer to the question but am unsure on how to put that onto a number line. The question is $-7+b≤6b-2<7b+1$. The answers i got for this ...
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3answers
178 views

Which courses from a math department would cover quaternions? [closed]

The subject of quaternions is often taught in engineering and physics courses due to its applications in 3D rotations and quantum mechanics. This treatment is often superficial and only presented as a ...
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1answer
42 views

Why is it from high to low if we show a decimal [closed]

From my experience, when we give a range we usually go from lowest to highest. EG, from 1 to 10 I was reading about mosquitoes and saw this The average mosquito bite drains 0.01 to 0.001 ...
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4answers
113 views

Intuitive algebraic explanation why $2+2$ does not always need to equal $4$?

This question will probably be subjective and somewhat disliked because of this, but I can't get it out of my head. In mathematics something that is often taken for granted and even used as insults to ...
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1answer
31 views

Finding the distance based off coordinates

Basically, I have a camera that gives me the (x , y) coordinates of an object. I need to figure out the distance from the camera to the object based on these coordinates. Is there a way to do so? (the ...
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0answers
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Term for maths education up to age 18

In the UK a school student can study mathematics up to the age of 18 to "A-level standard". In the US, a student can study mathematics up to the same age and this is known as "High School standard" (I ...
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3answers
170 views

What is the best way to test primality of this number $123456789101112131415161718192021222324252627282931$ for high school level?

I found that the number : $$123456789101112131415161718192021222324252627282931$$ which is prime number , I want to know if there is any simple method to show students its primality ?
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0answers
19 views

Random Walks and Electrical Networks Intuition

I am going to give a talk about Markov Chains to a group of high school students with very basic knowledge of probability. Because all of them have been introduced to EE, I wanted to demonstrate ...
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0answers
27 views

Bertrand series, not named/standard in English?

As a French high-schooler/undergrad, I learned about Bertrand series ("séries de Bertrand"), the things of the form $$ \sum_{n=2}^\infty \frac{1}{n^\alpha \log^\beta n} $$ as part of the curriculum. ...
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4answers
61 views

Is there a way to tell if a number is divisible by 4 if the figure is of 2 digits

I'm trying to help my daughter learn maths. She is struggling with factors, which is to work out what numbers go into a larger number (division). I've already learned that by summing numbers, if they ...
1
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1answer
59 views

Relevance of standard score

In this the modern age of computers, standard normal probabilities don't need to be looked up in a table. What is more, any normal probability can be easily calculated by a computer. So are normal ...
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2answers
73 views

Does $y''+ xy = 0$ admit a unique solution?

Does the solution of this equation even exist? even if it does, how am I supposed to check it if it is unique? Is it necessary to find the existing solution (if at all) to check if it is unique? What ...
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1answer
66 views

What is the height of the pyramid inside a cube?

A Cube labeled $ABCD$(base)-$EFGH$(top) has edge $8$cm. It has a pyramid with base $ABCD$ inside it, with the top-point labeled as $P$. It is also known that the distance from $Q$ (the midpoint of $FG$...
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2answers
136 views

I need advice in building self-study courses?

My course covers topics on calculus. Having looked at what I built, it will be a long process, I think that it is worth cutting down some topics of the topic that would not take too much time to study....
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0answers
143 views

Why are students being forced to memorize complicated proofs in Russia (and other Post-Soviet states)? [closed]

I'm not sure how well this question fits into MSE, but no other community (probably except mathoverflow) has as many mathematicians as MSE who might be able to answer this question. In the ...
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1answer
72 views

How to understand commutative algebra [closed]

I'm trying to study commutative algebra, but i cannot understand totally the arguments. I'm afraid to study all mechanically. What can i do to solve this problem? I need some advice!! Thank you
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2answers
63 views

Find the shaded part area?

Two squares of side 5 and 2 respectively. They are touching each other. Diagonals of the square are joined. find the area of the shaded part?
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0answers
14 views

Hinge Loss function, still shows loss when values are matching

This is Hinge Loss equation So Assume that y = 0.5 and f(x) = 0.5 this means that both have the same value. i.e. no error and no loss but when I apply Hinge Loss I get this 1 - 0.5 * 0.5 = 1 - 0....
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1answer
54 views

Which course should I take in my undergrad that also looks more challenging in my post grad Mathematics application? [closed]

Math 341 - Operations Research 1, or Math 409 - Calculus of Variations Also, which out of the two is more helpful generally that might also be used later in my masters and/or PhD? Can I have a ...
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2answers
65 views

Are variables always in brackets or just × (times)?

It has been a while since I had basic mathematics, let alone algebra, but I am trying to relearn it again. As I recall correctly, my teacher always said that if you have $xy$ in an expression (2 ...
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1answer
47 views

Write the polynomial $q(x) =2x^2-10x+5$ as a linear combination of the polynomials [closed]

Write the polynomial $q(x) =2x^2-10x+5$ as a linear combination of the polynomials $p_{1}(x) =x^2+2x-3$, $p_{2}(x) =2x^2+2x+3$, $p_{3}(x) =3x^2-2x+1$
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0answers
46 views

Which one is better to have as a degree title? Mathematics or Applied Mathematics? [closed]

Hi I'm a 3rd year undergraduate student yet to experience the graduate world. Initially I was fascinated by the world of abstract algebra but I am quickly coming to terms with the limitations set by ...
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0answers
119 views

A KinderGarten of binomial coefficients… [closed]

I tell the beginners that $(-n)!= \pm \infty$, if $n \in N$. Next, I tell them that the definition of ${\nu \choose k}$ as $$ \frac{\nu (\nu-1) (\nu-2) (\nu -3) ...(\nu-k+1)}{k!}~~~~(1)$$ is the most ...
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1answer
32 views

Simplify the expression below

enter image description here \begin{equation} \sum_{n}\left[\left(\frac{2 \pi n}{a}+k_{x_{0}}\right)^{2}+k_{y}^{2}\right] a_{n} \delta\left(\frac{2 \pi p}{a}-\frac{2 \pi n}{a}\right)=k_{0}^{2} \sum_{m}...
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2answers
101 views

Are child soroban (abacus) classes worth doing? [closed]

I'm considering enrolling my five year old child in a weekly soroban course after school ('soroban' is the Japanese word for abacus). They're quite expensive ($30 a lesson) but the companies running ...
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0answers
44 views

Can someone recommend me a book for the fundamentals of general mathematics?

I'm looking for a well explained book of general mathematics to acquire a well formed basic knowledge of mathematics. Does anybody knows a specific author or can tell me a good starting point where I ...
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1answer
21 views

Segment length by using trigonometry: absolute value of trigonometric function?

I'd like to compute the length $L$ in figure. Is it correct to do it in the following way ($H=0.247$)? $$ L = H \, \mid \sin(\gamma) \mid = 9.4 \,\, 10^{−4} $$ where $\gamma = \pi - \theta_1 - \...
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2answers
50 views

How to solve an linear system with b variable?

I have the following: $$ A = \begin{bmatrix}-1 & 2 \\ 3 & -5\end{bmatrix}; b = \begin{bmatrix}0 \\ \beta \end{bmatrix} $$ and I'm thinking how to analyse the Ax = b system. As I saw I could ...
0
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1answer
30 views

Explaining something simple

This is a question about math not finance but i will use the following formula to illustrate: A) Total return = Dividend yield + Price change B) Price change = (1 + change in 'price over earnings ...
1
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1answer
79 views

A question regarding the didactic motive for making a proof more complicated than logically necessary.

This has to do with the proof given in Thurston's The Number System, on page 61. My notation is different, and explained below. I'm asking about a style of presentation frequently appearing in text ...
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0answers
17 views

Question on the constant of proportionality

Currently we are learning variation and proportion and this is a sample question. I’m having trouble understanding or finding the answers, help would be appreciated. The strength of an electrical ...
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0answers
25 views

Resources for teaching calc III

So I was very unsatisfied with how I taught Calc III a couple years ago, and this summer I have to do it again. Are there any general resources for teaching this course? It seems like there should ...
0
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1answer
17 views

Question on Combined Variations [closed]

The answer I got for K is 192 but I felt that was too much. So any help clarifying would be great. y varies directly with the square root of p and inversely with the square of q. If y=6 when p=4 and ...
1
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1answer
47 views

Is there any Math assessment test I can take?

ever since I was a child I struggled with Maths. Just so you guys know I am 23-year-old system analyst. When I got into college, I realized how much Maths on a general sense is important to our lives ...
4
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0answers
60 views

advice on PhD proposal [closed]

I am a PhD student in pure mathematics, and I want to work in the field of $C^*$-algebras and operator algebras I am looking for a relatively comprehensive view of this subject. For example, what ...
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2answers
33 views

Solving PAT equation with 2 logs

Taken from the PAT (Physics Aptitude Test): $\log_x 25 = \log_5 x$ I've tried making them the same base but I ended up with: $\log_5 x (\log_5 x)= 2$ or $\log_x 25(\log_x 5) = 1$ which I then ...
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0answers
34 views

Where can I study polynomials online?

I have one good book on polynomials. It is called (Level of Knowledge of Polynomials) by its author S. L. Tabachnikov. In principle, I could study it, but I am still mastering the Agebra I. Not long ...
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2answers
42 views

If $a, b, c,$ and $d$ are integers and $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}+\frac{1}{d}$ where both sides of the equation be the same

If we have integers $a$, $b$, $c$, $d$ and $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}+\frac{1}{d}$,when will both sides of the equation be the equal. So what that means is that for integers $a, b, c,$...
0
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1answer
57 views

Help with inequality with one unknown

Please could you help how to solve the inequality $(\sqrt{x-9})(2^{x-8}+3^{x-9}-9)\geq 0$
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2answers
25 views

What is measurement of angle D? [closed]

Angle 1= Angle 2, Angle 3 = Angle 4, Angle A = 90º What is the measurement of Angle D?
2
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1answer
46 views

I'm halfway stuck solving an Integral derivation.

I apologize beforehand for my handwriting. I hope it is legible. I worked the problem on a piece of paper. Took a picture and attached it to this query. I wrote the problem starting with Page 1 and ...