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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15 views

Arithmetic Mean of a set including zero and null [on hold]

I know that the zeros in the dataset skew the results while calculating the average/mean of the dataset but what happens when the sample space contains nulls?
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17 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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23 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
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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 ...
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1answer
48 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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22 views

Which statistics courses should I take? [closed]

I don't know much about these topics. Which are most important? (for either academia or industry/data science) I can choose 2-3 courses from here for my undergrad degree. Introduction to Re-sampling ...
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43 views

How to study for university level math olympiads and competitions? [closed]

I participated in some high school level math competitions but I've never invested much of my time for it at that time, thing that I regret immensely, now being a engineering grad student I what to ...
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36 views

Why is EFF offering a prize for finding large primes? [closed]

Why is the Electronic Foundation Frontier offering a prize of $150 000 for anyone finding the first 100 million digit prime?
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2answers
70 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
64 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
111 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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135 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
69 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
62 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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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
51 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
64 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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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
118 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
31 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
98 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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42 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
49 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 ...
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1answer
27 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 ...
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1answer
78 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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15 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 ...
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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 ...
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1answer
44 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 ...
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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
32 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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33 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
41 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 $a, b, c,$...
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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?
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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 ...
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1answer
49 views

What is the meaning of sentence E | x?

How to read this math notation? Let closest(j) be the set of all points that are closest to centroid cj. The algorithm proceeds during several passes, during each of which it updates each centroid ...
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29 views

Calculating the asymptotes of an hyperbola from the general equation [duplicate]

Suppose that the conditions which ensure that the following equation is an hyperbola are verified: $$ax^2+2bxy+cy^2+2dx+2ey+f=0$$ What are the general expressions of the two asymptotes of the ...
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8 views

Q: How much overlap is there between pure and applied graduate courses, in the UK?

I am a final year BSc Mathematics student and I am seriously considering taking a Master's sometime soon. Some institutions have two separate courses for pure and applied maths. My question is, if I ...
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1answer
25 views

Rotation of a non rectangular hyperbola: equation of hyperbola referred to its asymptotes

I'm looking for a way in which I can rotate a non rectangular hyperbola; in particular I'd like to get the equation of a non rectangular hyperbola referred to its asymptotes. To do it I need to ...
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0answers
26 views

Partial derivatives and composite function

Given a function of two variables from $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$, we write/denote this function as $$f:(x,y)\mapsto (u(x,y), v(x,y)).$$ Consider another function, the polar coordinate ...
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1answer
23 views

Scalar relationships between the coordinates of two rotated coordinate systems

I'm wondering how come between the coordinate system $\xi \eta$, rotated -45° with respect to $x y$ coordinate system, and the $xy$ coordinate system there are the following relationships: $$x = \...
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2answers
24 views

Semi axes of a shifted rectangular hyperbola

I would like to know which are the semi axes of a shifted rectangular hyperbola: $$(x-c_0)(y-d_0)=A$$ In the classic case it is easy to find them: $$(x/a)^2-(y/b)^2=1$$ $a$ and $b$ are the semi ...
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1answer
35 views

is there a difference between the function y=x/x and the function y=1. [duplicate]

I have been asking people and have been getting mixed answers. some people think it is the same because when you simplify the first one you get y=1, but some people think that they are different ...
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1answer
73 views

If $x^y = xy$, what is $y$ in terms of $x$?

I know that $x=y^{\frac{1}{y-1}}$ but I cannot solve for $x$. Can somebody please help me? It should be possible because it is a very simple equation, can somebody please solve it.
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0answers
16 views

Meaning when a set has an accumulation point and its negation

Let $D'(a,r):=D(a,r)\setminus \{a\}$ be the punctured disc with centre $a\in \mathbb{C}$ and radius $r>0$. Let $A\subseteq \mathbb{C}$ be given. A point $a\in\mathbb{C}$ is called an ...
2
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0answers
51 views

Solving $x^x=y^y$ [closed]

In the equation $x^x=y^y$, how do you solve for $y$ in terms of $x$ when $y$ is not $x$? There is a small curve in the first quadrant which is not $y=x$. graph: https://www.desmos.com/calculator/...
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1answer
39 views

Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 6…5/1…5 [closed]

Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 6...5/1...5 Answer ASAP please