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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.

1
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0answers
101 views

A KinderGarten of binomial coefficients… [on hold]

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 ...
30
votes
9answers
28k views

Online Math Degree Programs

Are there any real online mathematics (applied math, statistics, ...) degree programs out there? I'm full-time employed, thus not having the flexibility of attending an on campus program. I also ...
-2
votes
0answers
32 views

Does a math language exist that can be put into a URL or codified in some way? [on hold]

If I want to put an equation into the URL is there a language or format that I can do that in to preserve that information? For example, to calculate the income per year of a $25 hr job you would use ...
0
votes
0answers
42 views

Is there a site that lets people link to math formulas? [on hold]

So you can write a simple sentence and then link to the math. For example, if I was writing a blog post and I wrote, "A \$25 an hr job is \$52K a year." The math would be: ...
1
vote
0answers
44 views

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

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 ...
0
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2answers
1k views

Get height of building with viewpoint angle and distance to top of building from the viewpoint

Im trying to find the height of a building with only the angle of incline and the distance from ground viewpoint to the top of the building. That distance is 90m and the angle is 40° I'm in a ...
0
votes
1answer
30 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}...
6
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3answers
1k views

Self-study High School Math Textbooks?

I'm new to this website so I apologize in advance if what I'm going to ask isn't meant to be posted here. A bit of background though: I haven't been to school in 6 years and the last level I've ...
-1
votes
2answers
81 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 ...
1165
votes
67answers
494k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain but are ...
0
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0answers
41 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 ...
1
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1answer
20 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 - \...
0
votes
0answers
43 views

Is my instructor's wording regarding a linear system and finding max value incorrect? [closed]

I apologize for not providing the original problem statement. The question concerns the maximum value of $a+b$. The result obtained after reducing the relevant system of equations is: $a+b=5$ Since ...
1
vote
1answer
76 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 ...
1
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2answers
48 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
votes
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 ...
10
votes
3answers
3k views

Good way to learn Ramsey Theory

What are some good books on Ramsey theory? I have Van Lint's book on Combinatorics: is this enough preparation to start reading about Ramsey theory? I want a book that includes important results and ...
0
votes
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 ...
0
votes
0answers
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 ...
111
votes
18answers
9k views

What parts of a pure mathematics undergraduate curriculum have been discovered since $1964?$

What parts of an undergraduate curriculum in pure mathematics have been discovered since, say, $1964?$ (I'm choosing this because it's $50$ years ago). Pure mathematics textbooks from before $1964$ ...
0
votes
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 ...
1
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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 ...
0
votes
2answers
268 views

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 ...
2
votes
3answers
146 views

How did Carina (in Pirates of the Caribbean $5$) determine the longitude with chronometer?

At first, let me quote some dialogues from Pirates of the Caribbean $5$: Dead Men Tell No Tales. In a scene when she wants to purchase a chronometer, she has accused that she is a witch, but she ...
4
votes
0answers
59 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 ...
0
votes
1answer
57 views

Help with inequality with one unknown

Please could you help how to solve the inequality $(\sqrt{x-9})(2^{x-8}+3^{x-9}-9)\geq 0$
-1
votes
1answer
47 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 ...
1
vote
2answers
29 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 ...
31
votes
3answers
25k views

The best symbol for non-negative integers?

I would like to specify the set $\{0, 1, 2, \dots\}$, i.e., non-negative integers in an engineering conference paper. Which symbol is more preferable? $\mathbb{N}_0$ $\mathbb{N}\cup\{0\}$ $\mathbb{...
0
votes
0answers
30 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 ...
0
votes
2answers
40 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 $a, b, c,$...
-3
votes
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
votes
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 ...
39
votes
26answers
2k views

What are some surprising appearances of $e$?

I recently came across the following beautiful and seemingly out-of-the-blue appearance of $e$: $E[\xi]=e$, where $\xi$ is a random variable that is defined as follows. It's the minimum number of $...
1
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0answers
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 ...
4
votes
2answers
1k views

Online homework/testing systems?

I have been using Pearson's MyMathLab Global with my Engineering students. I appreciate its convenience, but the students find its inflexibility annoying (if an answer is expected to be 1.5, then the ...
0
votes
1answer
24 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 ...
0
votes
0answers
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 ...
2
votes
2answers
1k views
0
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0answers
25 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 ...
0
votes
2answers
52 views

sigmoid function: an algebraic solution

if we have a sigmoid function $1/(1+e^a)$, where $a$ is in the form of $(x-b)/c$ and the sigmoid equals function a value, called $k$. This $k$ is in the form of $1/x^2$. So something like: $1/x^2= 1/(...
0
votes
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 = \...
152
votes
7answers
12k views

Why is Euler's Gamma function the “best” extension of the factorial function to the reals?

There are lots (an infinitude) of smooth functions that coincide with f(n)=n! on the integers. Is there a simple reason why Euler's Gamma function $\Gamma (z) = \int_0^\infty t^{z-1} e^{-t} dt$ is the ...
0
votes
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 ...
0
votes
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 ...
0
votes
1answer
72 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.
2
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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
votes
0answers
50 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/...
-3
votes
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
-2
votes
1answer
84 views

chessboard 7x 7

A 7 × 7 chessboard that is painted black and white, with the corners painted black;and we have the operator "inverse", which can be applied to a single row or single column in a table that it change ...