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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Minus operation and minus sign [closed]

Why (-1^2)=-1? I understand the minus here as the sign of the number not an operation. Because an operation should have two number like 0-1 but if we put just -1 it is the negative number
Rabih's user avatar
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1 answer
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Is there anything currently that generates rejection from the mathematical community? [closed]

Is there anything currently that generates rejection from the mathematical community, as happened with the complex roots of algebraic equations?
FRED ANTHONY VIGORIA HUALLA's user avatar
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Is privately tutoring Math or engaging with kids through learning, a cultural activity? How does it relate to the culture? [closed]

I believe it is but if somebody can elaborate. I need an answer for my immigration application but lawyers are very expensive. I am a self-employed Math tutor. Just need the answer to this question. ...
Simran's user avatar
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50 views

Fundamental Branches of Mathematics

I'm trying to drill down to the core branches of mathematics and it seems to me that Algebra, Analysis and Geometry are the fundamental branches of mathematics––every other 'branch' (topology, number ...
polarise's user avatar
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Looking for an example for Fubini's theorem

I am preparing a lecture about Fubini's theorem. For me, in "real life" the most common application of Fubini's theorem is to "change the order of almost-everywhere quantifiers". I....
the_lar's user avatar
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2 votes
2 answers
90 views

How to train myself to not think visually for simple math problems?

I have a problem where it is often very difficult for me to solve simple math problems without thinking about them visually, but at the same time, I have poor spatial reasoning and so I'm unable to ...
asdfasdf's user avatar
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0 answers
54 views

Resources for designing math degree programs

I'd like to know where I can find resources which are helpful when one has to design or improve grad and undergrad degree programs in pure and applied mathematics. In particular, I'm searching for up-...
Uagi's user avatar
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1 vote
1 answer
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Do the mathematicians/physicists that come up with these useful formulas picture the equations in their head? [closed]

For example in this three blue one brown video he shows the visualization of the derivative of x^2 it's relatively easy to see how it works and intuitively I could see how I could come up with this ...
Stef's user avatar
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2 answers
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When studying a book (like Rudin ) where the problems are not intended to be fully solvable by a student, what criteria show you're ready to advance?

When self studying a text where it is not expected to be able to solve all (or most) of the problems, what are the appropriate criteria to use for advancement? A word about the problems. There are a ...
SRobertJames's user avatar
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1 vote
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166 views

Doubt in proof of limit of $\frac{\sin(x)}{x}$ [duplicate]

Was reading Thomas Calculus and came across the limit of $\frac{\sin(x)}{x}$ at $x \rightarrow 0$. The method they used was comparing areas of sector and $2$ triangles to prove the inequality $\sin(x) ...
Macron's user avatar
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1 answer
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How do i stop the perfectionism with textbooks? [closed]

I have this problem that whenever i want to dip my toes into a new area of math that I'm either completely new to or have so little knowledge in it, I always go and google "Best books to learn [...
AmirMohammad Shakeri's user avatar
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57 views

Trigonometric equations: Finding the same solution for sin and cos

I am solving these trigonometric equations: $-10.0317 = 10.0458 \times \sin(7.1726 \times 10^{-4} \times t)$ $-0.5319 = 10.0458 \times \cos(7.1726 \times 10^{-4} \times t)$ I solved the sin equation ...
Need_MathHelp's user avatar
1 vote
0 answers
43 views

Is there a general consensus regarding which term is the multiplicand, and which is the multiplier in basic arithmetic multiplication?

Is there a general consensus regarding which term is the multiplicand, and which is the multiplier in basic arithmetic multiplication? In my notes I stated that in the expression $a \times b$ the left ...
Steven Thomas Hatton's user avatar
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2 answers
105 views

Alright this might sound stupid. Why do we expand by 10?

Specifically the math problem 90.5b+21*92/21+b=91.2. The math calculator on the internet kept giving me errors when I put it in like that. So I changed it to 90.5b+1932/21+b=91.2, and it gave me an ...
Ryan Malloy's user avatar
-1 votes
1 answer
68 views

Expected number of repetitions coin tosses [closed]

Suppose we flip a coin n-times. By a series of repetitions we mean successive tosses in which the same side of the coin lands (heads or tails each time). For example, in HHHTTHTH (𝑛 => 8) there ...
szni tos sznitos's user avatar
3 votes
2 answers
248 views

What are fun mathematical facts for non-mathematicians? [duplicate]

I like to spend my life with mathematics. I think it is the best thing I can do in my life. However, I have great difficulty explaining what I am doing to non-mathematicians, even educated ones. For ...
boyler's user avatar
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3 votes
1 answer
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Find Matrix for Linear Transformation Given Criteria

Suppose the linear transformation $T$ does the following: maps $R^2$ to the plane given by $x-2y+3z=0$, preserves angles and distances, and maps $(2,4)$ to $(-3\sqrt{2},0,\sqrt{2})$. I have two ...
mathclassfromscratch's user avatar
6 votes
1 answer
177 views

A literally challenging math book

The only way to learn mathematics is to do mathematics. - Paul Halmos Most books about uni-level mathematics follow a strict scheme of giving you the content and letting you practice with it with ...
Luca T. Castrillón's user avatar
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0 answers
19 views

Resources reference for engineering mathematics.

I am aware that this can be very subjective question but I am desperately in need of answer, I am undergoing maths heavy courses like mass transfer, heat transfer, fluid mechanics, momentum phenomenon,...
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Formula adjustment to get circumference of a sentence.

I want to calculate, automatically, the circumference of random words (written in Arial font) using the height and length. I used this formula : (H+L)*4. Nota : I ...
Clubcouleurs's user avatar
0 votes
2 answers
82 views

Farther and nearest points from an ellipse to the a line segment.

I really need your help in math, I've solved this problem in several ways, but I'm not getting anywhere... Given a straight line $x-3y-9=0$ and an ellipse $x^2/9 +y^2/4 = 1$, find the nearest and ...
Masha's user avatar
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1 vote
0 answers
61 views

Using predicate logic to solve text questions for 10-years-old?

I am going through a exam preparation book with a 10-years-old. I thought that predicate logic would make it easier to solve questions like the one below. My hope was to use Rules of Inference, but I ...
SevenD's user avatar
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4 votes
1 answer
187 views

How to determine the monotonicity of this function

Given the definition of the function: $$ f(x) = e^x - e^{-x} + \frac{2x}{(x^2+1)^2} , x∈(-∞,0]$$ What's the monotonicity of this function in the given range? I tried to calculate the derivation to ...
xmh0511's user avatar
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4 votes
1 answer
143 views

Tropical geometry for high school

Recently, I've found out about tropical geometry and its application in algebraic geometry. As I read about it, I thought that this would be a subject that can be taught in school as it is very simple ...
marilou64's user avatar
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1 vote
0 answers
50 views

What should I study to prepare for Stochastic Calculus

Context, I am an undergrad looking to take graduate stochastic calculus next semester. Unfortunately I do not have a whole lot of experience with probability theory as a whole. I've taken a first ...
person's user avatar
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1 vote
1 answer
102 views

Distance of a point from a straight line

For the straight line point distance there are several proofs. Several years ago I have proved (but I no longer remember the proof), the point-right distance by remembering that for a line $$r: ax+by+...
Sebastiano's user avatar
  • 7,419
0 votes
2 answers
157 views

Why is Leibniz notation more popular than Newton's notation?

I need help ascertaining which calculus notation is more preferred amongst mathematicians according to their home countries, and why. I have tried looking for a census or survey of some sort that ...
Luddssss's user avatar
1 vote
1 answer
79 views

Rotations alternative proofs?

Let $P(x,y)$ be any point and let $\rho$ and $\alpha$ be its polar coordinates. We have \begin{align*} x &= \rho\cos\alpha \\ y &= \rho\sin\alpha \end{align*} the point $P'(x',y')$, image of $...
Sebastiano's user avatar
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1 answer
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Problems on lcm and gcd.

Mario has a rest shift every $8$ days; Luigi every $24$ days; Paolo every $16$-th days. Today all three are off. In how many days will all three be back in rest shift for the first time? There are ...
Sebastiano's user avatar
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0 votes
0 answers
25 views

Calculating coordinates of vertices, given dimensions in an architectural floorplan

So, one of my friend is trying to learn autocad. They were given a floorplan. The floorplan had the dimensions. And they were asked to find the coordinates of the all the vertices of the plan. So we ...
user3851878's user avatar
0 votes
0 answers
58 views

How are two matrices similar?

I am aware that this question has been asked before, but I would like to see if anyone can come up with a better explanation. So what I have been stuck on is, what are the requirements for two ...
N G's user avatar
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0 answers
32 views

Suggestion required | Book on Mathematics Education Research

I am looking for books/ resources on Mathematics Education Research (problems, discussion on possible research topics etc.), preferably which are freely available online. Fascinating world of ...
Lemon's user avatar
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2 votes
1 answer
66 views

Explicit example of a Fourier transform of $f \in L^2(\mathbb R) \setminus L^1(\mathbb R)$

The Fourier transform shall be defined by $$ \hat f(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i \cdot \xi x} dx $$ The Fourier transform is well-defined for $f \in L^1(\mathbb R)$, that is, $f$ ...
shuhalo's user avatar
  • 7,465
-1 votes
1 answer
44 views

Make a new sequence (bn) by swapping values a0 and a1 of an old sequence (an) then figure out the closed sequence for bn

This question is 4 parts and I think I did Parts 1-3 right, I am just unsure of what or how to do part 4. If I messed up prior parts I wouldn't mind some input on them as well Choose four integers a, ...
Akihiko Hishimoto's user avatar
0 votes
0 answers
21 views

Overview understanding of space, function, and transformation by an idea of plasticine. Need some comments for correction.

I would like give a overview idea of Space, Function, and Transformation by using plasticine as an idea. About elementary geometry mathematic, it could be said that the basic things are basic shapes ...
Kanokpon Arm's user avatar
4 votes
0 answers
114 views

A textbook with a lot of intuitive explanations in advanced probability theory

I am studying Durrett's Advanced Probability Theory, 5th ed. However, I find it very helpful to have more intuitive explanations like this. May I ask if there a textbook or online course or online ...
dodo's user avatar
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0 votes
1 answer
105 views

Do observations of phenomenon drive the development of equations or does a conceptual need for a tool drive their development instead?

I'm attempting to develop an understanding of how equations are developed and wondered whether or not all equations started their development in the quest to document observable phenomenon or are ...
A L's user avatar
  • 137
0 votes
1 answer
91 views

Divide people, who can access to exactly 5 blueprints, into groups that no group can access to whole 20 blueprints

A very secret company develops a hi-tech machine. There are 20 different blueprints needed to construct it. Every employee has access to exactly 5 different blueprints and every combination of 5 ...
longnh's user avatar
  • 59
0 votes
0 answers
40 views

Doing mathematical research alone.

Currently I am no researcher in mathematics, but in the future I might consider becoming one. Before that, I want to know, out of my curiosity, that whether anyone can perform mathematical research ...
Soumyadip Das's user avatar
2 votes
1 answer
45 views

A direct proportionality problem: alternative proof

The price of artisanal ice cream is $60\%$ labor cost and $40\%$ ingredient cost. Production costs then experience increases: $32\%$ for labor, $52\%$ for ingredients. Write the law that expresses the ...
Sebastiano's user avatar
  • 7,419
0 votes
1 answer
29 views

An exercise on the linear function

A square $ABCD$ has a side that measures $5$. Denote by $y$ the area of the rectangle $A'B'C'D'$ that is obtained by decreasing the sides $AB$ and $CD$ by $x\%$ and leaving the measurements of the ...
Sebastiano's user avatar
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2 votes
0 answers
56 views

How to find an identity of $n=3$, $n=4$, $n=5$ all the way up until $n=13$ and prove it

Problem: https://www.desmos.com/calculator/hv0sfm020w The problem presented in the provided link displays a rectangle that can be adjusted from the stages of $n=3$ up to $n=13$. With each increase in ...
Ella's user avatar
  • 31
2 votes
2 answers
96 views

Determine equation of circle tangent to both the $x$-axis at $(4, 0)$ and the line $y=x+1$ (and perhaps modify question to be a better exercise)

The context is I am writing for a high school level math competition and was thinking of this interesting question to include. I briefly checked MSE and there's nothing directly similar (most similar ...
Garrett's user avatar
  • 53
5 votes
1 answer
154 views

When number theorists use the notation $\sum_{d|n}$, why don't they count the "multiplicity" of a divisor? Why is it not-so-interesting to count it?

This is a question a student asked me when I was teaching a class. When I use the notation $\sum_{d|n}f(d)$, each divisor is only counted once without multiplicity. If $n=4$, then $\sum_{d|4}f(d)=f(1)+...
No One's user avatar
  • 7,889
4 votes
2 answers
97 views

Is converting a mixed-fraction to an improper fraction is just adding the remaining part to the whole?

For example, if you're simplifying $3 \frac{1}{2}$, the conventional way is to do $3 \cdot 2$ and then add the numerator $1$. Isn't this the same as adding $3/1$ and $1/2$?
Curiousnoob72's user avatar
2 votes
0 answers
41 views

Seeking collection of Universiade "Lomonosov" past problems [closed]

I'm looking for an anthology of past years' qualifying exam for Moscow State University's Universiade "Lomonosov" in mathematics and mechanics. I only found the 2022 problems and solutions ...
user2607's user avatar
0 votes
0 answers
48 views

How to motivate the teaching of relations?

I am teaching an introduction to pure maths module. Are there any really good resources on relations? I want something that will have an impact and motivate the learner. I am not really looking for ...
matqkks's user avatar
  • 2,850
-2 votes
1 answer
78 views

How to know if an expression is a solution to a linear system?

I have to very simple question, that I am having some trouble with. I am given an inhomogeneous linear system over $\mathbb{R}$ with four rows and three columns. We know that $v_p$ is a particular ...
N G's user avatar
  • 11
0 votes
1 answer
48 views

the logic of numeral systems [closed]

i have a question about numeral systems that use the place value concept , in the decimal system the position is a power of ten and it has set of ten unique digits, the ...
maryam's user avatar
  • 21
5 votes
1 answer
119 views

How do we formalize the derivation of the ideal gas law from Boyle's Law, Charles's Law, and Avogadro's Law?

Given: $V \propto 1/P$ $V \propto T$ $V \propto n$ Prove that: $V \propto \frac{nT}{P}$ Here is the intuitive argument I have: We can see that $V = \langle \text{mystery meat} \rangle  1/P$ $V = \...
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