# Tagged Questions

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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### Is it too much rigor to turn a set into a vector space?

I was reading some online notes on vector spaces and one authors insisted on turning a set $\mathbb{X}$ into a vector space. I thought it was quite insane but maybe I am not seeing the point. The ...
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### Difficult to read about different subjects simultaneously, should I leave one for now? [closed]

I learn math by reading books. Usually I read 3 books (about 3 different subjects) simultaneously and switch focus every couple of days. The books i'm studying right now are Rudin's functional ...
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### Factoring bivariate quadratics with real coefficients (for high school students).

I was tutoring a Year 10 student last night (he's learning about quadratics). Unfortunately, we ran into a class of problems that I couldn't explain how to solve (beyond simply guessing and checking), ...
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### New idea to solve this equation

I was teaching $\left \lfloor x \right \rfloor$ function properties and equation . I solved this equation in my class . My works are show below. Some students ask me for new Idea...,and now I am ...
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### Proper name and access of the constituents of an equation.

In any math problems for example: ... B = (1 + B) A = (A + B) ... How can I definitely define a variable that points to the ...
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### Opportunities to learn algebraic geometry outside of PhD education [closed]

After a lot of deliberation, I decided to go to professional school instead of pursue academic mathematics. I don't have research aspirations, but I do have an obsession with "getting" esoteric ...
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### Any idea how to approach this problem

A rectangular meadow will have a fence around it. The long side is $130$ m longer than the short side. The sides lengths can be written $x$ and $x+ 130$. Write a simplified expression for 1) ...
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### Probability of 2 students being chosen the both have under 100 books at home

Suppose we select two students at random from the class of fifteen. What is the probability that both students chosen have less then 100 books at home? Data provided is the amount of books each ...
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### When I was teaching absolute function properties, I suddenly made this question …

I was teaching absolute function properties in a K-12 class. I made this question in my mind. Suppose $f(x)$ is a one-to-one function, and its definition is $f(x)=max\left \{ x,3x\right \}=ax+b|x|+c$...
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### Demonstrative geometry around the world and its significance.

This is not exactly a mathematical question. I am from Pakistan; and over here students are taught a subject 'demonstrative geometry' (as a part of mathematics) from secondary level education. ...
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### How to calculate percentile?

I am reading a document issued by UK Gov about minimum salary for work visa, it is using word percentile, which I don't understand, Could anyone explain what would be the 50th or 75th percentile IF, ...
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### Which background is more suitable to study “Cryptography” [closed]

I am a student of Pure Mathematics and also interested in programming .I have learnt C++,SAGE . Recently I have started learning "Cryptography" .But there are many definitions involved here like ...
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### Reading mathematics at the graduate level - does every single proof matter?

I would be interested in hearing from PhD students (and upwards) specializing in pure maths (in particular, the more algebraic aspects). My question is this: When reading to learn mathematics at ...
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### A harder long division puzzle than the first; what should “Algebra I” solution look like?

Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine: ...
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### “Long-division puzzles” can help middle-grade-level students become actual problem solvers, but what should solution look like?

This is my first post. I hope it's acceptable. EDIT Since there are people to whom such notation is foreign, I will point out that the problem represents KRRAEE / KMS, where PEI is the quotient and ...
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### Is this Applied Mathematics?

I wanted to learn Applied mathematics, mostly due to it being similar to or having relation to Object Orientated Programming (OOP), and thought it would help alot. I searched all over the internet. (...
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### Most natural intro to Complex Numbers [closed]

This is a soft question but I'm willing to ask. There are few ways to introduce the field of complex numbers, but if You had the opportunity to write an elementary textbook, what would be the most ...
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### Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
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### Cartesian Product how can this be used in real life situations [closed]

I am learning about the cartesian product as defined by The New Oxford American Dictionary as: the product of two sets: the product of set X and set Y is the set that contains all ordered pairs ...
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### simple SAT question. confused.

My friend selected option B, I did C. We're confused. Can someone please explain this for my friend?
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### Easy math proofs or visual examples to make high school students enthusiastic about math [closed]

I'm a teacher in mathematics at a high school. Math has fascinated me for almost my entire life, so I would like to bring that enthusiasm to my students with beautiful yet easy to understand proofs or ...
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### Where to study type theory? [closed]

I want to learn more about (homotopy) type theory, constructive mathematics and univalent foundations. To my knowledge, there are only few faculties with large type theory groups. In Europe, most of ...
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### The $\epsilon$-$\delta$ definition of a limit of a linear vs a non linear function

I am teaching elementary analysis and introducing the concept of $\epsilon$-$\delta$ definition of the limit to first time learners. For example, we take $\displaystyle\lim_{x \to 2} (2x - 1) = 3$, ...
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### An applied problem in ODE leading to Interval of Existence issue

ODE books have a section on interval of existence of a solution with a standard set of problems, such as what is the interval of existence for $y'+(\tan t) y = t/(t-2), y(3)=5$, or $y'=y^3, y(0)=2$. I ...
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### Sketching a nice graph of $f(x) = x^2 + 2x – 8$ [closed]

I would like to sketch a nice graph of $$f(x) = x^2 + 2x – 8$$ including labeling the coordinates of the vertex and intercepts. I tried to graph it using this tool: But I don't know how to label ...
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### Is theoretical Linear Algebra still an active field of research?

Numerical Linear Algebra seems to be a very active area right now, but is there any work still being done on the purely theoretical side? To put it another way...is it possible for someone to write a ...
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### How values of the constants are derived mathematically? [closed]

As said by Jan regarding constant value $\pi$ ,Imagine you have a circle and you are able to measure its circumference "c". Then, you can also find out what its diameter "d" is. When you divide ...
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### Proving a quadrilateral is an isosceles trapezoid

Warning: You'll probably need pencil and paper to follow this. Recently I came across the following problem in a middle/high school geometry textbook: $\ast$ Suppose $\ QUAD\$ is a quadrilateral ...
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### How big a text file will be for a wordlist composed of 10 HEX characters given certain conditions?

While discussing with another friend the insecurity with some wifi systems against dictionary attacks we couldn't reach a common ground on how big a WPA wordlist dictionary would be for the most ...
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### How do authors make their problems/exercises for their math books? [closed]

I want to be a math professor one day, but I'm wondering how to make my own original problems to give them to my students. I think that it is a responsibility of the professor to create original and ...