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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4
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8answers
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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 ...
1
vote
1answer
104 views

New idea to solve $\int x^n e^x dx$

I have this problem $$\int x^n e^x dx= x^ne^x -nx^{n-1}e^x +n(n-1)x^{n-2}e^x- \cdots+(-1)^nn!e^x $$ my try was to use integration by part . $$I_{n}=\int x^n e^x \, dx=e^x x^n -\int (nx^{n-1})e^x \, ...
4
votes
1answer
309 views

Books on complex analysis (Ahlfors, Conway and Lang)

To make my question slightly different from others, I would like to know how would you rate on the complex analysis books by Ahlfors, Conway and Lang? I had a basic course on complex analysis during ...
3
votes
7answers
308 views

Alternate ways to prove that $4$ divides $5^n-1$

I was working for various method to solve this: For all $n\in \mathbb N$: $4\;\mid\;(5^{n}-1)$. My try was: 1st: $$n=1 \to 4|5^1-1\\n \geq 2 \to 5^n=25,125,625,3125,...\\ n\geq 2 \to 5^n=\...
2
votes
1answer
105 views

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 ...
3
votes
1answer
72 views

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), ...
7
votes
5answers
446 views

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 ...
0
votes
0answers
25 views

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 ...
3
votes
0answers
94 views

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 ...
-1
votes
1answer
31 views

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) ...
1
vote
1answer
45 views

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 ...
16
votes
5answers
2k views

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 $f(x)=max\left \{ x,3x\right \}=ax+b|x|+c$...
0
votes
0answers
104 views

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. ...
1
vote
1answer
70 views

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, ...
5
votes
3answers
917 views

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 ...
7
votes
1answer
219 views

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 ...
1
vote
0answers
59 views

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: ...
6
votes
3answers
256 views

“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 ...
0
votes
1answer
91 views

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. (...
7
votes
8answers
991 views

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 ...
3
votes
0answers
51 views

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 ...
0
votes
1answer
320 views

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 ...
12
votes
5answers
290 views

Is $1 : 7 = 1 / 8$ or is it $1/7$?

In a certain (non-mathematical) Stack Exchange, when I wrote $n : m = n / m$ where $n$ and $m$ are positive integers, one of the moderators said "No! $n : m$ is usually the notation for "$n$ parts in $...
0
votes
3answers
291 views

Factoring Trick - Adding Up Coefficients

My professor told me this for factoring polynomials: Add up the coefficients and if they equal 0 then the polynomial has root of 1. Add up, but switch the signs of the coefficients with odd ...
1
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1answer
180 views

Proving Odd & Even Functions

For the following: If $f(x)$ is an odd function, then $|f(x)|$ is _______. If $f(x)$ is an odd function and $g(x)$ is an even function then, $(f~o~g)(x)$ is _______. If $f(x)$ is an odd ...
1
vote
1answer
35 views

Domain of the definition of a composite function

If $$f(x)= \sqrt{3|x|-x-2} \\ g(x)=\sin(x),$$ then the domain of definition of $(f\circ g)(x)$ is ...? How do you calculate the domain of a composite function like this?
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vote
2answers
526 views

Can any function represent something in the real world?

We know that the volume of a cube can be represented by the function: $V(x)=x^3$, where $x$ is side length. $x^2$ can represent the volume of some material that has a constant side ($1$). The function ...
-1
votes
1answer
48 views

Inverse function simple question [closed]

Please explain question no. c in detail
0
votes
2answers
55 views

Can the difference between a number and a set of numbers be calculated as follows?

I have a number $X$ (lets say $45$) and I have five other numbers, lets say $(3, 4, ,5, 6, 7)$ I want to know the difference between my number and the other numbers like this: ...
0
votes
1answer
29 views

Adding a variable in an equation

Recently while doing some math problems, me and my friend came up with some equations. I forgot what the real problem was, but lets say for a moment the equation was more like this: $\omega = \psi + 1$...
1
vote
3answers
147 views

Improving Mathmatical Skill [closed]

I am a student of computer science and engineering. My understanding of mathematics is not very good. I am getting very hard time studying subject that require a background on mathematics. So, I ...
2
votes
2answers
219 views

What do we mean by 'defining a function'?

First I will start by quote from Wikipedia about function's defining methods : There are many other ways of defining functions. Examples include piecewise definitions, induction or recursion, ...
2
votes
2answers
90 views

what is the definition of numbers? [duplicate]

Well the question may seem obvious but I can't really find a proper answer to this. Mathematics all seem kind of difficult to understand so please help. I believe it is a quantity. Thanks in advance.i ...
4
votes
1answer
182 views

Students and Real Analysis

I am currently working on a project investigating why students tend to struggle when they first encounter Real Analysis and what can be done to improve the situation. I would be very grateful if any ...
0
votes
1answer
239 views

How should I start learning Actuarial Science? [closed]

I recently completed my under-graduate studies in pure mathematics, and have been accepted for Masters at one of the top 10 math schools. I have great interest in research and would like to continue ...
1
vote
1answer
39 views

Log, find the following values in term of m and n

I have a hard time on this log question, can you explain it? Given log(x)p = m and log(x)q = n find the following values in ...
0
votes
1answer
60 views

Hessian null - Point of saddle

Given the function $f: \mathbb{R}^3 \to \mathbb{R}$ defined by $f(x,\,y,\,z) := 3 x y^2 + 6 y^2 + x^2 z + 3 z^2 $ is not difficult to show that $f$ presents a unique critical point of coordinates $(0,\...
1
vote
2answers
47 views

simple SAT question. confused.

My friend selected option B, I did C. We're confused. Can someone please explain this for my friend?
70
votes
34answers
8k views

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 ...
4
votes
0answers
69 views

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 ...
0
votes
0answers
85 views

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 $\displaystyle\lim_{x \to 2} (2x - 1) = 3$, ...
2
votes
1answer
105 views

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 ...
0
votes
3answers
138 views

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 ...
5
votes
1answer
349 views

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 ...
-3
votes
1answer
142 views

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 ...
0
votes
0answers
94 views

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 ...
1
vote
1answer
132 views

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 ...
20
votes
8answers
2k views

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 ...
4
votes
1answer
68 views

What book offers strategies and heuristics for theorem proving in the same spirit as Polya's How to Solve It?

Polya's How to Solve It is all about heuristics and strategies for problem solving, but it's mainly written for problems which require students to find values, not to prove theorems. While Polya's ...
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votes
1answer
92 views

What are some good mathematical journals? [closed]

I would like to study mathematics when I'm older, but I want to read some of the current literature to learn what mathematics is truly about, maybe direct my studies into some particular field. What ...