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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2
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2answers
63 views

Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$

my question is too simple. We know all that if we define the exponential function on $\mathbb{C}$ then we define the real part and imaginary part of $\exp{it}$ as $\cos{t}$ and $\sin{t}$. So if we ...
18
votes
7answers
6k views

How to show every subgroup of a cyclic group is cyclic?

I'm teaching a group theory course now, and I wanted to give my students a proof that every subgroup of a cyclic group is cyclic. The easiest way I could think to do this is to say that any cyclic ...
0
votes
1answer
27 views

Finding formula [on hold]

X Y Z Answer 8 2 4 0.5 8 2 2 0 8 2 8 1 My professor gave this as a sort of riddle to figure out, and it's ...
19
votes
1answer
732 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
59
votes
14answers
10k views

Why is radian so common in maths?

I have learned about the correspondence of radians and degrees so 360° degress equals $2\pi$ rad. Now we mostly use radians (integrals and so on) My question: Is it just mathematical convention that ...
632
votes
162answers
39k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament,...
2
votes
1answer
73 views

Instructive video content for High School kids?

I need some math Youtube channels (or any other visual media, movies maybe...) that I can recommend to High School students, not solely as a method of learning math but more to illustrate the beauty ...
16
votes
5answers
461 views

Visualization of surface area of a sphere

I help mentor some really young, bright kids in mathematics. We were looking at geometric properties of various shapes, and one of the kids noted that the surface area of a sphere $S = 4\pi r^2$ ...
2
votes
0answers
79 views

Is group theory and in general pure maths useful in applied mathematics?

I've just finished the first year of Mathematics at University. I've already encountered groups, in a soft mini-course that took around half semester. My idea would be to study applied mathematics, ...
1
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0answers
21 views

What is the best way to teach trigonometry and higher level mathematics to young students?

I am teaching some kids (ages 13-15) some basics of functions and trigonometry in a summer camp. I have noticed that 90% of the class is above average and quickly resolve most of the problems. Soon ...
3
votes
0answers
63 views

Are there any modern mathematicians whose research interest is in “Probability Theory”?

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
1
vote
1answer
30 views

How to solve task? With simultaneous movement

Sorry for my bad English. I was preparing for entry into physical and mathematical School high school in my city. But I am stuck while trying to solve this task: On a river, at the same time from ...
4
votes
1answer
74 views

Theorem 2.27 (a) in Baby Rudin: Is his proof complete enough?

Here's Theorem 2.27 (a) in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition: If $X$ is a metric space and $E \subset X$, then $\overline{E}$ is closed. Now here's ...
9
votes
3answers
118 views

The case for L'Hôpital's rule?

While this may seem very subjective — and, admittedly, my own dislike of L'Hôpital's rule is not entirely devoid of subjectivity — I am looking here for argumented, factual answers. From what I ...
0
votes
0answers
14 views

problem on the concept equation

in this equation why we want to tend the epsilon to zero? What the application of this work? Do we want to calculate of limit value? enter image description here
-1
votes
0answers
20 views

Where can I practice + - * / and some percentage everyday

I just want to exercise my brain with simple math. My goal is to calculate things in my mind without using a calculator and those things are something happen in my real life. For example: I'm ...
0
votes
0answers
8 views

Simple Composite of Relations

My lecturer has given this simple composite of relations question; R = {(1,2), (3,4), (2,1)} S = {(2, 1), (5, 3)} R o S = {(1, 1)} is the answer i acquire. he acquires the answer R o S = {(2,2), (5, ...
1
vote
1answer
24 views

Finite differential?

on my electronics book I found some equations in which there are $\Delta x$ and these are handled with the same rules of differential. For example, if $a$ is a constant: $$\Delta \left(ax\right)=a\...
3
votes
3answers
560 views

How do I accept that math is hard? [closed]

Ever since I began studying mathematics, there were times where I really enjoyed doing so, and then there were times where I didn't enjoy it at all and simply wanted to quit. I guess everyone knows ...
5
votes
2answers
515 views

Re-write a quadratic equation in another form?

$x^2 + \sqrt{2}x = \frac{1}{2}$ I need to find the real solutions for this equation and write it in this form: $$\frac{-\sqrt{A} \pm B}{C}$$ So when I work the problem out with the quadratic ...
10
votes
3answers
271 views

How exactly does Mathematics help me becoming more intelligent (at least, in high school)? [closed]

[Please reditect me to a different site/sub-site/pretty-much-any-relevent-place if I've posted the question in the wrong forum, please do not downvote before attempting to redirect me to the adequate ...
30
votes
5answers
7k views

Mind maps of Advanced Mathematics and various branches thereof

I would like to get a list of mind maps of advanced mathematics topics. As an example, I have posted one below. I would be happy if you post such other maps. Making one and posting it here is also ...
10
votes
2answers
300 views

Do people with average intelligence stand a chance making a tenure track math professorship at a research university? [closed]

I am interested in math and have been thinking about going for grad school and becoming a research professor since graduating from college. However, a few things that happened recently really make me ...
24
votes
9answers
17k 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 ...
720
votes
53answers
423k 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 ...
7
votes
10answers
22k views

Explain for students: Why does 0 mod n equal 0 (zero)?

I told my students that the mod operator basically gives the remainder of division, so upon seeing: 0 mod 10 Some students (apparently) reasoned that, "10 goes ...
6
votes
6answers
173 views

How to explain to a school kid that on a sphere the shortest path between 2 points is given by a great circle?

I will be teaching some "topology" to high school students. I was wondering how to explain to such a school student that on a sphere the shortest path between 2 points is given by a great circle? ...
5
votes
4answers
858 views

Roman Numbers - Conversion to decimal number

I have read that if a smaller number is to the left of a larger number means that the smaller number has to be subtracted from the larger number. Ok I can understand quickly for below Roman Numbers : ...
0
votes
1answer
13 views

How to find equation of a sphere

i'm having difficulty to find equation of a sphere in Mathematica. I already found the radius and center. ...
1
vote
1answer
46 views

How to create a counter example of a matrix with non orthogonal eigenvector?

I am trying to understand this orthogonal eigenvectors $$T = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}$$ let $$u ...
18
votes
6answers
5k views

No radical in the denominator — why? [duplicate]

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to $\sqrt{3}...
95
votes
20answers
20k views

Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
2
votes
2answers
76 views

Studying mathematics as an Undergraduate [closed]

This is not a question related to a certain topic in mathematics, but more a question about studying mathematics generally. (please forgive me if my vocabulary isn't appropiate, I'm not a native ...
1
vote
2answers
59 views

Text for honors college algebra and trigonometry

I am looking for suggestions on algebra and trigonometry for students who are interested in majoring in mathematics. So typical texts written for average freshman who is forced to take math as a core ...
3
votes
3answers
77 views

What is the Pedagogical Justification for Substitution?

My mom is re-learning calculus for the third time (She tutors High School students). And she asked me a question invovling limits: $$\lim_{x\rightarrow \infty} \frac{\ln 2x}{\ln 3x}$$ I led her ...
31
votes
1answer
4k views

GRE past papers

As it is required for most students who wish to do a Ph.D in maths in the US to sit the GRE subject specific mathematics exam, I hope this question will be of interest to the mathematical community ...
1
vote
0answers
17 views

Technical Language Usage: Verb for an Equivalence Relationship “Forgetting” an Attribute that is “Modded Away”

This question is one of English usage, but I'm sure only mathematicians can answer it for me. I want to say in a technical report that an attribute is "ignored" or "forgotten" by an equivalence ...
2
votes
1answer
674 views

The NES mathematics accreditation test

I have to take the NES mathematics test to get accreditation as a High School teacher to become highly qualified to teach mathematics. I have a PhD in physics so I thought that I wouldn't have to ...
8
votes
2answers
225 views

What is the right way to define a function?

Most authors define functions this way: Given the sets $A$ and $B$. A relation is a subset of $A\times B$. Then given a relation $R$, we define $Dom_R=\{x|(x,y)\in R\}$ and $Img_R=\{x|(y,x)\in R\}$. ...
0
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0answers
21 views

subtraction method

I have studied long ago different method for subtracting two numbers, for instance the borrow method or the Austrian method (I hope I am using the right names; I am not an english native speaker and ...
0
votes
1answer
66 views

How do I get good at calculus in specific, Mathematics in general? [closed]

I understand that this question might look like a duplicate to some others asked before, but I assure you, read on, you'll find my case different (hopefully). I am a 12 grade student from the ISC ...
2
votes
3answers
60 views

Switch from $a\cdot \sin(t) + b \cdot \cos(t)$ to $c \cdot \cos(t+f)$ [closed]

How could I switch from $a\cdot \sin(t) + b \cdot \cos(t)$ to $c \cdot \cos(t+f)$? Thank you for your time.
-1
votes
2answers
40 views

Differential equation with absolute value $ax'+bx=|\sin(\omega t)|$ [closed]

How could I solve the follow differential equation? $$a\cdot\frac{\text{d}x(t)}{\text{d}t}+b\cdot x(t)=|\sin(\omega t)|$$ Thank you for your time.
16
votes
4answers
591 views

Gaining Mathematical Maturity [closed]

I was redirected here by a kind fellow from math.overflow. This is not a typical math question, so I apologize if that is discourteous. I am currently a sophomore in my undergraduate mathematics ...
62
votes
27answers
5k views

Is there a great mathematical example for a 12-year-old?

I've just been working with my 12-year-old daughter on Cantor's diagonal argument, and countable and uncountable sets. Why? Because the maths department at her school is outrageously good, and set ...
1
vote
1answer
36 views

Geometry (Locus and constructions)

I want to find the equation for the locus that is at the same distance from the point $(2,3)$ to the line $x=1$. Im not sure if I am right or wrong? Is the locus just the two point at a distance=1 ...
1
vote
0answers
50 views

MIT ocw math/computer science courses for a grade 11 student? [closed]

I am 16 years old and I have decided to take the MIT math and maybe computer science courses online. I love math and computer science and I want to finish the learn the undergraduate courses as soon ...
59
votes
9answers
32k views

Why is $\pi $ equal to $3.14159…$?

Wait before you dismiss this as a crank question :) A friend of mine teaches school kids, and the book she uses states something to the following effect: If you divide the circumference of any ...
0
votes
2answers
24 views

Equivalence between trigonometric functions

could you help me to understand why: $\sin\left(x-\frac{2\pi}{3}\right)=-\cos\left(\frac{\pi}{6}-x\right)$ ? Thank you for your help.