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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3
votes
4answers
47 views

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

How could I switch from $a\cdot \sin(t) + b \cdot \cos(t)$ to $c \cdot \cos(t+f)$? Thank you for your time.
0
votes
2answers
35 views

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

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.
15
votes
4answers
522 views

Gaining Mathematical Maturity [on hold]

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 ...
1
vote
1answer
29 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
42 views

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

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 ...
54
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 ...
0
votes
2answers
23 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.
1
vote
0answers
11 views

E convergence set in $C^n$ for example

Definition. A subset E of $\mathbb{C}^{n}$ is said to be a convergence set in $\mathbb{C}^{n}$ if $E=Conv(f)$ for some divergent series f of Class $(1,0)$. what is for example $E$?
-2
votes
1answer
12 views

Parallelogram how to construct [closed]

I have a parallelogram with the perimeter of 0,18m. One side is a=6cm. The height of the ...
3
votes
3answers
49 views

Why do we introduce groups using division?

I am only starting to really study algebra so I apologize if this is an ill-formed question. When learning about groups, why is division used so heavily in the beginning? Would it not be simpler to ...
1
vote
1answer
33 views

How do i calculate the area of shaded region?

I wouldn like to find the area of shaded region which it's circulated by a triangle as show in the below picture ? Note: I tried to draw other circle arround triangle ,but it's seems hard to me to ...
0
votes
0answers
15 views

A Venn diagram of possible points (critical, stationary, maximum, minimum, inflection, etc.)

I'm looking for a Venn diagram that classifies these points: Critical points, stationary points, maximum points, minimum points, inflection points, etc. This is aimed at intro Calc students. Such a ...
-1
votes
2answers
71 views

Proof without words for logarithmic funtions [closed]

I'm looking for a PROOF WITHOUT words for logarithms. The only one I've seen is calculus based and I need one for a younger audience. Any help/suggestions would be appreciated! This is the example I ...
0
votes
1answer
56 views

Soft Question: Do most mathematicians agree that the function is “the most important concept in all of mathematics”?

Spivak (Calculus, 3e, p. 39) writes: Undoubtedly the most important concept in all of mathematics is that of a function---in almost every branch of modern mathematics functions turn out to be ...
0
votes
0answers
23 views

prove de Rham cohomology of S,the “spherical universe,” is 0-dimensional?

How to prove de Rham cohomology of S,the "spherical universe," is 0-dimensional?(Here, S is a rectangle where if you exit the right, the enter from the top and if you exit the left, the enter from the ...
1
vote
0answers
23 views

Solution of equation $z=a((x-a)e^{2x/a}+x+a)$

I want to solve the equation for $x$ $a((x-a)e^{2x/a}+x+a)-z=0$ Conditions on $a$ and $z$ are: $a,z>0$ and both real. I made some research but couldn't find a lot. Maybe something with the ...
0
votes
1answer
73 views

Why this is not true : ${i}^{n}=0$ for every even positive integer $n$?

Let $i$ be a unit imaginary part , we have for $\theta=\frac{\pi}{2}$: $\left(\cos \theta + i \sin \theta \right)^n = (0+i\sin(\frac{\pi}{2} ))^n=i\sin(n\frac{\pi}{2})=0$ (Using Moiver formual) , ...
55
votes
8answers
8k views

How to debug math?

May seem strange as I'm good in programming, but I just started diving into math. ATM I'm learning combinatorics at Khan Academy, and here's an example of a question that I struggled with (that's not ...
-1
votes
2answers
60 views

What are the books that I should study for college? [closed]

Baccalaureate exam approached Real Analysis (limits, differentiation and integration), Abstract Algebra, Functional Algebra, Linear Algebra, Combinatorics, Complex numbers, Vector Geometry, Analytical ...
-1
votes
0answers
20 views

How to find the longest diagonal if you fold a piece of rectangular paper in half?

An 8-inch by 12-inch paper napkin is folded in half three times with each fold resulting in a smaller rectangle. What is the longest possible diagonal for the final rectangle? Express your answers in ...
0
votes
4answers
56 views

BEDMAS where the order of Addition before Subtraction matters?

Here is a recent "tricky problem" that is making the rounds on FB: BEDMAS is explained here in a video, with this being the upshot: Everyone understands that ...
1
vote
1answer
24 views

generalization of the Pythagorean theorem

In school, students learn that in a triangle ABC, ACB is a right angle if and only if AB^2=AC^2+BC^2. This deep relation between geometry and numbers is actually only a partial result as one can say ...
0
votes
1answer
33 views

Course or book - Math Foundations in CS

I want to improve my math skills, now I'm trying to find good route for this purpose. I'm using Khan Academy, and recently found "CS103 - Mathematical Foundations of Computing" course which looks good ...
1
vote
1answer
32 views

What means to publish views/ideas are used, instead of blogs, among mathematicians today?

My question is motivated by the feeling that some mathematics blogs publish less and less over time. Are there other communication means which are used now instead with a similar role, or is it ...
0
votes
1answer
45 views

Is the Science and Knowledge Publishing Corporation a spam journal publisher? [closed]

I submitted my paper entitled " A new result for divisibility among sum power divisor from 3 month ago to this journal ,I have received in this day this message : Title: A new results for ...
1
vote
1answer
29 views

Find the value of the Infinite product in terms of k which is a positive integer

$$\prod_{n=k+1}^{+\infty}\left(1-\frac{k^2}{n^2}\right)$$ The only help we have been able to find is that of Euler, anything would be amazing!
2
votes
1answer
101 views

How to succeed in upper-level math [closed]

This question will essentially be more of a how-to plea or general help request. I'm currently studying math and I'm at the point where I've transitioned into upper-division classes, most if not all ...
1
vote
2answers
87 views

a healthy perspective on “knowing everything” [closed]

This is a question about attitude, but related to math studies. I have trouble with two things: 1. making "normal" progress in my learning and 2. having the satisfaction that I understand what is ...
1
vote
2answers
94 views

Integral as “Area Under the Curve”

I'm a high school math teacher teaching an introductory calculus course, and I'm having a problem teaching one particular student about the physical definition of an integral. The intuition is that ...
-3
votes
1answer
39 views

Formula Derivation

What is the formula that can be derived using the values and formulas below to get the value of K43? Here's what I have, so far, but no luck in getting the correct formula: 0 = 925191 - 119355 - ...
5
votes
2answers
55 views

Where is a good source for serious math (wall-size) posters?

Where is a good source for math wall posters that give glimpses of serious and beautiful mathematics? I'm a faculty member looking to find some wall posters (e.g. 2 ft x 3 ft) to hang in a handful of ...
2
votes
1answer
27 views

An error on the BBC maths revision website?

The multi-choice question, for revision for 12 year olds, is here: A company exchanges foreign currency. They offer $\$1.5$ for each pound. On top of this, they charge a fee of $£4.50$. Which ...
1
vote
0answers
37 views

how to solve y^2<x^2 y^2>x^2

Can someone help me with the steps how to solve those inequistins? y^2<x^2 My wrong solution: y^2<x^2 /sqr y<x or y<-x or -y<x or -y<-x ...
1
vote
1answer
58 views

Should I remember the proof of mathematical theorems(every step)?

The problem is, that when I am reading the proof of mathematical theorem(in my case - it is calculus), U understand the idea and every step of proof. But i can't prove the theorem individualy even if ...
0
votes
0answers
55 views

Confused about 'staircases'

Hi I'm currently reading a paper, which contains an experiment I was to re-create - is there any chance someone can explain the staircase to me? I've had a quick Google - and I haven't really got ...
0
votes
2answers
38 views

Converting from decimal to any number base.

I know that this can a silly question. But I can not find the answer. When converting number bases (from decimal to any other number bases), we divide the decimal number by that base, and write down ...
15
votes
2answers
143 views

Math for blind people…

What happens if some blind person want to study math? Is there some "braille alphabet" for mathematical symbols? Are there math books, at least for undergraduate students, written for blind people?
0
votes
1answer
28 views

Statement and Proposed Negations

I know this may seem like a really unintellectual question however I was wondering what statements and proposed negations are. My teacher didn't really go over this and I can't seem to find it in my ...
0
votes
0answers
24 views

Algorithmic differentiation graph

I have very basic question about reverse mode algorithm calculation. It is well-known that we calculate derivatives according to chain rule, using sub expressions. I was trying to find kind of proof, ...
1
vote
1answer
114 views

Hypothesis Test Questions

I am currently teaching an introductory level statistics course and I had two quick questions on hypothesis tests. Just to be clear, I have a fairly good background in probability and analysis, but I ...
2
votes
1answer
82 views

Why is Gaussian elimination still being taught when there are more efficient methods? [closed]

Why is Gaussian elimination still being taught when there are more efficient methods? By efficient methods I mean less time and effort consuming ways to solve a system of linear equations. I have ...
2
votes
3answers
46 views

How to solve for $\theta$ in $130\cos(\theta) - 122\sin(\theta)=10$?

The original question was solve for $\theta$ in $65\cos(2\theta)-56\sin(2\theta)-55=0$. I reduced it to $\cos(\theta)((130\cos(\theta)-122\sin(\theta))-10=0$, therefore we have a $\theta=0$ but I ...
1
vote
2answers
50 views

Definition of manifolds with finite atlas

It is known that any manifold of finite dimension $n$ has an finite atlas (with at most $n+1$ charts). My question is then the following : why don't we define an atlas of a manifold (in the finite ...
4
votes
1answer
31 views

Systems of ODE to High-Order converstion: Why?

I am the TA for a course in ODE, and one of my students asked me a question yesterday: why in the world do we bother with converting between (constant-coefficient) systems and higher-order ODE? I ...
1
vote
0answers
45 views

Motivation for Non-Euclidean geometry: relativity

I'm looking for references to motivate the study of non-Euclidean geometry. In particular I would like something about relativity. I do not want texts to learn non-Euclidean geometry, only ...
4
votes
1answer
48 views

Corollary **to** Theorem 1.2 or corollary **of** Theorem 1.2?

I think both ways are possible in English, but should I say This is a corollary to Theorem 1.2 or This is a corollary of Theorem 1.2 ?
1
vote
0answers
34 views

Need help to visualise Topological Puzzle

I am curious about this puzzle on unlinking the fingers of a rubber man. (https://www.youtube.com/watch?v=olHV4qvSDg8) However, despite the illustrations in the above video, I can't visualize the ...
2
votes
0answers
54 views

Where to start with Euler and Ramanujan?

What are the specific qualifications for directly studying Euler and Ramanujan's works.Is Hardy's "A Course in Pure Mathematics" a good start?
2
votes
4answers
49 views

Numerical property $P(n)$ such that $\forall n P(n)$ is false but a counterexample is difficult to find

I would like to find a nontrivial property $P(n)$ for $n \in \mathbb N$ such that $\forall n P(n)$ is false but the first counterexample can be found only for "very high" $n$ (so high that it wouldn't ...
0
votes
1answer
21 views

Assistance with “Negative Countdown”

I'm trying to help my sister with this maths question: In "Negative Countdown" you can add or subtract all of the numbers given to make the target number. The numbers must be only used once, and all ...