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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1answer
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How do I get good at calculus in specific, Mathematics in general? [on hold]

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 ...
3
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3answers
51 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
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2answers
36 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.
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4answers
526 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 ...
61
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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
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1answer
30 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 ...
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 ...
1
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0answers
43 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 ...
58
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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
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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
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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 $E$?
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1answer
64 views

Help needed for a step by step calculation

I hope I can get some help to understand step by step calculations for formulas below. If I have a weighted distance formula like below: $d(O, P) = \sqrt{\frac{\hat{x_1^2}}{\hat{s_{11}}} + ...
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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 ...
1
vote
1answer
349 views

How to explain this question (about square perimeter and area) to a 6 year old

My daughter who is in 1st grade is learning to grasp he meaning of multiplication and has not yet been introduced to division. she is appearing for Kangaroo Math Competition. Following question has ...
1
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3answers
160 views

My brothers share from income.

My brother is driving a limo with his partner who told him that they will go $50-50$ on income and also $50-50$ on gas. So if my brother earns $\$1000$ by spending $\$200$ on gas, what will be my ...
14
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7answers
2k views

Defining the derivative without limits

These days, the standard way to present differential calculus is by introducing the Cauchy-Weierstrass definition of the limit. One then defines the derivative as a limit, proves results like the ...
42
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11answers
3k views

Refuting the Anti-Cantor Cranks

I occasionally have the opportunity to argue with anti-Cantor cranks, people who for some reason or the other attack the validity of Cantor's diagonalization proof of the uncountability of the real ...
3
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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 ...
0
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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 ...
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9answers
2k views

Elementary Papers at ArXiv

Inspired by this question, at MO i am asking this question. Can anyone list some elementary articles at ArXiv which can be understood by High-School/Undergrad Students. I am asking this because, i ...
1
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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 ...
8
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0answers
154 views

How can I begin reading journals and papers?

I am an undergraduate CS student but I love Math and spend most of my time doing and reading Maths books. I realise that it's important to get into the habit of reading papers and journals so it will ...
0
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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 ...
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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 ...
27
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20answers
975 views

What are some surprising appearances of $e$?

I recently came across the following beautiful and seemingly out-of-the-blue appearance of $e$: $E[\xi]=e$, where $\xi$ is a random variable that is defined as follows. It's the minimum number of ...
13
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3answers
588 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...
0
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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 ...
11
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6answers
4k views

Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical ...
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) , ...
28
votes
6answers
7k views

Teaching Introductory Real Analysis

I am currently helping teach an introduction to real analysis course at UC Berkeley. The textbook we are using in Rudin's "Principles of Mathematical Analysis" (aka baby rudin). I am trying to find ...
15
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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?
1
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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 ...
349
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35answers
42k views

Do complex numbers really exist?

Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious ...
4
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5answers
401 views

What mistakes, if any, were made in Numberphile's proof that $1+2+3+\cdots=-1/12$?

This is not a duplicate question because I am looking for an explanation directed to a general audience as to the mistakes (if any) in Numberphile's proof (reproduced below). (Numberphile is a YouTube ...
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 ...
74
votes
3answers
6k views

Getting Students to Not Fear Confusion

I'm a fifth year grad student, and I've taught several classes for freshmen and sophomores. This summer, as an "advanced" (whatever that means) grad student I got to teach an upper level class: Intro ...
7
votes
4answers
887 views

The meaning of various equality symbols

I'm interested in knowing what is the meaning of the various equality symbols: $=,\sim, \cong,\approx,\equiv$. For example, the speed of a car $V$ in m/s: what would be the meaning of each of these ...
34
votes
8answers
7k views

How can I learn to “read maths” at a University level?

When I look at math, it's like my mind goes fuzzy. The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
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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 ...
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 ...
12
votes
7answers
3k views

Should I do all the exercises in a textbook?

The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? ...
30
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1answer
3k 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 ...
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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
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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 ...
2
votes
1answer
659 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 ...
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1answer
137 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 ...
1
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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 ...
1
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3answers
157 views

Where could I learn basic math terminology?

I am an english learner and I would like to learn the etymology of Mathematics. I would like to know the most common phrases in Algebra, and Geometry as well. I want to know at a level of UK's A+. ...
27
votes
6answers
868 views

Open source lecture notes and textbooks

This question is inspired by the popular "Best Sets of Lecture Notes and Articles". Indeed, I would like to collect a "big-list" of open source (that is, with $\LaTeX$ code available) high-quality ...
13
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9answers
860 views

Elevator pitch for a (sub)field of maths?

When I first saw the title of this question, I forgot for a moment I was on meta, and thought it was asking about quick, catchy, attractive, informative one-or-two-liner summaries of various fields of ...