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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10
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1answer
2k views

Learning higher-mathematics on your own

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting. I graduated with an M.S. in Computer science about ...
16
votes
4answers
6k views

Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
0
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1answer
26 views

Conversion of Excel formula back to written Formula…if possible!

I turn to you as a last resort, in the hope that you will forgive my Maths ignorance and help me with what may be a simple problem. Essentially, this involves converting an excel formula to written ...
5
votes
6answers
253 views

Not $\pi$ - What if I used $3$? Teaching $\pi$ discovery to K-6th grade

So, in ancient Mesopotamia they knew that they didn't really have the correct number ($\pi$) to determine attributes of a circle. They rounded to $3$. If you acted as though $\pi=3$, what shape would ...
9
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7answers
3k views

What is the best base to use?

When I typed this question in google I found this link: http://octomatics.org/ Just from the graphic point of view: this system seems to be easier (when he explains that you can overlap the line). He ...
5
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5answers
445 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 ...
10
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5answers
3k views

Mathematics, Philosophy and writing.

Do you know of any famous mathematicians who were also philosophers? I have heard of Descartes, Plato and Leibniz. Are there other good examples, especially more modern examples? Also welcome are ...
3
votes
1answer
126 views

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

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
2
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1answer
97 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
2
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1answer
110 views

Undergraduate Project Suggestions

A student of mine has expressed interest in doing an independent project next quarter with me. This would not be for credit and it is purely for her own educational stimulation. She wants to study ...
25
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2answers
1k views

Collections of undergraduate research projects [closed]

I would like to compile a "big list" of undergraduate research projects in the following areas of mathematics: calculus; analysis; abstract algebra; linear algebra; number theory; geometry; ...
9
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0answers
186 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 ...
-2
votes
0answers
38 views

what are the number of ways to select a 4 digit number with a 3 digit number always included? [on hold]

Number of ways to select 4 digit number( X X X X ) should have three digit number ( say 1 2 3 ) It should be in same order.
1
vote
1answer
77 views

Does anyone know a no-nonsense intro to “logic for mathematics” that I can give to a Year 11 student?

I'm looking for material on propositional and first-order logic to give to a Year 11 student that explains how they're used "in practice." For example, I want to be able to write the null-factor law ...
0
votes
1answer
16 views

Plotting triangles based on a single point with distance and angle.

I'm tasked with creating an arrowhead within a pdf program. I have a single point with at $x=5.6$, $y=4$ this would be point A of my triangle I want to make the sides equal at $90$ degrees angles ...
4
votes
3answers
375 views

Does introducing penalties for getting true/false questions incorrect result in higher skill penetration (less luck/variance)?

A student is asked to answer 50 true/false questions and he would get 35 right and 15 incorrect if he had to put his best guesses for each question down. Now, for each question he has a certain ...
4
votes
5answers
4k views

Difference between Pure and Applied Mathematics?

So, I have been looking into college courses to see what I want my major to be, and I noticed that M.I.T offers two specified types of Mathematics. Pure and Applied. What is the major differences in ...
26
votes
14answers
780 views

$2\times2$ matrices are not big enough

Olga Tausky-Todd had once said that "If an assertion about matrices is false, there is usually a 2x2 matrix that reveals this." There are, however, assertions about matrices that are true for $2\...
0
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0answers
27 views

How can I make separate sentences or paragraphs? [migrated]

Hello I am new to Stackexchange and I'm trying to learn how to make separate sentences, paragraphs and to write proper math script. So, everytime I try to make a paragraph or separate 2 sentences ...
-1
votes
1answer
43 views

Long Division and why we need it? [closed]

Why do we still teach Children Long Division when we'll never use it in life? Whats the point of all that stress vs a few strokes of a calculator?
14
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5answers
389 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 ...
11
votes
7answers
2k views

What are the practical uses of $e$?

How can $e$ be used for practical mathematics? This is for a presentation on (among other numbers) $e$, aimed at people between the ages of 10 and 15. To clarify what I want: Not wanted: $e^{i\pi}+...
42
votes
12answers
5k views

Does “Doing a thing to both sides of an equation” have a name?

A two part question. 1 True or False: when working with an equation or inequality, everything that you do is either: a substitution, or an operation performed on each side Note that algebraic or ...
1
vote
0answers
47 views

Applied mathematics job [closed]

I am on course applied math and I don't understand where can i find job by my education. Our teachers got their long time ago and others just working as teacher. My question: "Is there are opportunity'...
1
vote
1answer
37 views

Geometry and trigonometry Courses [closed]

I have recently finished my higher maths in Scotland which is equivalent to A-Level maths in the uk or APs in the USA (I think). I want to concentrate fully on geometry and trigonometry so I don't ...
0
votes
1answer
47 views

Integer solution to the equation below

I wanted to know integer solutions to the equation (1/k1) + (10/k2) + (100/k3) + ..... + (10^18/k19) = 1 (where k1,k2,k3.... are integers) which I believe is ...
0
votes
1answer
29 views

Proving the concurrency of angle bisectors in a triangle analytically

I'm taking a course at teaching and we have some geometry questions. Among the questions there was one I couldn't solve. I'm trying to prove that angle bisectors in a triangle intersect at a single ...
0
votes
0answers
18 views

Change the intersection's points of a paraola

I have the parabola $$y=-10\cdot x^2+10$$ I want to obtain a parabola which passes in $(-10^{-6},0);(10^{-6},0);(0,10)$. Is it possible to write the equation modifying the above equation? Thank ...
33
votes
7answers
3k views

Why does topology rarely come up outside of topology?

I am currently taking topology and it seems like a completely different branch of math than anything else I have encountered previously. I find it a little strange that things are not defined more ...
2
votes
1answer
47 views

Trying to prove that geometric and algebraic interpretations of the dot product are equal.

I am a Classics major trying to teach myself physics. I am on summer vacation at the moment, and I am going through a book called Classical Mechanics by J. Taylor. I am on the first chapter, and I ...
-1
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0answers
26 views

how can i now position my character set in Pi?

i have characters (10 numerals) how can i count position number of beginning my collection in PI like ...
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0answers
22 views

Quick question regarding the work of a dynamical system

I'm sitting in on a course in dynamics and I've noticed something very strange that I can't get my mind around. So when they do problems that involve springs, they are saying that the work is $$U_s=-...
7
votes
4answers
453 views

How to stay motivated when solving diffucult problems? [closed]

From your experience, what is the most effective way to solve competition math problems without getting discouraged/frustrated because you cannot find the solution? For example, I was trying to solve ...
12
votes
4answers
570 views

Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$?

First I have checked the search option but found nothing relevant to my problem and also level of math. I just started learning the language of mathematics, on my own and I have trouble understanding ...
0
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0answers
54 views

How can I understand the step by step calculations for the formula from the blog below?

I am studying clustering and found a useful article on the blog post here Finding the K in K-Means. But I am having difficulty in understanding the formulas below and how I can do step by step ...
0
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1answer
40 views

Grading a question about the continuity of $f(x,y)$

If $\displaystyle \ \ f(x,y) = \begin{cases} \frac{3x^2y}{x^2+y^2}, &(x,y) \neq (0,0) \\ a, &(x,y)=(0,0) \end{cases}$ find the value of $a$ such that $f$ is continuous at the origin. I ...
1
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0answers
27 views

What topics would be included a restudy of mathematics? [closed]

Assume that up until this point my entire mathematics experience has been gone about in a terrible way. What topics would I start with in order to rebuild to a level in which I could approach ...
33
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 ...
0
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0answers
25 views

Can somebody help me understand the formulas in the image below?

I got the image from this web site. The site talks about how to determine optimum number of clusters. I understand the first two but having a hard time to understand the last two. And what does "a ...
2
votes
1answer
689 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 ...
0
votes
1answer
22 views

Adding and Subtracting Powers of 10

I am entirely new to this subject and am already lost. The problem is Five x Ten to the power of Negative Two, + Four x Ten to the power of Negative Three. I was told that I have to make the exponents ...
43
votes
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 ...
2
votes
0answers
58 views

Online Video Lectures for Graduate Level Mathematics?

I am wondering if there is a nice compilation of good video lectures in graduate level mathematics? I mean a website, or a forum, or maybe something like course-era (which is mostly undergraduate ...
0
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3answers
4k views

How to find multiples of numbers under a certain range

I recently found a 'question' that requires me to find the sum of all multiples of 3 and 5 under 1000, I sadly cheated and found some code online to help build a code in python: ...
11
votes
4answers
850 views

Is advanced college math (eg analysis, abstract/linear algebra, topology) supposed to be as intuitive as elementary math? [closed]

So I don't know if I'm not smart enough for math, but lately, it seems to me as if some advanced topics are just too unintuitive in my opinion. For example, I have no idea what eigenvalues, ...
96
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 ...
18
votes
4answers
625 views

Is it necessary to prove everything and solve every problem in the books? [closed]

I am an undergraduate really passionate about the mathematics and microbiology. I have few big problems in learning which I would like to seek your advice. Whenever I study mathematical books (...
18
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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 ...
19
votes
1answer
737 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 ...