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1500 questions
10
votes
2 answers
Summer opportunities for math undergrads as an alternative to REU
I am currently helping my advisees (undergraduate math majors) plan their summer. As the obvious option, they've already applied to lots of REUs (some have gotten in and others not heard a positive response yet), but of course REUs can be very…
Idempotent
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10
votes
4 answers
Creativity in mathematics
I have recently been engaging more and more with my creative side by drawing, writing, and (trying to) playing piano. I have come to see mathematics as much more of a creative field of study than I have previously and it got me thinking...Is there…
celeriko
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10
votes
7 answers
Looking for software for plotting exact and beautiful (function-)graphs
I am looking for some software producing beautiful and exact pictures of functions, plots, etc. I really love those images in the german textbook “Höhere Mathematik 1(2)”, Meyberg, Vachenauer:
And this one (created with POV-Ray) is truly…
Dennis Wydra
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votes
4 answers
Is it a good idea to use past questions in examinations?
When it comes to writing examinations, there are two options I am considering.
Write the entire exam originally (which will of course mean some well-known proofs, thereby technically not making it completely original)
Use a ratio of 'original'…
Trogdor
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votes
3 answers
Discrete Math text before a proof course
Our department has decided to offer a "Discrete Math" course that students would take before their "Intro to Proofs" course. The idea is that the Discrete Math course would focus on the computations and techniques that are used in discrete settings…
Aeryk
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10
votes
2 answers
advantage of handwritten materials for course documents
I am curious, is anyone aware of a study which determines the advantage of typed vs. handwritten material in mathematics?
Of course, ideally, we would compare the best of both worlds. Say a beautifully $\LaTeX$ed document vs. the notes of someone…
James S. Cook
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10
votes
1 answer
Language to Distinguish Between Variables and Arbitrary Constants
Today in second semester calculus, I found myself stumbling a bit to provide a natural-sounding explanation for all the letters involved in the expression
$$
\lim_{t \rightarrow \infty} \int_1^t \frac{1}{x^p} dx,
$$
where $p$ is an arbitrary real…
Austin Mohr
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10
votes
2 answers
What are some good or neat examples of computing a function's Taylor series?
Starting from
\begin{equation*}
\frac{1}{1-x} = 1 + x + x^2 + x^3 + \cdots,
\end{equation*}
which holds when $|x| < 1$,
we can conclude that
\begin{equation*}
\frac{1}{1 + x^2} = 1 - x^2 + x^4 - x^6 + \cdots
\end{equation*}
when $|x| < 1$.
Now…
littleO
- 1,007
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10
votes
2 answers
How to differentiate between mathematical skills and understanding of mathematical concepts?
How would my Colleagues here on Math Educators differentiate between mathematical skills and understanding of mathematical concepts?
I'm a community college instructor and high school instructor looking for examples from my colleagues. I have…
Gerardo
- 455
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10
votes
2 answers
When to encourage students to read mathematical literature written in English (in non-English speaking countries)?
There is a lot of mathematical literature in some non-English languages (French, German, Spanish, etc.) that students from these countries don't need to read English literature (at least) for their undergraduate studies. However, in more advanced…
Markus Klein
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10
votes
2 answers
Quotations of Great Mathematicians as a Source of Inspiration for Young Students
I like using quotations of great mathematicians as a source of inspiration for young students. I think even a short sentence could have a great influence on forming their research interests and point of views in future. Just as an example look at…
user230
10
votes
2 answers
Project/Assessment based on Flatland for Secondary Geometry Class
One of my favorite books is Flatland by Edwin Abbott, which is incredibly rich in geometric concepts especially relating to dimensionality. I would really like to assign it to my secondary geometry class to read but I am struggling with a final…
celeriko
- 5,070
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- 18
- 56
10
votes
2 answers
Notation of points with coordinates
At least in Germany, nearly all teachers and textbooks use the notation
$$P(x,y)$$
for the point $P$ with coordinates $x$ and $y$.
My own math professors at university always cried about this, as the notation should be
$$P=(x,y)$$
and I've come to…
Toscho
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10
votes
8 answers
How early and how much can you teach kids and teenagers about vectors?
I have met kids and teenagers who I believe are capable of understanding the concept of a vector. However, I have only heard of a select number of schools who teach it to young people. Here's my main question: how early and how much can you teach…
Stan Shunpike
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10
votes
1 answer
Can math movies help us in teaching?
There are many cinematic and documentary movies about mathematics and mathematicians in every field of mathematics. Particularly in logic, set theory and philosophy of mathematics, which are my research fields one can find plenty of such…
user230