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1500 questions
9
votes
3 answers
Evaluating textbooks in math and physics
I’m currently interested in textbooks, especially the ones in math and physics that are used at the high school, undergraduate and graduate levels and, given the experience of the people on this website in using and teaching from these textbooks I’d…
lorenzo
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9
votes
2 answers
Fear of 3-dimensions
Contrasting 2D and 3D in my field (Discrete & Computational Geometry1) is essential. For example, every 2D polygon can be triangulated (with vertex-to-vertex diagonals), but not every 3D polyhedron can be similarly tetrahedralized.
I experience…
Joseph O'Rourke
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9
votes
8 answers
Are there any proofs of Euler's Formula that do not rely on calculus?
The most common way I have seen Euler's formula
$$
re^{i\theta} = r(\cos\theta+i\sin\theta)
$$
introduced in a classroom environment is to substitute $i\theta$ into the series expansion of the exponential function, and then notice that this can be…
MadScientist
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9
votes
1 answer
Equality as "makes" vs equality as "equals"
A problem I often encounter while introducing students to equations is that of changing the conceptual image of the equation symbol $=$ from "results to" to "is equal to". To be more precise:
In the expression $2+3=5$, equality is often…
Vassilis Markos
- 1,120
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9
votes
1 answer
How to (or should one) distinguish between lowercase and uppercase letters orally when lecturing?
I sometimes teach calculus in English whereas it's not my native language.
For example, during a course about antiderivatives, how do you (orally) pronounce $f$ vs $F$?
Which are the best?
"the function small $f$" vs. "the function big $F$" ?
"the…
Basj
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- 7
9
votes
2 answers
Exercise database
edit: Thanks for all your answers so far.
I have decided to develop my own solution, both because it is fun and I can then form it exactly as I want to. Once I am done (which might take some time, because I first have to learn some Python for it^^),…
Dirk
- 1,308
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9
votes
3 answers
Take-Home Examination on Ordinary Differential Equations?
I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my students question such as
Solve the following…
Zuriel
- 4,275
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- 48
9
votes
5 answers
Does anyone use the cubic formula these days?
I am writing a story for young people about the history of the development of the cubic formula and complex numbers, partly because it has so much drama and partly because it's amusing that complex numbers were born of this almost farcical…
Sue VanHattum
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9
votes
2 answers
What's the point of exercises without answers?
What is the point of exercises for which answers aren't provided? (That is to say, what is the pedagogical justification for such exercises? - Edit by someone other than original poster.)
Commentary behind the question by original poster:
Most if…
Erik
- 207
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- 1
9
votes
5 answers
Real-life exceptions to PEMDAS?
What are some real-life exceptions to the PEMDAS rule?
I am looking for examples from "real" mathematical language --- conventions that are held in modern mathematics practice, such as those appearing in papers, books, and class notes, that are not…
Caleb Stanford
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9
votes
4 answers
How and when should I introduce my students to WolframAlpha?
I teach grade 8, 9, and 10 maths students who are blissfully ignorant of great mathematical tools available to them such as WolframAlpha or graphing calculators (which are not used in our school). At present I am aware and grateful that I don't have…
David Ebert
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9
votes
3 answers
How to motivate students to do proofs?
I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this.
How can I inspire them to love essential kind of…
matqkks
- 1,243
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9
votes
3 answers
Physical devices for exploring calculus or pre-calculus
I saw this partial derivative machine yesterday, and it got me excited about other physical devices for exploring calculus concepts in a "lab" setting (e.g. make a prediction, collect data, etc.) Do you use any devices like this?
There are certainly…
Nick C
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9
votes
1 answer
Real World use of the Function $(\sin{x})^x$
Today in my calculus class we were going over L'Hopital's Rule and were dealing with limits of the following form
$$h(x)=f(x)^{g(x)}$$
Three examples we considered are as follows:
$(1)\; \displaystyle \lim_{x\rightarrow…
Eleven-Eleven
- 463
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- 8
9
votes
6 answers
Book recommendations on mathematics education focusing on geometry
I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education).
Is there some recent (as concise as possible and maybe classic) mathematics education…
Sumac
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