Questions tagged [notation]

For questions about good use of notation, comparison of specific notation, motivation of notation.

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11
votes
1answer
552 views

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{...
8
votes
6answers
352 views

Helping high school students remember inequalities and division

Background I sometimes tutor high school students and I have come across various problem types that are best represented by the following two problems. They are unable to keep track of the correct ...
8
votes
2answers
3k views

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 ...
1
vote
1answer
164 views

Is there a conventional function notation that takes a polynomial and order and yields the coefficient corresponding to the order?

I am writing a book and for the sake of simplicity I want to do something as follows. Coef((-3x^2 +5x -1)(x^2 +1), 2) = -3 -1 = -4 where the first argument ...
7
votes
1answer
119 views

Resource about notation for students

Others have already here pointed out that students can struggle with notation in mathematics. I can often think that the lack of proper notation gets in the way of solving a problem correctly. ...
9
votes
2answers
506 views

Is this example of Leibniz notation sloppy?

In helping a family member who is studying calculus, I was asked about the meaning of the following, which is straight out of a calculus text book (Varberg and Purcell) $v'(t) = \frac{{\rm d}\,v}{{\...
4
votes
1answer
119 views

On using different notations for the same objects

Historically, in set theory we use two different notations to refer set theoretically same objects $\aleph_{\alpha}$ and $\omega_{\alpha}$. The folklore justification of this dual notation is that we ...
33
votes
9answers
1k views

Reasons for (not) distinguishing $f$ from $f(x)$

Formally, if $f$ is a function, $f(x)$ is a value. So for instance, $f$ can be continuous, but not $f(x)$. In teaching at school and university, notation is quite often mixed up, e.g. the function is ...
3
votes
1answer
185 views

Better use “Integrate a function”/“Calculate the definite integral” or use terms like “primitive function”, “antiderivative”, “Aufleitung” (German)?

When one wants to let students calculate (Riemann) integrals in calculus, what is a good term to call this task? If you want to focus on what the main task is, you may call it "Calculate the definite ...