Questions tagged [notation]

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

Filter by
Sorted by
Tagged with
5
votes
1answer
148 views

Notation in the definition of matrix multiplication

When matrix multiplication is introduced, it is usually introduced with an additional variable: Given two multiplicable matrices $A$, $B$, one defines the product $C=AB$ to be the matrix given by some ...
4
votes
2answers
162 views

Undergraduate Vector Calculus Notation Mess

Question 1: What are your arguments in favor of the big array of different notations used in the context of undergraduate vector calculus: line integrals, surface integrals (of scalars and fields), ...
4
votes
2answers
137 views

What is the role of the efforts to change the fundamentals of maths? [closed]

One is often drawn to offbeat mathematical ideas and how they could revolutionize mathematics or at least make maths more easy to learn. Current examples are: Rational Trigonometry Tau Dozenal ...
4
votes
3answers
242 views

Students writing $f(x^2+1)$ when they probably mean $f(x)=x^2+1$

Over the past years teaching freshmen calculus I've repeatedly seen students make the following type of error: Suppose they have to express some quantity $y$ as function of $x$, when the relation ...
4
votes
1answer
131 views

What is the notation for polynomial long division in Norway?

I will be teaching a calculus-type course in Norwegian. Our textbook is unfortunately in English (the curse of a small language), but any custom exercises should be and all exams have to be in ...
4
votes
2answers
5k views

Notation of line segment and its length

I have sometimes seen a notation where $AB$ could mean either the line segment or its length. Why do the same notation can be mean both? Should one teach pupils to use for example notation $d(A,B)$ or ...
4
votes
1answer
130 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 ...
3
votes
1answer
187 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 ...
3
votes
1answer
148 views

Naming arbitrary constants: subscripts, primes, or just more letters?

When choosing names for arbitrary constants either during a lesson or while working with a single student, should one use$\{n_1,n_2,n_3,\dotsc\}$ or $\{n, n', n'', \dotsc\}$ or $\{a,b,c,\dotsc\}$? Is ...
3
votes
1answer
297 views

How to explain “fractional terms”?

as I can see there are mainly two ways to introduce fractional terms. Two examples to demonstrate the two variants: $\frac{a^2+3}{a}; \frac{3}{2c}$ $T(a) = \frac{a^2+3}{a}; T(c) = \frac{3}{2c}$. In ...
2
votes
2answers
199 views

How should one approach the concept of “plus or minus”, such as in the numerator of the quadratic formula?

The numerator is structured like: $$(-b)\pm\sqrt{b^2- 4ac}.$$ Is it confusing or acceptable to distinguish between the following two things? An idiom; and What is or seems to be a compositionally ...
1
vote
1answer
195 views

What to call a symbol that denotes an “undisclosed” given number? [closed]

Students like to categorize notations to pin down their understanding of exactly what these notations stand for. Thus, given the expressions $f(x_{0})=f(x)|_{x\leftarrow x_{0}}$, $x=x_0+h$, or $lim_{x\...
1
vote
1answer
183 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 ...
1
vote
1answer
171 views

Can $y^{(n)}$ be used as a way of representing higher order derivatives?

I have never seen this notation, but I think that it follows in a similar vein for function notation. So if $y=f(x)$, then $y''=f''(x)$. Then by that, can we say that $$f^{(n)}(x)=y^{(n)}$$
1
vote
1answer
94 views

Moving lines in schematic diagrams

I am self-teaching myself precalculus.My biggest sticking point is to move lines within a diagram, especially, functions in the coordinated plane. For instance, doing horizontal and vertical shifts of ...
-1
votes
1answer
193 views

Duodecimal by Stealth

It is widely recognised that the Duodecimal number system is superior to the decimal system. However, it is plainly obvious that trying to introduce such a system would be difficult, especially in a ...

1
2