Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

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0
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2answers
242 views

Is there a difference between these integral notations?

I've come across these two notations for calculating an indefinite integral but I'm not sure whether or not they are equal: $f(x)dx$ $\int f(x)dx$ When calculating the indefinite integral, the ...
4
votes
3answers
2k views

What does the notation n* mean?

Are there any conventions about the use of $n^*$ as notation of a variable? I have seen it for the first time here.
5
votes
1answer
270 views

Where does the notation $\mathrm{Ad}(U)$ for $a\mapsto UaU^*$ come from?

I have often seen, in the context of operator theory and operator algebras, the notation $\mathrm{Ad}(U)a=UaU^*$, where $U$ is a unitary operator on a Hilbert space $H$ and $a$ is a bounded linear ...
6
votes
1answer
157 views

Why is there a derivative in this formula?

This is a very simple question. Why is Rademacher's formula presented with d/dx in it? Why not just "do" the derivative? Then replace x with n? Is it so there is only one transcendental ...
1
vote
1answer
137 views

rational functions notation in Dummit&Foote

A problem in Dummit and Foote states: Let $k$ be a field and let $k(x)$ be the field of rational functions in $x$ with coefficients from $k$. Let $t \in k(x)$ be the rational function ...
6
votes
4answers
568 views

What differences are between $\mathbb{E}^n$ and $\mathbb{R}^n$

What differences are between the two notations $\mathbb{E}^n$ and $\mathbb{R}^n$? Do they represent/define the same space set with the same structure(s)? Thanks and regards!
1
vote
1answer
164 views

What does the notation $A_a^n$ mean?

Given a set of matrices $$M = \left\{\begin{bmatrix}1&a\\0&3\end{bmatrix} \mid a \in \mathbb R\right\},$$ what does the notation $A_a^n, n \in \mathbb N$ mean?
0
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1answer
125 views

what is the meaning of the notation $ C^q_c(0,1)$

Please let me know the meaning of the notation $ C^q_c(0,1)$
3
votes
4answers
134 views

fractions inside of a decimal?

$\frac{1}{3} = 0.333333.... $ $\frac{1}{3} = 0.33\frac{1}{3} $ I ran into this fraction-in-a-decimal notation in a course I'm helping somebody with. I have never seen this before, and google ...
4
votes
3answers
8k views

What is “multiplication by juxtaposition”?

I was reading http://www.purplemath.com/modules/orderops2.htm it shows = 16 ÷ 2[2] + 1 (**) ... = 5 The general consensus among math people is that ...
3
votes
0answers
209 views

How did Bessel functions come to be denoted by $J_n$?

The $n$th Bessel function of the first kind is usually denoted $J_n(x)$. Where did the use of the letter $J$ to indicate the Bessel function come from?
13
votes
4answers
21k views

What is 48÷2(9+3)? [duplicate]

There is a huge debate on the internet on $48÷2(9+3)$. I figured if i wanted to know the answer this is the best place to ask. I believe it is 2 as i believe it is part of the bracket operation in ...
13
votes
2answers
1k views

Etymology of $\arccos$, $\arcsin$ & $\arctan$?

Does anyone know the origin of the words $\arccos$, $\arcsin$ & $\arctan$? That is to say, why are they named like this? What connects "arc" with inverse? Can't seem to find out via Google. ...
1
vote
0answers
109 views

How to interpret the sum notation on $\sum_{r:i(r)=i} \langle R_{r\alpha} \rangle^{(t)}$

While doing research for my thesis, I ran into a paper called "Statistical Models for Co-occurrence Data". In the early pages, when talking about an iterative numerical method (a custom EM-method, to ...
3
votes
1answer
219 views

Question on notation of differentials

Is the following notation acceptable, specifically last part of the last line? $$f(x) = \csc^4(x) = (\csc(x))^4$$ Let $$u =\csc(x) \rightarrow f(x) = u^4$$ $$f'(x) = \frac{du}{dx} \times ...
1
vote
1answer
169 views

Notation to describe vector

I want to describe a vector of n length, where each element is described by it's index. What is the correct notation? As it is now, to describe the vector [ 1 4 9 16 ] i write: ...
1
vote
1answer
76 views

Any concise way to represent this in a formula?

I'm doing a presentation and I have to include this in it: for j in 1..j_max b_offset = copy(b) b_offset[j] = b_offset[j] + 1 I can't do b_offset = b + ...
1
vote
2answers
414 views

A question on notation: What does $\nabla |\vec{a} \times \vec{r}|^n$ mean?

I sort of asked a version of this question before and it was unclear; try I will now to make an honest attempt to state everything clerly. I am trying to evaluate the following, namely $\nabla w = ...
0
votes
2answers
562 views

a question on notation for function spaces

If $X$ is some topological space, such as the unit interval $[0,1]$, we can consider the space of all continuous functions from $X$ to $R$. This is a vector subspace of $R^X$ since the sum ...
10
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1answer
1k views

What does the math notation $\sum$ mean?

I have come across this symbol a few times, and I am not sure what it "does" or what it means: $\Large\sum$
6
votes
1answer
11k views

What are the common abbreviation for minimum in equations?

I'm searching for some symbol representing minimum that is commonly used in math equations.
6
votes
1answer
1k views

Mathematical symbol to reference the i-th item in a tuple?

Given a tuple e=(x,y), how do I reference the 2nd item (y)?
1
vote
1answer
3k views

What does the symbol $\otimes$ mean? [closed]

I am familiar with the direct sum of sets, $\oplus$.
0
votes
1answer
132 views

Correct form of sum expression

I want to create equation that represents following piece of code (it is much more complicated I simplify it for clearance) int v = 23; sum = 0; for (int i = v; i > 0; i= i - 2) { sum = sum + i; } ...
3
votes
0answers
164 views

bar index notation

For complex manifolds , people usually write the first fundamental form as $ds^2=g_{a\bar{b}}dz^ad\bar{z}^b$ (at least physicists) with a bar over the second index of the metric, but don't usually ...
0
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1answer
91 views

Superscript wedge on an $R$-module

I'm reading these lecture notes here about the tensor product and the author uses $M^\vee$ where $M$ is an $R$-module. Look at page 2 for an example (example 2.1). What does it mean? I looked through ...
14
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1answer
864 views

$\arcsin$ written as $\sin^{-1}(x)$

I know that different people follow different conventions, but whenever I see $\arcsin(x)$ written as $\sin^{-1}(x)$, I find myself thinking it wrong, since $\sin^{-1}(x)$ should be $\csc(x)$, and not ...
0
votes
1answer
351 views

What does 'card' stands for?

I read some book where 'card' symbol is used to signify number of elements in the set. But where is it from? What the full word could be for 'card'?
18
votes
12answers
2k views

Alternative notation for exponents, logs and roots?

If we have $$ x^y = z $$ then we know that $$ \sqrt[y]{z} = x $$ and $$ \log_x{z} = y .$$ As a visually-oriented person I have often been dismayed that the symbols for these three operators ...
2
votes
1answer
602 views

Complex math symbols, and definitions

I find it difficult to explain this because I'm not sure what is the correct term to use. Symbols such as the triple-bar-equal sign, and a few other symbols that I find difficult to describe. I was ...
7
votes
4answers
1k views

How does one pronounce $a \odot b$?

I have seen authors use $\star$, $\ast$, $\cdot$ and $\odot$ to represent arbitrary binary operations on sets. I'm wondering, what is the standard way to read or pronounce something like $a \star b$? ...
3
votes
1answer
1k views

What does matrix multiplication have to do with scalar multiplication?

Why are matrix and scalar multiplication denoted the same way and treated as the same operation in standard mathematical notation? This is always a source of confusion for me because they have ...
1
vote
0answers
105 views

All elements of a matrix as a set

Suppose you have a matrix $A$. Is there a "standard"/mathematical elegant way to denote all members of the matrix as a set? So suppose there is a matrix $A = \left[ \begin{array}{cc} a & b \\ c ...
6
votes
1answer
337 views

Why do they use $\equiv$ here?

I thought I had pretty much figured out the difference between $\equiv$ and $=$. Then I came across this while reading about partial derivatives (in Colley's Vector Calculus): $$ ...
1
vote
1answer
105 views

Question about notation / terminology

I'm given the following in a homework question: Let $G$ be a group and $k$ an algebraically closed field. (a) Show that the action of $G \times G$ on $C_k (G)$ defined by $$ (g_1, g_2) \varphi (x) ...
14
votes
5answers
1k views

When should I use $=$ and $\equiv$?

In what context should I use $=$ and $\equiv$? What is the precise difference? Thanks! (I wasn't sure what to tag this with, any suggestions?)
1
vote
1answer
377 views

Conventions for function notation with multiple variables

Consider the following expression: $x\cdot a\cdot b$ In programming you could define a function $f(x,a,b)$ to assign values to all the variables. However, since I cannot remember seeing such ...
1
vote
3answers
2k views

Notation for the set created from the combination or permutation of a set

For a set $S$ with $n$ elements, the notation for a combination $\binom{n}{k}$, or $C(n, k)$, indicates the number of combinations of $k$ elements from $S$, but how does one indicate the actual set ...
8
votes
5answers
593 views

General Introduction to Functional and other Mathematic Notations

I've been a programmer for a good while now. Fairly experienced at a bit of math as far as coming up with algorithms and such but I am far far behind on understanding quite a deal of notation. Here ...
1
vote
2answers
3k views

the symbol for translation, transformation, or conversion

What is the symbol for demonstrating syntactic conversion (transformation or translation)? For example, I want to show a calculation sequence, from $ \neg ( A \wedge B ) $ to $ \neg A \vee \neg B $. ...
21
votes
5answers
28k views

How does one denote the set of all positive real numbers?

What is the "standard" way to denote all positive (or non-negative) real numbers? I'd think $$ \mathbb R^+ $$ but I believe that that is usually used to denote "all real numbers including infinity". ...
0
votes
1answer
296 views

Help understanding math notation

What does the "^" represent in the statement below? It definitely doesn't mean to the power of as that makes no sense in this context. Thanks for the help! Since X(t) is a pure death process with ...
3
votes
1answer
281 views

Help with definition of group realization

I am reading a document it says A group realization is a map from elements of G to transformations of a space M that is a group homomorphism, i.e. it preserves the group multiplication law. Thus if ...
2
votes
1answer
568 views

Matrix bracket notation

I am reading a section in a book that talks about normal matrices, and I see the following: A normal matrix is a matrix that commutes with its adjoint, Eh? ...
1
vote
1answer
269 views

Why are there two different Leibniz notations?

Why do we have dy/dx with the regular d, and 'del y/del x' with the 'funny' d? I can easily find definitions for each expresion, but the definitions appear to be logically equivalent. However, they ...
7
votes
3answers
508 views

What does $(m, n) = 1$ mean?

I have to solve a problem which states that $(m,n) = 1$, but I have no idea what this means. Maybe, the problem itself will help: Suppose $m, n \in \mathbb{Z}$, with $n > 0$ and $(m,n) = 1$. Show ...
1
vote
8answers
11k views

What does a hat or star means in math?

What are the general uses of the hat and star symbol in math? Or could you please point me to a page that discusses this? Thanks.
9
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2answers
251 views

In generatingfunctionology, for a polynomial $P$ and a differential operator $D$, what does $P(xD)$ mean?

I'm working through some of the exercises in generatingfunctionology. One of the questions is to find the generating function where the $n$th term $a_n=P(n)$ for $P$ a polynomial. The answer is ...
9
votes
2answers
762 views

Number Theory: confusion with notation

In elementary number theory, I find the following notations being used interchangeably, which leads me to have many ambiguous assumptions: $\mathbb{Z}_p^\times$; $\mathbb{Z}_p$, where p is any ...
3
votes
1answer
501 views

The big O notation

Hey guys, I have this ex in Data structure course. This ex is about big o notation, and as far I remember It means that $f_1$ and $f_2$ bound asymptotically $g_1, g_2,$ but i'm not quite sure. The ...