All Questions
542 questions
3
votes
2
answers
957
views
Simple definition of the Hausdorff measure using squared paper
I am giving a "non-technical" seminar in which I would like to give an elementary introduction to the Hausdorff dimension and measure.
For simplicity, I was hoping to give a more intuitive ...
- 20.2k
6
votes
2
answers
2k
views
Notation: Exponent of a group
The exponent of a group $G$ is the least positive $n$ such that $g^n = e$ for all $g \in G$. This is obviously a sensible name for the concept.
A notational awkwardness arises however when the group $...
- 1,793
6
votes
2
answers
945
views
Notation/name for "Artin-Schreier roots"?
If x is an element of a field K and n is a positive integer, we have both a symbol and a name for a root of the polynomial t^n - x = 0: we denote it by x^{1/n} and call it an nth root of x.
Of course ...
- 65.4k
2
votes
1
answer
439
views
Notation arb(x)
Suppose we have extended $ZF$ by adding to $ZF$ an unary function symbol $arb$ (an arbitrary element of a set) and a corresponding axiom "For every non-empty set $S$, $arb(S)$ is in $S$".
Will be the ...
- 897
3
votes
4
answers
514
views
Better terminology than "equivalence class of functions"
Let $X = C(\mathbb R)$ be the Fréchet space of real-valued continuous functions. For each $f \in X$ and each compact set $D \subseteq \mathbb R$, let $$[f]_D = \{ g \in X : \mbox{$g(t) = f(t)$ for ...
- 8,512
2
votes
1
answer
340
views
Name of a lattice-property
Assume that we have a complete lattice $(L,\leq)$.
I would like to know whether the following property has a specific name and whether lattices with this property have been studied somewhere:
For ...
- 1,498
2
votes
1
answer
275
views
A question about some notation involving the exclamation mark [closed]
What does the symbol ‘!’ signify? Is it $ \text{argmin} $? For example, $ \| A x - y \| = \min! $.
- 37
1
vote
1
answer
594
views
Understanding Sweedler's notation for the structure map of a comodule
I was hoping someone might be able to shed some light on the choice of indices for expressing the coaction using Sweedler notation.
For example, in the paper of Andruskiewitsch About finite-...
- 151
11
votes
1
answer
2k
views
Good chalk in the UK
Sometime ago it was asked in Mathoverflow about good chalk in the US Where to buy premium white chalk in the U.S., like they have at RIMS?. I will be grateful for any recommendations on good chalk in ...
4
votes
3
answers
674
views
Is there a (standard) name for $\bar{A}\setminus A$?
This is a notation question:
If $A$ is a set in a topological space and $\bar{A}$ is its closure, is there a (standard) name for $\bar{A}\setminus A$?
- 2,882
1
vote
0
answers
2k
views
What does this notation mean: matrix norm with a two-number subscript
I recently came across this notation, without explanation, in a paper:
$||\mathbf{W}||_{2,1}$
From the context, I know that $\mathbf{W}$ is a matrix, which could be any size, and that $||\mathbf{W}||...
- 111
1
vote
1
answer
578
views
Choosing Notation for Variable Substitution into Derivative Expressed with Differentials [closed]
Consider function $f(x)$. I've counted 4 possible notations to write a derivative of $f(x)$ at point $x = a$:
$f'(a)$;
$\frac{\operatorname{d}{f(a)}}{\operatorname{d}x}$;
$\left.\frac{\operatorname{d}...
9
votes
3
answers
1k
views
Where can I find questions motivating important ideas in math?
I would like questions that demonstrate why a mathematical tool or technique is useful, and which can be used to introduce that idea. Ideally, this would be a compilation of problems organized by the ...
0
votes
2
answers
223
views
Conventional notation for the probabilistic functor
The probabilistic functor $P$ sends a measurable space $X$ to the space of probability measures on $X$ endowed with $\sigma$-algebra generated by evaluation maps, and measurable maps $f:X\to Y$ to ...
- 1,655
8
votes
0
answers
554
views
Lower semicontinuity of naive fiber size
I would like to present the following result in my algebraic geometry class, but it is seeming much harder than I would expect. Since my class is working with closed points over an algebraically ...
- 156k
0
votes
2
answers
562
views
Lines on degree 2n-3 Fermat hypersufaces
It is well known that a generic hypersurface of degree $2n-3$ in $\mathbb CP^n$ has finite number of lines. I would like to ask a couple of questions about lines on Fermat hypersurfaces and their ...
- 14.3k
2
votes
0
answers
3k
views
What is the geometric meaning of the third derivative of a function at a point? [closed]
What is the geometric meaning of the third derivative of a function at a point?
This question is now asked on the sister site: https://math.stackexchange.com/questions/14841/what-is-the-meaning-of-...
- 61
2
votes
3
answers
205
views
How to Express Undirected Integration
Is there an agreed way of expressing undirected integration in formulas?
my idea of doing so would be to use the absolute value of the differential
$$\int_a^b f(x)|dx| = \int_b^a f(x)|dx|$$
but I ...
- 13.2k
4
votes
0
answers
111
views
Is there a name for groups of the form $Sp(1)^n$?
A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...
- 4,729
2
votes
1
answer
568
views
Notation for ends of a string
I work now a lot with strings of characters and other finite sequences and found that I need many times a good notation for "cutting the end" a string. If $a$ is a finite sequence and $a'$ is its ...
user22882
1
vote
1
answer
231
views
Is the notation ${}^t g$ for the transpose of a linear transformation intended to be suggestive?
The notation ${}^t g$ for the transpose of a linear transformation is, in my view, quite unusual: otherwise (at least in many areas of math), one almost never sees subscripts or superscripts appearing ...
- 7,347
5
votes
2
answers
2k
views
Any suggestions for a course in Mathematical Logic?
I am teaching a topics course for Mathematics majors (at Temple), and am considering Logic as the topic. I was wondering if people (a) have suggestions for an appropriate text and (b) how much might ...
0
votes
2
answers
1k
views
What is a maximal set in the context of argumentation in AI [closed]
I am computer scientist, not a mathematician, I've been reading some papers on argumentation in AI that uses the term 'maximal' set without defining it. I think it's left undefined because it's a ...
- 187
6
votes
3
answers
1k
views
Names of noncompact riemannian symmetric spaces?
Irreducible riemannian symmetric spaces come in pairs: one compact and one not compact, usally called the noncompact dual.
The compact symmetric spaces include spheres, complex and quaternionic ...
- 33.3k
2
votes
2
answers
6k
views
Examples of random variables
I'm looking for a list of examples of random variables to use in teaching a measure-theoretic probability course. For example, the Rademacher functions are an explicit construction of independent ...
- 5,227
1
vote
0
answers
159
views
Notation clash between a representation and spectral radius
I am currently writing a paper where I need talk both about a representation of a semisimple Lie group (usually denoted by $\rho$), and about spectral radii of linear maps (also usually denoted by $\...
- 1,574
2
votes
2
answers
1k
views
Decomposition of $K_{10}$ in copies of the Petersen graph
It is a well-known and cute exercise in algebraic graph theory to show that $K_{10}$ cannot be written as the edge-disjoint union of three copies of the Petersen graph $P$. Indeed, the graph $G$ whose ...
- 10.9k
10
votes
2
answers
2k
views
What is a convenient shorthand notation for a category
Set theory has a very convenient and well established curly brace notation to specify a set by its elements: $\{2,3,4,6\}$ or $\{\text{finite subgroups of }SU(2)\}$ are simple examples.
There should ...
- 491
4
votes
1
answer
2k
views
When is the Siegel-Walfisz theorem non-trivial?
The following paragraph appears in Analytic Number Theory (Iwaniec, Kowalski):
The Siegel-Walfisz theorem asserts that:
$\displaystyle \hspace{5cm} \psi(x;q,a) = \frac{x}{\phi(q)} + O(x(\log x)^{-A})...
- 489
2
votes
0
answers
118
views
What does the square root sign tells us in the wave equation? [closed]
I have been reading the paper on wave equations, and I have some confusion in notations.
Consider the initial value problem(IVP)(Wave equation):
$\frac{\partial ^2 u } {\partial t^2}(x,t) = \...
- 1,051
2
votes
0
answers
1k
views
Linear Algebra Text Book [closed]
In our department we do not like our current linear algebra book and so we would want to find a better book. This is for the first course in linear algebra and the title of the course is
Elementary ...
1
vote
5
answers
452
views
Notation: Vector space spanned by all finite polynomials in $x$ and all finite polynomials in $y$
This is a simple question about notation: Given two generators $x,y$ how does one denote the vector space spanned by all finite K-polynomials in $x$ and all finite polynomials in $y$. If I use K**$[x] ...
- 1,479
6
votes
1
answer
877
views
Is $O(10^{-6})$ an acceptable notation in numerical analysis? [closed]
The following question has been on math.SE for several days. Without having a satisfying answer, I'd like to ask the experts here.
In mathematics, the big $O$ notation is used to describe the ...
user14319
1
vote
1
answer
994
views
What exactly does \gg and \ll mean?
For example,
$f(T)\ll_T 1$ where $T$ is a positive number.
- 3,804
5
votes
1
answer
1k
views
Is Diagonalization worth to be taught? [closed]
When students come to the College (first two years of the University system in most of the developped countries) to train in mathematics, they get a linear algebra / matrix analysis course. After a ...
0
votes
1
answer
552
views
Teaching profession:Differential Equations and Mean Value Theorems
Usually I teach Algebra,Algebra and Geometyry, Topology, at various University levels. This semester (Spring 2014) I have to teach Differential Equations to University second year students (4th ...
- 1,422
2
votes
3
answers
410
views
Pedagogical notes on line bundles on complex projective manifolds
I would like to find some notes (or book), that explains on a very basic level what is a line bundle on a complex projective manifold. Maybe even, what is a line bundle on $\mathbb CP^n$. It seems ...
4
votes
2
answers
869
views
Terminology question on covering spaces
I'm teaching an elementary class about fundamental groups and covering spaces. It was very useful to use "fool's covering spaces" of a space $X$, defined as
functors $\Pi_1(X)\to Sets$, where $\Pi_1(X)...
- 407
11
votes
2
answers
1k
views
Social Reading Platform for Math or LaTeX texts
Social reading is considered to be one of the big trends that could be catalysing learning by reading. Features could include:
Highlighting or annotating paragraphs or single steps in a proof for ...
1
vote
1
answer
2k
views
What does $\mathcal{N}$ mean? [closed]
I'm reading a paper that refers to a set $\mathcal{N}$, without defining it. It's a CS paper so it's not complicated maths. Is this the set of natural numbers? I don't get why they're using this style ...
- 11
0
votes
1
answer
860
views
Sierpinski Triangle and the Chaos Game
The chaos game is a way to construct (an approximation) of Sierpinski triangle. It's clear (using Thales' theorem!) that if we begin with a point on the sierpinski triangle, then we will never leave ...
- 87
1
vote
1
answer
224
views
Lefschetz fixed notation
If $f\colon X\to X$ is a self-map of a nice space with isolated fixed points, then the Lefschetz fixed point theorem relates a global number to local numbers. Some write: $L(f)=\sum_{x\in \mathrm{Fix}(...
- 8,727
1
vote
1
answer
598
views
Set Exponentiation: Is Y always disjoint from Y^X? [closed]
If $y \in Y$ and $g \in Y^X$, we often write $y+g$ as shorthand for the map $x \mapsto y+ g(x)$. Similarly if $f \in Y^X$ then $f+g = x \mapsto f(x)+g(x)$. However this presupposes that we can ...
- 3,793
3
votes
2
answers
395
views
Integration in several variables and elementary applications
This fall I'm teaching the "second half" of the standard entry-level undergraduate multivariable calculus course: the focus is on double and triple integrals, path integrals, Green's theorem, Stokes' ...
0
votes
1
answer
155
views
Help with notation for the state of a dynamical system defined by a PDE
Before my question let me briefly describe a simplified version of the dynamical system I'm working with. Suppose that I have a density function $m(\boldsymbol{x},t)$, that describes the abundance of ...
0
votes
1
answer
630
views
Useless question on rank
What is the rank of $A^{n}$ if A is the zero ring? It's clearly not $n$ as many careless authors claim, since it's not even invariant. I don't think it's 0 either because it does have a linearly ...
- 2,857
1
vote
0
answers
59
views
Notation for largest universal subclass and class of arrows "locally in" a given class of arrows
Let $\mathcal M$ be a class of arrows in a category $\mathsf C$. I would like suggestions for good notation for the following two classes.
The smallest universal (pullback stable) subclass $\mathcal ...
- 10.5k
4
votes
1
answer
3k
views
Notation for algebras
Is there standard notation for
(1) exterior algebras
(2) free graded commutative algebras
(3) divided polynomial algebras ?
I've seen (and used) $\Lambda$, $\Gamma$, $\Delta$ etc. used for ...
- 12.5k
1
vote
1
answer
265
views
Notation of a pregallery
I'm transcribing parts of Harm van der Lek's thesis 'The homotopy type of complex hyperplane complements' and due to it being written in 1983 the typesetting isn't very detailed. In latex, how should ...
- 13
2
votes
1
answer
222
views
Meaning of notation $\mathbb{Q}^\wedge k$, $-\infty^\wedge \mathbb{Q}$ for linear orders
I am reading Friedman & Stanley A Borel reducibility theory for classes of countable structures (J. Symbolic Logic 54 (1989), 894–914; MR1011177) and a caret (${}^\wedge$) appears as notation in ...
- 1,601