All Questions
542 questions
14
votes
3
answers
3k
views
Open source LaTeX lecture notes/slides/books [closed]
In the mathematics community it's quite common for professors to write their own notes for the classes they are teaching. The notes are then usually published in both PDF and PS form on the course ...
- 3,322
2
votes
1
answer
193
views
Terminology for system of equations and...
I am looking for the standard term for a system that consists of things of the form
$p_i(x_1,\ldots ,x_n)=0$ and of the form $q_j(x_1,\ldots,x_n)\neq 0$ with the $p_i$ and $q_j$ polynomials. I have ...
- 47.4k
11
votes
1
answer
1k
views
Teaching Experience for Graduate Students. [closed]
I am currently a graduate student, who will (hopefully!) graduate in the next year (or two..). I have slowly come to realize that I enjoy teaching, and consequently want to do more of it! My main ...
- 151k
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 ...
- 12.6k
0
votes
0
answers
166
views
Is $\{x_{zt}\}_{Z\times~ T}$ a good notation for specifying the indexed family of entities $x_{zt}$ with $z\in Z,\, t\in T$?
I have a model with lots of variables indexed over a few sets.
After having introduced the model, i.e. having already said that $x_{zt}$ has indexes $z\in Z$ and $t\in T$, instead of writing
"we ...
- 151
24
votes
2
answers
2k
views
Direct proof that the centralizer of $GL(V)$ acting on $V^{\otimes n}$ is spanned by $S_n$
Let $V$ be a finite dimensional vector space over a field of characteristic zero. Let $A$ be the space of maps in $\mathrm{End}(V^{\otimes n})$ which commute with the natural $GL(V)$ action. Clearly, ...
- 33.8k
0
votes
0
answers
379
views
Terminology for the image of the diagonal embedding.
Let $X$ be a topological space equipped with maps into two spaces $\bar X_1$ and $\bar X_2$. Is there a standard notation/terminology for the closure $\bar X$ in $\bar X_1 \times \bar X_2$ of the ...
- 5,359
7
votes
1
answer
677
views
What does the t in t-category stand for?
To my knowledge the notion of a t-category was first introduced Beilinson, Bernstein and Deligne's Faiseaux Pervers. But while they explain the name "perverse sheaf", they don't give any indication ...
- 52.9k
24
votes
7
answers
8k
views
How do professional mathematicians learn new things? [closed]
How do professional mathematicians learn new things? How do they expand their comfort zone? By talking to colleagues?
- 12.7k
11
votes
4
answers
3k
views
Topological examples of profinite groups
I am preparing a course on profinite groups, to be delievered to early graduate students. The first part of the course will discuss the equivalent characterizations of profinite groups. I will first ...
- 9,627
1
vote
0
answers
430
views
Professional skills advising for math jobs [closed]
Hi,
I am a postdoc at the University of Nottingham (UK) and I am beginning to apply for Assistant Professor positions in US.
I would like to receive a feedback on the material that I am sending (...
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 ...
- 2,754
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 ...
CommunityBot
- 1
61
votes
10
answers
10k
views
Teaching proofs in the era of Google
Dear members,
Way back in the stone age when I was an undergraduate (the mid 90's), the internet was a germinal thing and that consisted of not much more than e-mail, ftp and the unix "talk" command ...
- 20.2k
24
votes
2
answers
9k
views
Explanation why $x,y,z$ are always variables
I heard or have read the following nice explanation for the origin of the convention that one uses (almost) always $x,y,z$ for variables. (This question was motivated by question
Origin of symbol *l* ...
CommunityBot
- 1
5
votes
1
answer
461
views
Is there a standard notation for a "shift space" in functional analysis?
I'm writing up some notes on the nLab about things like embedding spaces and infinite spheres and similar things (can't link to them yet as I haven't put them up yet). One aspect that crops up time ...
- 31.5k
13
votes
5
answers
2k
views
How to make a lecture series useful
I have been to a number of advanced lecture courses (of between 3 and 10 lectures) over the years, given (in principle) by experts to graduate students and experts in neighbouring fields. Examples of ...
- 50.6k
27
votes
17
answers
9k
views
Using slides in math classroom
I am toying with the idea of using slides (Beamer package) in a third year math course I will teach next semester. As this would be my first attempt at this, I would like to gather ideas about the ...
- 1,037
1
vote
1
answer
742
views
proofs of stochastic boundedness
I'm looking at some statistical literature and trying to compare the results given there in probabilistic big-Oh notation with statements I'm more familiar with.
In particular, I'm trying to ...
- 6,711
0
votes
0
answers
678
views
Notation for isometric spaces?
Metric spaces are isometric if there exists a bijective isometry between them.
Is there a standard notation for this, along the same lines as $X\approx Y$ for homeomorphic spaces and $X\simeq Y$ for ...
- 35.9k
4
votes
0
answers
795
views
Almost linear ODE: how node becomes a spiral
Most introductory ODE books contain a discussion of almost linear systems, and there are two cases when the behavior of an almost linear system near an equilbrium point can differ from the behaviour ...
CommunityBot
- 1
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 ...
- 44.4k
3
votes
3
answers
2k
views
What to teach in a second graduate course in algebra? What textbook to use?
There is a standard syllabus for a first graduate course in algebra. One teaches groups,
rings, fields, perhaps a little bit of Galois theory, perhaps a little bit of
category theory, perhaps a ...
- 822
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 ...
CommunityBot
- 1
12
votes
11
answers
2k
views
Giving a math talk with no blackboard or projector
I need to give a math talk to a group of undergraduates. I am asking for advice because this talk will take place at a department picnic and there will be no blackboard or projector. I would like to ...
- 1,701
7
votes
5
answers
2k
views
Commutative algebra final project
I'm looking for a topic for a final project in commutative/homological algebra, for first year master's students (in a decent European university). During the course, they will cover the following ...
CommunityBot
- 1
4
votes
1
answer
690
views
What does $L^\infty_\varepsilon$ mean?
In Volume 4 of Reed and Simon on page 83 the authors refer to the space $(L^\infty(\mathbb{R}^3))_\varepsilon$,
and later on page 119 they use $L^\\infty_\varepsilon$.
Are these two spaces the same? ...
CommunityBot
- 1
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 $$[f]_D = \{ g \in X : \mbox{$g(t) = f(t)$ for ...
- 17k
1
vote
1
answer
2k
views
What does $\mathcal{N}$ mean? [closed]
I'm reading a paper that refers to a set $\mathcal{N}$, without defining it. It's a CS paper so it's not complicated maths. Is this the set of natural numbers? I don't get why they're using this style ...
CommunityBot
- 1
3
votes
2
answers
550
views
What are some resources discussing mathematical notation?
I'm looking for resources discussing mathematical notation, the theory, the philosophy, the distinct advantages of various notations. Stuff about notation for computer algebra systems is interesting ...
- 18.7k
2
votes
4
answers
6k
views
Undergraduate Derivation of Fundamental Solution to Heat Equation
It is well known that the 1-dimensional heat equation $$\frac{\partial}{\partial t} u(x,t)=a\cdot\frac{\partial^2}{\partial x^2} {u(x,t)}$$ has the fundamental solution $$K(x,t)=\frac{1}{\sqrt{4\pi a ...
- 3,322
3
votes
0
answers
431
views
Concrete questions that turn into math problems [closed]
I'm writing an article about the way we teach math, trying to find out why so many people are discouraged from learning, and have no interest for math and logic.
At some point, I want to show that ...
- 131
3
votes
0
answers
311
views
Tensor power- Notation question
Hi everyone
I have a notational question, which is written usually in papers, but I can not figure it out what could be. Let $M$ be an $A$-module. I have seen this notation
$$M^{\otimes -n}$$
I ...
- 30.3k
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] ...
- 30.1k
1
vote
1
answer
286
views
Notation for growth $a_n \le c (n!)^\epsilon$
This is just a stupid question about a good terminology. I'm interested in sequences $a_n$ with a growth that can be bounded by an arbitrarily small positive power of $n!$, i.e. for every $\epsilon &...
- 60.6k
1
vote
4
answers
1k
views
Kro-necker versus Kron-ecker: which hyphenation is preferred? [closed]
Synopsis and concrete practices
Everyone is thanked for their comments, and in view of the diversity of views expressed, I have converted this question to a community wiki.
Here is a working ...
- 1,389
12
votes
44
answers
5k
views
Mathematical ideas named after places [closed]
This question is quite unimportant, so feel free to close if you think it is inappropriate.
I've been thinking about how mathematicians come up with names for the ideas/objects they study, and how ...
CommunityBot
- 1
12
votes
5
answers
2k
views
Introducing Cryptology to Undergraduates
This summer I am going to give some lectures to some REU students. I am still tossing around ideas for what I am going to talk about, but one thing I would at least like to give one or two lectures on,...
- 3,867
2
votes
2
answers
28k
views
How to write Matlab's dot operators in mathematical expressions?
Matlab has a set of dot operators, such as .*, ./, .^. Each of these operators consists of a dot and a normal algebraic operator. They perform element-wise algebraic operations on a matrix. For ...
CommunityBot
- 1
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 ...
- 4,577
3
votes
0
answers
131
views
Isomorphism modulo the residual
Given a group $G$ let $R(G)$ be its residual, that is the intersection of all the normal subgroups of finite index. Is there a name for the relation between $G$ and $H$ defined by $G/R(G) \cong H/R(H)$...
- 5,450
10
votes
8
answers
2k
views
Undergraduate Probability Topics
I am teaching undergraduate probability this semester, and I am looking for some suggestions about inspiring applications that could be reasonably covered over the course of two one-hour lectures or ...
CommunityBot
- 1
19
votes
9
answers
5k
views
Mathematics and autodidactism
Mathematics is not typically considered (by mathematicians) to be a solo sport; on the contrary, some amount of mathematical interaction with others is often deemed crucial. Courses are the student's ...
CommunityBot
- 1
22
votes
4
answers
5k
views
What is the best way explain to undergraduates that all 1-dimensional manifolds are orientable?
Let's suppose that $M$ is a connected $1$-dimensional smooth manifold (Haussdorf and paracompact). We know that there are exactly two types, up to diffeomorphism (even up to homeomorphism), namely $\...
- 3,540
8
votes
1
answer
4k
views
Who is this guy : Z.A. Melzak (wrote Companion to Concrete Mathematics) ? [closed]
Author : Z.A. Melzak
Book Title : Companion to Concrete Mathematics.
Publication : Dover renewed 2004 2 volumes in one. Copyright 1972/1976.
I found this book extremely nice.
To whet your appetite ...
- 1,306
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})...
- 11.4k
4
votes
3
answers
2k
views
Does f(x)~g(x) imply $f(x) \asymp g(x)$?
I'm going to be clear about definitions before I start so there's no ambiguity. Let D be a subset of the complex numbers and let $f: D \to \mathbb{R}^{+}$ be a positive real-valued map defined on D. ...
- 489
0
votes
2
answers
383
views
"X \in \cdot" in Probability Measure [closed]
My question is quite simple, but I was unable to find an answer by googling, since you can't exactly google syntax. What does the $\in \cdot$ mean in:
$$\lim_{n\to\inf}||P(S_n\in\cdot)-P(S_n+k\in\cdot)...
- 29.8k
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 $...
CommunityBot
- 1
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)...
CommunityBot
- 1