All Questions
495 questions
4
votes
2
answers
287
views
Teaching suggestions for Kleene fixed point theorem
I will take over two lectures from a colleague in which we discuss fixed point theory in the context of complete partial orders, and culminates in showing the Kleene fixed point theorem (see f.e. ...
- 41
4
votes
1
answer
173
views
Numerical equality testing
I am working on developing an online homework system.
One thing I would like to have is something which compares a student's answer (like $2\sin(x)\cos(x)$) with the intended answer (maybe $\sin(2x)$)...
- 12.1k
4
votes
1
answer
441
views
How to teach generalizing the induction hypothesis? [closed]
I just finished teaching a class on using proof assistants (in this case, Agda) to write provably correct programs. Reflecting on how it went, the biggest difficulty I noticed the students having was ...
- 9,201
4
votes
0
answers
238
views
Applications of Freiman's theorem?
What are some interesting applications of Freiman's theorem or, better-yet, its recent generalizations (eg Green-Ruzsa) that could be included in a graduate course in additive combinatorics?
I'm ...
4
votes
0
answers
176
views
Are injective modules flabby on basic open sets?
In order to give a simple proof of a basic fact about quasi-coherent modules (see below), I'm interested in knowing whether the following statement holds:
Statement: If $A$ is a commutative ring and $...
- 1,064
4
votes
0
answers
286
views
MathJax (or something like it) as a classroom “blackboard”
(I tried this first at https://math.stackexchange.com/questions/187265/mathjax-or-something-like-it-as-a-classroom-blackboard , but didn't get satisfactory responses.)
What is the best desktop ...
- 17.6k
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 ...
- 29.1k
4
votes
0
answers
652
views
Probability in Math Education [closed]
Why is probability an under-emphasized subject in most math programs? Why does it seem that the hot topics these days are category theory and algebra? What do you think about the following: A student ...
- 65
3
votes
4
answers
2k
views
Less-known conjectures of significant influence and the contrary
In mathematics, it is common that theorems/results and problems appearing dull in one generation get revitalized and become the center of research in another one.
Sometimes conjectures that are ...
3
votes
6
answers
2k
views
Teach a course in 1 month
I need to teach an intro course on number theory in 1 month. I was just notified. Since I have never studied it, what are good books to learn it quickly?
3
votes
2
answers
651
views
Can this informal argument (for the fact that almost all reals in the unit interval are irrational) be saved?
In the textbook from which I am teaching a Discrete Math course, the authors propose randomly generating an infinite sequence of decimal digits $d_1, d_2, \dots$. We are to think of this as the ...
- 6,292
3
votes
3
answers
1k
views
Pedagogical question concerning $\Gamma(z)$
Pedagogically speaking, I see two problems with defining
$\Gamma(z)$ (at least for real $z$) by the limit
$$\Gamma(z)=\lim_{m\to\infty}\frac{m! m^z}{\prod_{i=0}^m (z+i)}$$
as compared with the formula
...
- 17.6k
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
3
votes
2
answers
432
views
A logarithmic cotangent inequality
I must be a terrible googling searcher but I cannot find a reference to the following inequality:
$$ \forall_{\phi\in(0;\frac \pi 4)}\ \ln(\cot(\phi)))\, <\, \cot(2\!\cdot\!\phi) $$
I have just ...
- 7,500
3
votes
3
answers
550
views
Solving interval problems without outer measure
Is it possible to solve the following two problems on intervals using elementary methods, without using the outer measure ?
Problem 1
If $(I_n)$ is a disjoint sequence of subintervals of interval $I$ ...
3
votes
1
answer
271
views
Elementary classification of division rings
Are there examples (other than the two mentioned below) of fields $K$ such that the classification of all finite dimensional division $K$-algebras is possible using only elementary theory (lets say a ...
- 26.5k
3
votes
3
answers
515
views
undergraduate handle decomposition. Reference
As the title says, I'm searching for a nice textbook for introducing the theory of handle decomposition of manifolds to undergraduate students.
- 829
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 ...
3
votes
2
answers
141
views
Accessible literature on fractional dimensions of subsets of $\mathbb R^n$
I am currently wondering whether it is realistically possible to choose the topic "Fractals and fractal dimensions" for a seminar aimed at undergraduate students in the 2nd semester, with ...
- 1,942
3
votes
3
answers
2k
views
Good Books on the history of Zero
I am looking for books that discuss the origins of the zero, specifically the differences in the use and concept of the zero number among different civilizations (considering also the Mesoamerican ...
- 221
3
votes
1
answer
806
views
What are some problems for research in functional analysis that can possibly be solved by someone with basic knowledge of the subject? [closed]
I wanted to know are there any problems in Functional Analysis (FA) that can possibly be successfully tackled by someone like me who does not have any expertise in this area but is only familiar with ...
- 167
3
votes
1
answer
2k
views
Cambridge Mathematical Tripos papers from late 19th century
Are the scanned images of Cambridge Mathematical Tripos papers from late 19th century available anywhere on Internet?
- 33
3
votes
2
answers
598
views
Math and social commitment [closed]
I am a master's student and am looking for ways that link a certain social commitment with serious math. Since I have not found such an overview yet and in order to raise public awareness of such ...
- 129
3
votes
2
answers
1k
views
Function with all but mixed second partial derivatives twice differentiable?
Let $f(x,y)$ be a a real valued function on an open subset of $\mathbf{R}^2$ with continuous partial derivatives $\frac{\partial^2 f}{\partial x^2}$ and $\frac{\partial^2}{\partial y^2}$. Is $f$ twice ...
- 107
3
votes
2
answers
222
views
Which W W Sawyer titles exist in non-English language editions?
In this community question asking about books that teach the practice of mathematics, the author mentions the works of W W Sawyer.
Which of Sawyer's books were translated into languages other than ...
user159323
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' ...
3
votes
3
answers
3k
views
Battle of the brains; cultural mathematics [closed]
Firstly, I apologize if my question is long.
Three years ago, I watched a video with the name Battle of the Brains. It was a wonderful video about challenging some famous peoples to solve some ...
3
votes
1
answer
234
views
Geometric construction exercises
Many of you know dynamic geometry exercises in Euclidea; if not, here is one example.
It lets you do a geometric construction and sends a message once you achieve the result.
I am looking for a way to ...
- 45k
3
votes
1
answer
507
views
What are some interesting grading/curving systems you have seen for a course? [closed]
It seems like every math course has something unique in how things are graded.
1) What are some interesting grading systems you have seen/used? (include curving types, etc.)
2) What are some pros ...
3
votes
0
answers
167
views
Suitability of formal type theory for mathematical thinking (vs. traditional set theory)
Type theory has advantages over set theory for the (computer) formalisation of mathematics, but has anybody who does mathematics with pen and paper found proof assistants or automated theorem provers, ...
3
votes
0
answers
873
views
Hard problems solving tricks
This question is motivated by this one that I posted on math.stackexchange.
When I fail to solve a hard math problem (like the ones I presented in the linked post), I read a solution and I noticed ...
- 161
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
2
votes
4
answers
4k
views
Best way to introduce the Chinese Remainder Theorem (to a high school student)
What do you think to be the most effective way to teach the Chinese remainder theorem to a smart high school student, which is supposed to only have a soft idea about how modular arithmetic works, and ...
- 1,269
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 ...
- 5,935
2
votes
3
answers
9k
views
How can I combine my interests for pure mathematics and computer science in college? [closed]
I’m a high school senior who's gone through quite the self-introspection the past few months while applying for college, and I have a bit of a dilemma. All my life, I've loved & excelled at ...
- 169
2
votes
1
answer
806
views
Math major at 36 [closed]
I decided to go for math at 36. Is this idea possible? I studied literature, political science and international relations and still I am not really sure what I am doing.
Since I was kid, I was not ...
2
votes
3
answers
274
views
learning sources about Ihara Coefficient
Do we have any good sources(lecture notes or books) for learning about $Ihara$ Coefficient?
Is there any relation between $Ihara$ Coefficient and the eigenvalues of graphs?
Thanks for any help.
- 4,784
2
votes
4
answers
1k
views
Eigenvalues of powers of linear mappings
Let $\tau$ be a linear map on a finite dimensional complex vector space. Clearly, if $\lambda$ is an eigenvalue of $\tau$ then $\lambda^n$ is an eigenvalue of $\tau^n$, for any natural (integer, on ...
- 4,096
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
2
votes
1
answer
2k
views
Finding permutation matrix $P$ that minimizes the trace of $P C P^T D$
I have a problem that is really important for my thesis and i am not studding math so i will be very glad if you help me in this case...
thanks for your help in advance
I want to find permutation ...
- 59
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 ...
2
votes
1
answer
628
views
Does some published texbook take a particular approach (described here) to the transition from discrete to continuous probability distributions?
(I posted this question at matheducators.stackexchange.com and it seems to be considered an inappropriate question for that site. I don't understand why.)
Imagine an introductory probability course ...
2
votes
1
answer
897
views
Text/structure for an analysis course for students with pre-existing understanding of some applied aspects of analysis
Greetings,
I'm teaching a one-off course (perhaps never to be repeated) in a curriculum that's in transition, and I'm looking for advice on a textbook, or stories from people who have taught similar ...
2
votes
2
answers
349
views
Characterizing triangles unembeddedly
The mathedu mailing list has a recent longish thread at
http://www.nabble.com/Why-do-we-do-proofs--to25809591.html
which discussed among other things whether we should teach triangles as labeled or ...
- 1,160
2
votes
2
answers
1k
views
How should I find a tutor for math-overflow level mathematics? [closed]
Searching for maths tutors online finds people willing to teach up to A-level. I'm looking for help at a more advanced level.
At the moment I'm trying to teach myself category theory from downloaded ...
- 150
2
votes
1
answer
295
views
Examples of new results found via exams [closed]
I suspect that there have been many instances throughout history where a new proof of an existing result has been discovered by a student while taking an exam. Does anyone have an example of this?
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
2
votes
1
answer
359
views
Defining integrals by residue theorem
I have always been interested in alternative definitions of mathematical objects. I wonder if one can craft an useful definition of definite integral by using the Residue Theorem from complex analysis....
- 341
2
votes
0
answers
237
views
Solve the recurrence relation with 2 variables
We have the following recurrence relation:
\begin{equation}
f(n,m) = f(n-1,m) g_{\alpha, \gamma}(n,m) + f(n,m-1) g_{\beta, \gamma}(n,m) \\
g_{\alpha, \gamma}(n,m)= \sum^{n}_{i = 0} \sum^{m}_{j = 0} \...
- 105
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 ...