Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with teaching
Search options answers only
not deleted
user 290
For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.
174
votes
What are the most misleading alternate definitions in taught mathematics?
Here's another algebra peeve of mine. The definition of a normal subgroup in terms of conjugation is pretty strange until it's explained that normal subgroups are the ones you can quotient by. Again …
121
votes
What are the most misleading alternate definitions in taught mathematics?
In my experience, introductory algebra courses never bother to clarify the difference between the direct sum and the direct product. They're the same for a finite collection of abelian groups, which …
33
votes
Demystifying complex numbers
If the students have had a first course in differential equations, tell them to solve the system
$$x'(t) = -y(t)$$
$$y'(t) = x(t).$$
This is the equation of motion for a particle whose velocity vect …
33
votes
Why should one still teach Riemann integration?
I haven't really thought this through, but how does one actually compute integrals? For the Riemann integral one can either prove the fundamental theorem and have a large table of derivatives handy, …
24
votes
Is Euclid dead?
As long as this question is open I might as well throw in my two cents. I think it is not useful to teach Euclidean geometry to high school students. Here are some reasons I can think of for people to …
22
votes
Integrating powers without much calculus
This may not be in the spirit of what you want, but... by scaling arguments it suffices to establish that $\int_0^1 x^p dx = \frac{1}{p + 1}$. Consider the following probabilistic argument (not entire …
- 118k
22
votes
Why should one still teach Riemann integration?
Paul Siegel mentioned that to teach undergrads the Lebesgue integral you have to spend half the semester on measure theory. This is actually not true. There is a self-contained definition of the Leb …
20
votes
How to mentor an exceptional high school student?
Tell him about his other opportunities (although perhaps being on AoPS he is already aware of them). Summer programs like
Ross
PROMYS
the Canada/USA Mathcamp
HCSSiM
and others come highly recomme …
18
votes
Collecting proofs that finite multiplicative subgroups of fields are cyclic
Let $G$ be a finite subgroup of $F^{\ast}$ of order $n$. Then all the elements of $G$ satisfy $x^n = 1$ in $F$. Since polynomials of degree $n$ over a field have at most $n$ roots, it follows that the …
16
votes
Accepted
Can this informal argument (for the fact that almost all reals in the unit interval are irra...
You can make sense of the uniform probability distribution on lots of infinite sets, notably any compact topological group $G$, where "uniform probability distribution" should mean "normalized Haar me …
- 118k
14
votes
Applications of knot theory
Colin Adams' The knot book discusses the following applications:
Knotting in DNA,
Molecular knots,
Statistical mechanics (e.g. the Potts model).
Constructing invariants of knots is also related t …
13
votes
Math books for advanced high school students
The list I give undergraduates and strong high schoolers is here.
11
votes
Math History Question about the exponential function
Short answer: Most likely undefined.
Long answer: The "naive" definition of $f(x) = a^x$ where $a, x \in \mathbb{R}$ and $a > 0$ is as follows. You know how to define $f(n)$ where $n$ is an intege …
- 118k
10
votes
Category theory sans (much) motivation?
The Unapologetic Mathematician covers category theory before it covers group theory, so after a little more experience with abstraction you might want to expose your friend to the beginning posts. I …
9
votes
Elementary applications of linear algebra over finite fields
Suppose you want to compute the period of the Fibonacci sequence $\bmod p$. This reduces to examining the powers of the matrix $\left[ \begin{array}{cc} 1 & 1 \\\ 1 & 0 \end{array} \right]$ over $\mat …