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Results tagged with teaching
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user 1106
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/.
8
votes
Accepted
Mathematics of sustainable development and energy sobriety in the classroom
Tom Murphy has written an open textbook called Energy and Human Ambitions on a Finite Planet.
He uses this course to teach a "gen ed" class in his physics department for non-majors.
I think that the b …
36
votes
Teaching homology via everyday examples
A cool example I learned from Jim Fowler:
Yeast colonies have a life cycle which repeats on a regular interval. We can associate to each yeast colony a phase $\theta \in S^1$. If yeast colonies are …
5
votes
Teaching homology via everyday examples
I am not sure the best way to formalize it, but "Rock-paper-scissors" always felt like it should have one dimensional first cohomology group. Maybe just that there is a cycle in the directed graph of …
28
votes
Integrating powers without much calculus
You can derive all of the integrals $\displaystyle \int_0^1 x^p dx$ by chopping them in half, and rescaling each half to fit in $[0,1]$ again.
The proof is by induction on $p$, and by "recovering the …
- 12.1k
43
votes
"Mathematics talk" for five year olds
Giving a little "Magic show" about Möbius strips might be fun. Make a huge number of Möbius strips and cylinders, and hand them out to the kids along with safety scissors. You could have a predrawn …
2
votes
Another chicken or egg: sequence or series
Most calculus students will see limits of sequences first, because definite integrals are limits of sequences of Riemann sums.
9
votes
Applications of Liouville's theorem
There are many cool applications when combined with the uniformization theorem. Not sure if you count them as "complex analysis" or not - you could really think of them as algebraic geometry. For ex …
8
votes
Excellent uses of induction and recursion
The following famous puzzle is a great example:
http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/
7
votes
Interesting applications (in pure mathematics) of first-year calculus
I think you could probably show a smart group of first year calculus students how to get an exact formula for the Fibonacci numbers using generating functions, which basically just boils down to knowi …
20
votes
Resources for teaching arithmetic to calculus students
I have TA'ed a "Mathematics for Future Elementary School Teachers" course. The point of the course is to develop a deep understanding of elementary school math (read: An actual understanding, rather …
- 12.1k
7
votes
Real analysis has no applications?
I think out of all the fields of mathematics, analysis has the MOST application. We are talking about the subject Newton created to be able to even talk about physics here!