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Results tagged with teaching
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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/.
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
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 …
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!
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
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 …
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 …
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 …
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.
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 …
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 …
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/