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Results tagged with teaching
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user 3634
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/.
30
votes
The role of the mean value theorem (MVT) in first-year calculus
My view is that there are essentially two strands in a first calculus course.
The first is not really concerned with a rigorous presentation; rather it tries to get the main ideas, their interrelat …
27
votes
Accepted
Interesting Calculus Questions/Exercises
You only need integration by parts to prove the irrationality of $\pi$. I'm having
my Calculus 2 students do it as a long-term group project starting Monday.
Then when you've done partial fractions, …
99
votes
Why do we teach calculus students the derivative as a limit?
I'm teaching Calc 1 this semester, and I've stumbled onto something that I like very much. …
14
votes
Teaching Steenrod Operations
I like to observe that the diagonal map $X\to X\times X$
is $\mathbb{Z}/2$-equivariant, hence induces a map of homotopy colimits.
Analyzing this map with $X = K( \mathbb{Z}/2,n)$ gives the squares.
Th …
- 12.5k
10
votes
Collecting proofs that finite multiplicative subgroups of fields are cyclic
Lemma: Let $G$ be a finite abelian group, and let $x\in G$ with maximal order. Then for any other element of $y\in G$, $|y|$ divides $|x|$.
Proof. If not, then there is an element $y\in G$ and a pr …
13
votes
Why should one still teach Riemann integration?
In introductory calculus classes, I work hard to get my students to understand the heuristic: break complicated problem into simple (close enough to constant) pieces; find the answer to the simple p …