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Results tagged with mathematics-education
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For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/
15
votes
Historical (personal) examples of teaching-based research
While thinking about teaching finite fields for students who knew some group theory and what a field is, but had not seen abstract linear algebra, I wondered if there might be a way to show them a fin …
58
votes
Cool problems to impress students with group theory
Here is a striking application of a particular finite non-abelian group.
Explain to your students the issue of check digits as an error-detecting device on credit cards, automobile identification num …
33
votes
Examples of common false beliefs in mathematics
After learning that the Witt vectors of a finite field of size $p^n$ is the ring of integers of the unramified extension of ${\mathbf Q}_p$ of degree $n$, I think lots of people then think that the Wi …
17
votes
Accepted
The interrelationship problem of modern mathematics – How to deal with it in first year grad...
Of course you should show students, taking into account their backgrounds, that the material they are learning in one course is relevant elsewhere. It makes it clearer to the students that topics th …
5
votes
Accepted
Text/structure for an analysis course for students with pre-existing understanding of some a...
If you want a reference that will not bore them, supplement the main text with "Metric Spaces: Iteration and Application" by Victor Bryant. The book is short and it shows in several contexts how the c …
12
votes
Applications of Group Theory Which Motivate Theoretical Questions?
I had the same question before I taught a course that was largely group theory.
Here is the webpage I created to address the issue:
http://www.math.uconn.edu/~kconrad/math216/whygroups.html
11
votes
Place of Analytic geometry in modern undergraduate curriculum
To answer your first question, that the label "analytic geometry" is found in the title of a calculus book doesn't mean what you might think. The reality is that in the 1960s and 1970s most calculus b …
- 50.6k
15
votes
Pedagogical question about linear algebra
To understand a definition, show the students (a) lots of examples, (b) lots of non-examples and why they don't work, (c) misconceptions related to the definition
(e.g., coordinates and real/imag. par …
63
votes
Accepted
Interesting results in algebraic geometry accessible to 3rd year undergraduates
If you want to teach something intriguing, you should do something that introduces a new geometric idea while also involving algebra in an essential way. I recommend that you give an introduction to t …
- 50.6k
56
votes
Why do we care about $L^p$ spaces besides $p = 1$, $p = 2$, and $p = \infty$?
Tim, I've got two words for you: interpolation theorems (e.g., Riesz-Thorin and Marcinkiewicz interpolation theorems). Such theorems let you pass from information about some operators on $L^1$ and $L …
19
votes
Strong induction without a base case
I hope the following will satisfy Bjorn. It is a proof by induction which naturally skips over the base case and is at the undergraduate level. I saw the argument for the first time today in the pap …
10
votes
Math History books
Here are three possibilities. You'll have to judge if they will be accessible to non-science majors.
Mathematics and Its History by John Stillwell. Since Stillwell is on MO, perhaps he can say mor …
- 50.6k