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Results tagged with mathematics-education
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user 9449
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/
3
votes
Motivating Algebra and Analysis for Average Undergraduates
I wonder if abstract algebra arose in response to certain questions in number theory. E.g. Gauss's arguments for modular integers precede LaGrange's theorem about orders of subgroups. I would try to …
1
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Good/Economical textbook for undergraduate intro to diff.eq. for engineers?
my favorite ode books for teaching are the ones by either tenenbaum and pollard, or martin braun. these are cheap and excellent. of course arnol'd is incredible but at a higher level. good for me …
46
votes
Too old for advanced mathematics?
In my late 20's I was a lugger in a meat market. I got my PhD in my mid 30's, and spent the next 3 decades on the faculty at UGA. To be honest, getting a PhD was hard and not especially lucrative, a …
0
votes
Examples of common false beliefs in mathematics
I don't know how common this is, but it occurs as a corollary of a theorem in the fine, and widely used, text by Shafarevich on algebraic geometry: namely, if $f \colon X \longrightarrow Y$ is a surje …
29
votes
Teaching undergraduate students to write proofs
I have tried teaching proofs for years, and I have had a lot of trouble, both in "proof" courses, and in ordinary courses. The hard part for me was getting the student to think about what the stateme …
7
votes
The role of the mean value theorem (MVT) in first-year calculus
Although this topic may not contain research level mathematics, perhaps the perspective of a researcher is useful in creating new ways of presenting it. After many years of teaching the MVT is variou …
2
votes
Possibility of an Elementary Differential Geometry Course
I support the previous suggestions, especially Ted Shifrin's fine notes.
I am quite ignorant of differential geometry myself, hence am sympathetic to this proposal. I have recently realized, through …
5
votes
Which edition of Philosophiae Naturalis Principia Mathematica of Isaac Newton would you reco...
Here is a free copy offered by its author, (edit: the translator, Ian Bruce),
http://www.17centurymaths.com/contents/newtoncontents.html
- 12.4k
15
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How to present mathematics to non-mathematicians?
As has been said, the main point is to give up the idea of communicating your actual research topic. Even job seekers giving colloquium talks should usually not attempt this. The best such talks ins …
174
votes
How to memorise (understand) Nakayama's lemma and its corollaries?
It's sort of like the inverse function theorem, and that is why it is so strong. If you have $n$ functions vanishing at the origin of $k^n$ and want to know if they give a local coordinate system, yo …
- 12.4k
14
votes
Good ways to engage in mathematics outreach?
the park city programs in summers are excellent opportunities to meet and interact with high school teachers. I am also impressed with "the wisconsin idea", that university research should affect the …
19
votes
Euclid with Birkhoff
Have you taught this course before? After teaching it several times from Millman/Parker and other materials using Birkhoff's axioms, I suggest you consider using Euclid himself plus Hartshorne's guid …
14
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How do you not forget old math?
When I was young I could remember everything just by studying it repeatedly. Now I basically cannot remember anything (except what I learned well when young) unless I "discover it myself". The quote …
5
votes
Insightful books about elementary mathematics
Euclid's elements. i find it much more useful than Klein's books, but that may mean i misunderstand the question. indeed after many years of perusing them, i find Klein's "from an advanced standpoin …
6
votes
An example of a beautiful proof that would be accessible at the high school level?
i suggest the proof archimedes wanted on his tombstone and its relatives. i.e. since two solids with the same horizontal slice area at every height have the same volume, hence by pythagoras, the vol …