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Results tagged with gm.general-mathematics
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user 29316
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
80
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Is rigour just a ritual that most mathematicians wish to get rid of if they could?
"No". That was my answer till this afternoon! "Mathematics without proofs isn't really mathematics at all" probably was my longer answer. Yet, I am a mathematics educator who was one of the panelists …
- 4,713
11
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4
answers
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Why do mathematicians prefer one definition over the other when they both define the same co...
Here is a basic, though very important, example:
Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of construct …
- 4,786
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votes
4
answers
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When did you "meet Polya"? [closed]
I guess most of us didn't meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess that most of us have met one of his writings (or alike) on problem solving, and i …
- 91.8k
81
votes
22
answers
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Are there proofs that you feel you did not "understand" for a long time?
Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed my question was ins …
- 6,039
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votes
2
answers
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How should you respond to a student who asks whether a very nice physical example constitute... [closed]
"Is this really a proof?" is the exact question e-mailed to me today from an undergraduate mathematics student whom I know as a highly competent student. The one sentence question was accompanied with …
- 6,039
9
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4
answers
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Is there any monoid in which the product of two non-invertible elements could be invertible?
I think the title speaks for itself. Thus I just explain the story behind the question. Of course, you may want to skip the story.
Story: Currently, I teach a course in linear algebra and matrices wi …
- 8,803
1
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Another chicken or egg: sequence or series
I have a rather radical idea. I start with Maclaurin Series! Let's see how it works. You first see graphically and "globally" that you get closer and closer to the function and when adding infinite te …
- 2,437
22
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Is rigour just a ritual that most mathematicians wish to get rid of if they could?
Here is an "uncommon" answer in favor of rigour from an old paper of Atiyah (Bull. Inst. Math. App. 10 (1974), 232-234): "How research is carried out?" In particular, I like the first part of the quot …
- 53.3k
7
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5
answers
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What does a mathematician expect from mathematics education? [closed]
Consider that my question is not a personal and/or subjective question. Perhaps, you have hired a mathematics educator in your department and you are interested in finding a way to communicate with hi …
- 2,437
8
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When should a supervisor be a co-author?
In my situation (in Iran), it is obligatory for a PhD student to publish one or two papers to graduate. Thus, I have a personal and strict rule: I won't be a co-author since I'm getting paid to help …
- 2,437