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May
10 |
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Embeddings of smooth projective surfaces
oops. I was thinking geometric surface, but algebraic curve. |

May
10 |
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Embeddings of smooth projective surfaces
I am not an expert on this, but at least over C, cant you always embed into P^3? Just by taking lines through a point which is not on any chord or tangent reduces dimension by by one. Dimension the variety of chords and tangents shows you can keep finding such a point until you get down to P^3. |

May
3 |
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Is rigour just a ritual that most mathematicians wish to get rid of if they could?
The update is the real answer to the question. I do not really care about a proof if it does not enhance my understanding. |

Apr
20 |
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What does a mathematician expect from mathematics education?
@Scott: great link. |

Apr
20 |
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What does a mathematician expect from mathematics education?
comes down to too many intangibles. It is a real relationship with real people, and I think that those are too varied and complex to have anything like universal solutions. I have participated in wildly successful classes which had charismatic leaders who have completely opposite perspectives on how to teach. |

Apr
20 |
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What does a mathematician expect from mathematics education?
@Scott: I have high hopes for big data in education. The computer can get a huge amount more information about a student than I ever could in an even moderately sized classroom. Being able to look at the whole pattern of a students history, pinpoint what the difficulties likely are, and then address those will revolutionize everything in my opinion. Only time will tell I guess. Things like "classroom best practices" are important, and I have a lot of personal opinions about these. These opinions are subject to revision based on what I see others doing. But fundamentally, I think it |

Apr
19 |
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What does a mathematician expect from mathematics education?
I can say that I personally know some great math ed people, who are just fantastic teachers. I also think that the teacher education courses at my university really are some of the best math classes being offered. I also think Sybilla Beckman's contributions have been outstanding. But I also think that all of these are opinions. |

Apr
19 |
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What does a mathematician expect from mathematics education?
@Benjamin: I will read some of Kilpatrick's work. Thanks for recommending it. Is it okay for me to email you sometime to chat about it, whenever I get around to reading it? I guess this is really the heart of my troubles: Mathematics education research can only address implications. If I do this, then this is likely to be the outcome. That is a matter of science. It cannot decide which outcomes are the desirable ones! That is a political question, or a moral question. It seems very often that mathematics educators are trying to address the moral question. Do you agree? |

Apr
19 |
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What does a mathematician expect from mathematics education?
For example, think about teaching double digit arithmetic. There are a lot of mathematics educators who will tell you that teaching the algorithm is essentially killing any chance that the student will understand it. There are others who say that you have to learn the mechanics first, and then you have the structure to start trying to understand what is going on. Put these two people in a room, give them access to the whole internet worth of studies, and there is basically no chance that either person will budge an inch. |

Apr
19 |
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What does a mathematician expect from mathematics education?
I think one reason that I got turned off to the field is that is not really being done as a science in my opinion. Everyone involved cares deeply about education (a good thing!), but there is so much opinion. I mean, you might say "Even though students using such and such approach score lower on these tests, they are actually thinking more as evidenced by such and such". In the end, everything is subjective enough that people basically stand by what they think is the best way to teach. |

Apr
19 |
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What does a mathematician expect from mathematics education?
@Benjamin - I have read a lot of papers in mathematics education. I thought about getting a Ph.D. in mathematics education at one time. It is not an objective science, and there are huge culture wars in the field. For example, between constructivists and people who encourage rote memorization. Read en.wikipedia.org/wiki/… for example, including the criticism section. |

Apr
19 |
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What does a mathematician expect from mathematics education?
Also I would like to comment that the ultimate solution is probably economic - find a way to fund mathematicians to do research without having to teach. This way the people who want to teach can be hired on the merits of their teaching, and the people who want to do research can be hired on the basis of their research. Until this changes, I really do not see hope - there are too many researchers who are only teaching because that is how you get access to a university job, not because they want to be teachers. You will never help those. |

Apr
19 |
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What does a mathematician expect from mathematics education?
Was this downvoted for being rude? I sometimes have difficulty understanding rudeness. I did not intend any ill will with my answer, only to give my real perspective on this issue. |

Apr
17 |
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Weierstrass factorization with $L^2$ estimates?
Ah, I had not thought to use Jensen's formula. I will see if I can cook up a concrete counterexample. I was thinking of L^2 wrt lebesgue measure. I will wait a day or so to accept your answer. Thanks. |

Apr
16 |
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Newton integration without integration
This is basically how I think about the fundamental theorem... |

Apr
3 |
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functions of one complex variable: geometric theory
Algebraic Curves and Riemann Surfaces |

Mar
21 |
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Smooth analgoue of Dehn Invariants?
I would guess that you would need to capture geometry, not just topology. I was thinking something like normal vectors to the boundary faces converging to normal vectors to the surface. |

Feb
28 |
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Interesting Calculus Questions/Exercises
When you fill the horn, it is painting the inside of the horn. It is just that the coat of paint is getting thinner and thinner as you go down the horn. |

Feb
28 |
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Integrating Powers without much Calculus
@Ben Crowell: You can also integrate x^2 using geometry: Interpret $$\int_0^r \pi x^2$$ as the volume of a cone. |

Feb
21 |
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Undecidability and holomorphic functions (Reference request)
@Joel: I think he is saying that he would like to be able to downvote some answers to more freely reorganize the rankings, but he does not feel comfortable doing so if someones points are on the line. It is more appropriate to downvote a CW answer. |