stablemap

I should have said real manifolds; I thought that was what the parent comment had in mind but the brevity wasn't worth it.

Of course, I've learned a lot about these things from your writings.

I would expect him to spell this out in lectures 15 and 16. It does take work. What is surprising is that despite their all looking the same -- certainly they are the same as real manifolds -- there are tons of elliptic curves. The difference is in the complex analytic structure.

It believe mathematicians will continue to favor boards. Sitting in the audience I greatly prefer this; however, such lectures have less chance of being posted at all.

For this topic we are lucky to have Silverman's book [1], which everyone seems to like.

[1] https://www.math.brown.edu/~jhs/AECHome.html

One example:

http://www.bradford-delong.com/2016/03/the-benefits-of-free-...

It is probably logically unnecessary but I think it's best to have experience with the "computational" aspects of linear algebra before diving into Axler's book.

What he gives is the identity matrix—multiply on the right by any 2x1 vector and you will get that vector back. So any such vector, provided it is not the zero vector, is an eigenvector with eigenvalue 1.

There's also a post, which this links at the end, describing algorithmic improvements:

https://research.googleblog.com/2017/05/efficient-smart-repl...

I thought the author would mention the new collection of essays After Piketty: The Agenda for Economics and Inequality, particularly since he is one of the editors.

http://www.hup.harvard.edu/catalog.php?isbn=9780674504776

I hesitate to hold up mathematics as a good example. There are an encouraging number of female majors but further down the pipeline the numbers get much worse. For tenured faculty positions the latest number [1] I've seen is 14%.

[1] http://www.ams.org/profession/data/annual-survey/

Was this the case in 2011 when MathJax began offering this? I don't know the answer.

Often I do want to output x/3; is there a way to do that here?

Gross links to this archive, which has more material:

http://wayback.archive-it.org/3671/20150528171650/https://ww...

My short advertisement is that it has proven very useful to study Diophantine equations by reducing mod n. The Chinese remainder theorem [1] tells you to focus on reducing mod p^r, where p is a prime. If r = 1 then you are working in a field but in the ring Z/4, for example, I know 2 ≠ 0 and yet 2·2 = 0.

To make the p-adics Z_p I stitch all of these Z/p^r together: an element is a choice of a_r in each Z/p^r and these have to be compatible: a_2 reduces mod p to a_1 and so on. The resulting Z_p has no "zero divisors", and if I allow myself to invert p I get a field Q_p.

This is a huge improvement, a foundation on which to build analysis and geometry as we did over R.

[1] https://en.wikipedia.org/wiki/Chinese_remainder_theorem

Look at the end, past the bibliography.

Apart from the typesetting, is this different from this submission from earlier in the day?

https://news.ycombinator.com/item?id=13686519

There's a big list of proofs on MathOverflow [1]. Not a lot of pictures in it but there are many to be drawn.

My favorite is probably top answer: a polynomial f(z) gives you a map from the Riemann sphere ℙ^1 to itself. Topology tells you it's closed and analysis tells you it's open because locally a holomorphic map always looks like z^n. It follows that the map is surjective.

[1] http://mathoverflow.net/questions/10535/ways-to-prove-the-fu...

I wouldn't read too much into the number. Their department claims that Math 55, for example, is the hardest undergraduate math class in the country and I believe them.

It's not as obvious as I'd remembered. I think these instructions work:

http://help.washingtonpost.com/link/portal/15067/15080/Artic...

Maybe this doesn't count as supporting, but: you also get free access with a .edu, .gov, or .mil email address.

Maybe I'm missing your point, but for δ I think the hack is using the word "function"; as a measure or distribution it's a pedestrian object.

It's focused on the resulting economics but I've heard great things about the book Misbehaving by Thaler. The remarks under "Outtakes" here give some context:

http://www.misbehavingbook.org

The Wayback machine does not absolve me—probably I just missed it twice. Thank you.

Everyone I know who went to his MAA farewell address said it was wonderful. Definitely follow their link to read or hear the whole thing:

https://mathyawp.wordpress.com/2017/01/08/mathematics-for-hu...

I appreciate that the proposal [1] was put out for comments half a year before its implementation last month, although I wonder what comments it would have taken to get this thing reversed. "Optional" is a menacing word here—has anyone followed up on this?

[1] https://www.federalregister.gov/d/2016-14848

It seems to me that the logo is a second sticker.

I've heard ex-staffers say that emails are worthless but calls—in volume, as you say—have an impact.

Yes, sorry: I was afraid of changing the given title and there's nothing new here if you run purple Safari. I assume they put this up to go along with the public betas for macOS 10.12.4 and iOS 10.3. I don't get much out of the release notes attached to the tech previews so this was welcome to me.

I don't have any recommendations, but they do exist:

http://mathoverflow.net/questions/22141/how-do-i-see-latex-m...

Maybe it's better to write his equation as ae² - ce + b = 0. The proof would say that e isn't degree ≤ 2 over the rationals.

I still see this, particularly when it would be awkward to create a new symbol: "when the discriminant is ≤ 1". I feel that Halmos [1] wouldn't have liked it, but it does lessen the distance between what is written and the equation the reader will want to have in his mind.

[1] http://www.math.washington.edu/~lind/Resources/Halmos.pdf