Reminders - Paper due Monday - no exceptions.  Colloquium today 2p, Newton 203.  Picnic today 4p, Highland Park.  SOFIs.  Final exam a week from Tuesday - Milne 105 - bring computers.  

Quick Answers -§11.4.2

It is my impression that there is no more famous bridge engineering failure than the Tacoma Narrows.  Here's some video.  As you can see from the video, this was an extreme situation from the beginning.  The Golden Gate Bridge has never moved like that, or anywhere near that. 

Differential geometry is like the geometry you see in calc III more than the geometry you see in 335. 

The institute at Göttingen still exists and is important today, but it did need a time of recovery after it was so depleted. 

Einstein did work on the Manhattan Project.

CBS is the same network.  Before it was on telivision, it was on radio. 

Veblen opposed a journal for applied mathematics because he thought anyone who used mathematics in their work would publish there, and it would become too broad to be meaningful. 

To the extent to which I understand it - the ergodic theorem is a result in stastical mechanics, which concerns the behavior of a large amount of particles.  Ergodic functions are functions preserving size (measure) which also have other technical properties.  G.D. Birkhoff (the elder) proved that the average of such a function over all space is the same as the average of the function over time.  Basically the time randomnes and the space randomness are around the same values. 

The rise in US mathematics in the 20th century is definitely largely due to the emigration from Europe at the time.

"What would the differences between an applied mathematics program look like to a theoretical mathematics program?"  Good question, and I'm not sure I can fully address it.  Here's my idea, related to the warehouse discussed in the text:  in theoretical mathematics you learn how to start with extant mathematics and think about ways to extend it, ways to prove more or different things from it.  In applied mathematics you learn a thorough overview of the tools that are out there, how to select ones that are appropriate, and how to apply them when necessary. 

Morse theory generally analyses maxima, minima, and other turning points of higher dimensional functions.

There was clearly pressure to fit into Nazi ideals.  Whether Bieberbach did so because of pressure or not is not clear, but it is probably more clear that he tried to paint his mentor Felix Klein into these ideals because of those pressures. 

"Aryan mathematics" was only a political description to further attempt to reinforce Nazi ideals - there is surely no validity in it.  The distinction is of no significance - although perhaps worth noting that it is the same attitude that you find in people dismissing abstract mathematics.  It's a lazy habit to dismiss things you don't understand.  Someone wrote "The concept of 'Nazi Aryan mathematics' seems so ridiculous to hear
today" - it's supposed to. 

"The reason pulp fiction is called so is due to the cheap wood pulp paper on which the magazines were printed.  The paper had ragged, untrimmed edges.  Magazines printed on better paper were called "glossies" or "slicks.""

The Rockefeller Foundation does still exist. 

The Courant Institute (at NYU) is definitely still around and important.  

Many people asked this "When Suzuki said that Otto Neugebauer enlisted to he could avoid examinations, what kind of examinations did he mean?"  Don't you have any exams next week?

Science fiction was definitely not only aimed at scientists.  I think, though, it did show scientists that their ideas could be explained to the general public and what power it would have in trying to do so. 

"I was wondering what 40 Wall Street was before it was the Trump Tower.  I looked on wikepedia, and it was The Bank of Manhattan Trust Building before turning into Trump Tower."



Past:  Emmy Noether