390 Quick Answers 26 April

Thank you to all who presented and even more to those who attended GREAT Day.  

Including today we have 4 class days left.  Your last reading is for a week from today.  On the last day you will have lecture reactions and a set of reactions to the course as a whole - not how it is taught, but what you learned.  

I am happy to talk to anyone about their papers.  I will try to get the straggling papers done this weekend.  Keeping thinking about the final is a good idea.  Note:  your final draft is due on the last day of classes.  The final exam is on a Monday a week later.  Be very very wise and aware of our remaining time.

I have updated current averages for those whose drafts I have read.  I still have to drop the one missing reaction.  If you have no zeroes, I need to wait until the end to see which one is your lowest.  



Lecture Reactions

"What is the difference between undergraduate and graduate level mathematics?"  Specialisation and depth.  Abstraction.  More recent work - more up to date, and then culminating in research. 

I reiterate that the AMS is focused on research in mathematics.  It is not very relevant for anyone who isn’t a research mathematician.  The MAA is far more welcoming to diverse levels, e.g. undergraduates or teachers or amateur mathematicians.  Oh, I also didn’t say this - anyone can join any of these organisations - merely pay the fees.  The fees are far lower for you than for me, for example.  The same goes for attending meetings.  You are all welcome.  The next Seaway Section meeting is at RIT in October.  Presentations are reviewed, but as long as you are talking about something reasonable there is probably a place to do so. 

"When people work in many different subject areas, do they typically interconnect in some way?"  That becomes more necessary the more modern we get.  This was asked about EH Moore, and I think he was just broadly talented.  That is becoming harder.  We will see the two last universalists today. 

“What would you say has been the most interesting/biggest takeaway you have had from attending mathfest.”

Oh, and I didn’t talk about SIAM, AWM, NCTM, ASA, AMATYC,  &c mostly because they weren’t in the book.  

Now that we have finished the chapter on USian mathematics.  Where does that leave it?  Still behind for a while, but rapidly catching up in the early 20th century as emigrees leave Europe.  This will be a theme in Chapter 11.  

Cauchy had early work on eigenvalues - decomposing a linear transformation into directions where it was merely a scalar multiple.  He applied this to differential equations by decomposing a system of differential equations into exponential terms.  Euler saw them earlier in terms of axes of rotations in connection with differential equations.  






Reading Reactions

Kovalevskaya’s French Academy prize was for a paper titled “Memoir of a special case of the problem of the rotation of a solid body around a fixed point where the integration is performed using the functions of ultraelliptical time.”  I don’t know what “ultraelliptical” is, but this is rotation in time, so not the same as revolutions in Calc II.  

Research mathematicians publish their results in journals.  This includes all of your professors (but probably not your lecturers).  How do people decide what goes into journals?  Each one has referees what read papers to see if they are 1. correct, 2. important enough, 3. good enough.

Hardy and Littlewood were lifelong collaborators.  We’ll see them (together and apart).  I like this excuse to say something about Hardy and Littlewood’s mathematics:  people (e.g. Gauß and Riemann) thought
[# of primes < n] < \int_2^n 1/(ln x)dx
H-L proved that there are infinitely many counterexamples to this (which is interesting to think about how to prove this without finding them).  I am very glad that _most_ people (ok, not this year, but over the years) see that the non-judgemental, free, and accepting nature of H-L collaboration is a positive.  People are better off doing what they _want_ to do than what they feel obligated to do.  

Wiener’s communication theory is more about electronic communication and sending messages than about interpersonal communication.

I’m not going to say much about relativity.  There is no independent frame of reference for measuring absolute velocity.  Velocity is always “with respect to” something.  Special relativity is E=mc^2.  General relativity is that space is curved by masses. 

PSA about coding again:  the NSA employs more mathematicians than anyone else in the world.  If you’re interested, that’s where you learn all about it.