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390 Quick Answers 25 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 very late papers done this weekend.  Keeping thinking about the final is a good idea.  In particular, I would love to hear more all-history topics.  Note:  your final draft is due on the last day of classes, Wednesday.  The final exam is on a Tuesday a week later.  Be very very wise and aware of our remaining time.

I have updated current averages as of the moment.  I still have to drop the one lowest reaction for those without zeroes (I have done it for those with zeroes).  If you have no zeroes, I need to wait until the end to see which one is your lowest.  (For those that can be proud - only 7 people have not missed a reaction, and only 2 have 10 for all.)  Of note, only 55% of the course is determined now.  There's lots of weight in the final exam and paper. 



Lecture Reactions

There are topic-based conferences around the country and world that people arrange on their own.  There is also the which meets every 4 years.  There was a famous one in 1900, which is part of today's reading. 

When you submit a paper to a journal they have the right to your paper until they reject it.  Which journal to send to is often a subtle and challenging question - different journals are considered more prestigious.  Explaining which is which is not easy.  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.

Canonical forms of matrices are ways to reduce matrices to simpler matrices to show that they are related.  Diagonalisation is the simplest of these, but there are others (with block diagonals, as studied by Jordan).

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

Some more about .  With swords, not guns, and no one died, but plenty of face scars. 

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.  

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. GauĂź 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.