Re:Donald Knuth's 20th Annual Christmas Tree Lecture: (3/2)-...
by deckar01 on Tuesday December 09, 2014 @12:19AM
(#8721161)
You probably just need a few prerequisites. Even if you did study data structures, algorithms, and combinatorics previously, you would need to have your head wrapped around the subjects to fully understand this lecture.
I would also keep in mind that Donald Knuth probably spent more than an hour before understanding the topic.
Something that I think anyone can take away from this lecture is a story of discovering new mathematical relationships. He starts with a function that correlates to a logical problem, changes the inputs in an new (strange) way, then studies the output to form a theory that connects to the original problem.
The key was recognizing old results in a new problem.
Re:Donald Knuth's 20th Annual Christmas Tree Lecture: (3/2)-...
by cowsandmilk on Tuesday December 09, 2014 @06:02AM
(#8722121)
> Something that I think anyone can take away from this lecture is a story of discovering new mathematical relationships. He starts with a function that correlates to a logical problem, changes the inputs in an new (strange) way, then studies the output to form a theory that connects to the original problem.
This type of mathematical exploration seems to be the story of his life. See Quarter-imaginary base for him doing the same thing in high school.
Re:Donald Knuth's 20th Annual Christmas Tree Lecture: (3/2)-...
by ecesena on Tuesday December 09, 2014 @12:36AM
(#8721223)
I'm just at minute 15 for now, however I can recommend you this link [1] to start with binary trees. The picture also explains why the coefficient of z^3 is 5.
Re:Donald Knuth's 20th Annual Christmas Tree Lecture: (3/2)-...
by brudgers on Tuesday December 09, 2014 @07:55AM
(#8722422)
Knuth tries to inspire anyone who doesn't settle for muttering "Oh well, maybe I can find a video of a squirrel on water skis". And his material is challenging enough that eventually everyone faces the question:
Re:Donald Knuth's 20th Annual Christmas Tree Lecture: (3/2)-...
by taeric on Tuesday December 09, 2014 @12:08AM
(#8721146)
I know I'm stupid in this regard.
My largest takeaway was just the joy of looking at the results of mathematical constructs for patterns. Not just symbolically manipulating expressions, but also simply listing the results and seeing what could be found.
That is, many of the techniques he showed involved simply recognizing patterns in output. Then, exploring the equations symbolically to see if he could explain these ideas.
I would also keep in mind that Donald Knuth probably spent more than an hour before understanding the topic.
Something that I think anyone can take away from this lecture is a story of discovering new mathematical relationships. He starts with a function that correlates to a logical problem, changes the inputs in an new (strange) way, then studies the output to form a theory that connects to the original problem.
The key was recognizing old results in a new problem.
This type of mathematical exploration seems to be the story of his life. See Quarter-imaginary base for him doing the same thing in high school.
https://en.wikipedia.org/wiki/Quater-imaginary_base
...fifty years writing a 1comprehensive 12 chapter book on compilers. The reason: things like this are relevant to its scope
[1] http://cs.lmu.edu/~ray/notes/binarytrees/
What am I going to do about it?
My largest takeaway was just the joy of looking at the results of mathematical constructs for patterns. Not just symbolically manipulating expressions, but also simply listing the results and seeing what could be found.
That is, many of the techniques he showed involved simply recognizing patterns in output. Then, exploring the equations symbolically to see if he could explain these ideas.
Though, again, limited intelligence on my end. :)