HANDOUTS FOR THE REU / VISP

HANDOUTS:

Prime Numbers, Elementary Number Theory Functions, Zeta(s) (42 pages, lot of background material)

Random Matrix Theory (Introduction, Semi-Circle Law, GOE spacings, Number Theory Example, 77 pages)

Fractional parts: n² x mod 1 (Denseness, Equidistribution, Poissonian Behavior, 22 pages)

Introduction to the Circle Method (66 pages)

Introduction to Probability Theory and Statistical Inference (38 pages)

Random Graphs: See PETER  RICHTER'S  INVESTIGATIONS  and KEVIN  CHANG'S  INVESTIGATIONS

PROGRAMS:

Mathematica Tutorial File (basic operations, random matrices, 3x+1 problem, histograms)

LaTeX FILES:

template.tex   (.tex file, source code);   template.pdf  (compiled .pdf file);   yl.eps  (image file used in template)

To work with .tex files on the math system, go to the directory 
where you've saved the files and type xemacs template.tex &; the 
ampersand opens another window. To compile, type CONTROL-C-F. If
it asks you to save, type y. To get the references right, you often
have to compile multiple times. To view the compiled file, which will
be in .dvi form, at the unix prompt type xdvi template.dvi &; again the
ampersand opens a new window. The advantage of using xdvi and not dvi 
is that when you work on the .tex file and recompile, if you click on
the .dvi window it automatically updates it.

Configurations: go to Options, Display, and then choose line numbering.
Also go to Options, Troubleshooting, and choose Debug on error. If you 
don't see many colors in the text, go to Options, Syntax Highlighting and
choose colors. When you are done, type CONTROL-X-C to exit.