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.