COURSE NOTES: Below are scanned copies of my lecture notes from when I taught a variant of this course as a senior seminar (click here for additional comments from each day's lecture from that class). Skimming these notes is a good way to prepare for lecture and to review the material; however, it is not the case that everything said in lecture will be in these notes for two reasons: (1) I hope to have a lot of class discussion, and these comments will undoubtably influence which direction we pursue; (2) detailed explanations of many arguments are given in the book, so often I have just jotted down notes to remind myself of what I wanted to mention.

SUPPLEMENTAL READING: For more on each topic, click below to go to a subpage with handouts and reading recommendations:

• n^kα mod 1 and Poissonian behavior
• Random Matrix Theory
• The Circle Method
• Benford's Law
• Riemann Zeta Function and L-functions
• Additive Number Theory
• 3x+1 Problem
• Continued Fractions
• Linear Programming
• Sphere packing, lattices and error correcting codes

COURSE NOTES AND HANDOUTS: Below are scanned copies of my lecture notes from teaching the course as a senior seminar in 2009.

• Errata for the book (if/when you find others, or places where the exposition could be clearer, please let me know)
• Additional comments from each day's lecture
• Complete set of notes (about 7 megs)
  • Overview (description of problems, table showing the interconnectedness of the questions and techniques / material)
  • n^kα mod 1 and Poissonian behavior (the chapter from the book is available online: click here for Poissonian behavior)
    • Mathematica program to investigate n^kα mod 1.
  • Fourier analysis for n^kα mod 1 (basics of Fourier analysis leading up to Fejer's theorem)
    • Mathematica program to investigate convergence of Fejer and Fourier series to a characteristic function.
  • Random matrix theory (the first of the four chapters from the book is available online: click here for Chapter 15, the introduction)
    • Plots for Random Matrix Theory.
  • The Circle Method
    • Prime races and Chebyshev's bias
    • Hardy-Littlewood Twin Prime Conjecture
  • Benford's law
  • Riemann Zeta Function and L-functions
  • Fourier analysis for Benford's Law and L-functions (Poisson Summation)