Expository Notes

Disclaimer: Many of these notes were hurridly written for my students, to give them a very rough idea of how certain theorems are proved. Thus, some of the writeups may have minor errors.

• Roth's Theorem on 3-term Arithmetic Progressions

  (course notes from Math 8813 I taught Spring 2004)

• The Convolution Method of Evaluating Sums of Multiplicative Functions

  (course notes)

• The Balog-Szemeredi Theorem

  (course notes) I thank Seva Lev for making some edits to this note. Seva himself has a writeup of Gowers's proof of the Balog-Szemeredi theorem, and his website can be found here .

• The Szemeredi Regularity Lemma

  (course notes)

• Introductory Notes on Bayesian Spam Filtering

  (course notes)

• Introductory Notes on Linear Recurrence Sequences

  (course notes)

• Introductory Notes on the Functional Equation of the Riemann Zeta Function

  (course notes -- a lot of material taken from Davenport and Montgomery's Multiplicative Number Theory).

• Notes on Pade Approximations and the Transcendence of Pi.

• Szemeredi's Proof for Three-Term Progressions, at a Glance.

• Stepanov's Proof for Weil Estimates (elliptic curve case)

• Meinardus's ``inverse mellin transform'' approach to the asymptotic formula for p(n) = number of partitions of n

• An Intuitive Proof Outline of the Thue-Siegel Theorem

• Note on proving Roth's Theorem using Bogolyubov's method (with O. Sisask)

  (Basically, this can be thought of a re-casting of a similar theorem due to Szemeredi into the language of `convoultions' and `Bogolyubov's lemma'.)

• Note on an elementary proof of David Bailey's ``Hotspot Theorem''

• Note on the Triangle Deletion (sometimes called Triange Removal) Lemma

• The basic Fourier proof of Littlewood-Offord