| SES # | Topics | KEY DATES |
|---|---|---|
| 1 | Infinitude of The Primes Formulas Producing Primes? | |
| 2 | Summing Powers of Integers, Bernoulli Polynomials | |
| 3 | Generating Function for Bernoulli Polynomials The Sine Product Formula and $\zeta(2n)$ | Assignment 1 due |
| 4 | A Summary of the Properties of Bernoulli Polynomials and more on Computing $\zeta(2n)$ | |
| 5 | Infinite Products, Basic Properties, Examples | |
| 6 | Fermat's Little Theorem and Applications | |
| 7 | Fermat's Great Theorem | Assignment 2 due |
| 8 | Applications of Fermat's Little Theorem to Cryptography: The RSA Algorithm | |
| 9 | Averages of Arithmetic Functions | |
| 10 | The Arithmetic-geometric Mean; Gauss' Theorem | Assignment 3 due |
| 11 | Wallis's Formula and Applications I | Topic proposal and full outline of the paper due |
| 12 | Wallis's Formula and Applications II (The Probability Integral) Stirling's Formula | |
| 13 | Stirling's Formula (cont.) | |
| 14 | Elementary Proof of The Prime Number Theorem I | |
| 15 | Elementary Proof of The Prime Number Theorem II: Mertens' Theorem, Selberg's Formula, Erdos' Result | |
| 16 | Short Analytic Proof of The Prime Number Theorem I (After D. J. Newman and D. Zagier) | |
| 17 | Short Analytic Proof of The Prime Number Theorem II: The Connection between PNT and Riemann's Hypothesis | First draft of paper due |
| 18 | Discussion on the First Draft of the Papers and some Hints on how to Improve the Exposition and use of Latex | |
| 19 | Euler's Proof of Infinitude of Primes Density of Prime Numbers | |
| 20 | Definition and Elementary Properties of Fibonacci Numbers, Application to the Euclidean Algorithm Binet's Formula | Second draft of paper due |
| 21 | Golden Ratio Spira Mirabilus | |
| 22 | Final Paper Presentations I | |
| 23 | Final Paper Presentations II | |
| 24 | Final Paper Presentations III | Final version paper due |