SES # | Topics | KEY DATES |
---|---|---|
1 |
Infinitude of The Primes Formulas Producing Primes? |
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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 |
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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 |
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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 |
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22 | Final Paper Presentations I | |
23 | Final Paper Presentations II | |
24 | Final Paper Presentations III | Final version paper due |