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Seminar in Analysis: Applications to Number Theory >> Content Detail



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SES #TopicsKEY DATES
1

Infinitude of The Primes

Formulas Producing Primes?

2Summing Powers of Integers, Bernoulli Polynomials
3

Generating Function for Bernoulli Polynomials

The Sine Product Formula and $\zeta(2n)$

Assignment 1 due
4A Summary of the Properties of Bernoulli Polynomials and more on Computing $\zeta(2n)$
5Infinite Products, Basic Properties, Examples
6Fermat's Little Theorem and Applications
7Fermat's Great TheoremAssignment 2 due
8Applications of Fermat's Little Theorem to Cryptography: The RSA Algorithm
9Averages of Arithmetic Functions
10The Arithmetic-geometric Mean; Gauss' TheoremAssignment 3 due
11Wallis's Formula and Applications ITopic proposal and full outline of the paper due
12

Wallis's Formula and Applications II (The Probability Integral)

Stirling's Formula

13Stirling's Formula (cont.)
14Elementary Proof of The Prime Number Theorem I
15Elementary Proof of The Prime Number Theorem II: Mertens' Theorem, Selberg's Formula, Erdos' Result
16Short 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
18Discussion 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

22Final Paper Presentations I
23Final Paper Presentations II
24Final Paper Presentations IIIFinal version paper due

 








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