JKU S2046

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- Prime Proving Algorithms (including the deterministic AKS algorithm)
- Prime Decomposition Algorithms (including Lenstra's ECM)
- Basic Theories on Elliptic Curves over Rationals (including proof of Mordell Theorem)
- Elliptic Curve Point Counting Algorithms and Torsion Point Algorithms
- Theory of Heights
- Elliptic Curve Rank Conjectures (including Birch Swinnerton-Dyer Conjecture)

- On Rings and Groups
- Carmichael Numbers and Prime Recognition
- Wilson's Theorem and AKS Theorem
- AKS Theorem and AKS Algorithm
- Quadratic Extensions and Square Root mod p
- Sieving B-Smooth Numbers and Basic Quadratic Sieve
- Quadratic Sieves. Elliptic Curve Primer
- Algorithms on Elliptic Curve Group Structure
- Elliptic Curve Factorization Algorithm
- Valuation Theory
- Computing Heights
- Elliptic Curve Rank Conjectures and Elkies Curve
- Birch-Swinnerton-Dyer Conjecture

*Algorithmische Zahlentheorie*,**O. Forster**, 2. Auflage, 2015 Springer*Prime Numbers*,**R. Crandall, C. Pomerance**, Second Edition, 2005 Springer*A Course in Computational Algebraic Number Theory*,**H. Cohen**, 1996 Springer

Open to all students with mathematical background (including computer science students).

Below are the pdf of lecture (late uploads). Please take note of the time/date of the uploaded pdf. I could upload newer versions if I need to correct some mistake or add some additional text to the lectures (you might need to sometimes refresh (press F5) the browser to see the new files).

Name | Last modified | Size | Description | |
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codes/ | 23-Oct-2018 13:02 | - | ||

lecture_15.pdf | 03-Feb-2019 13:48 | 64K | ||

lecture_14.pdf | 24-Jan-2019 13:19 | 47K | ||

lecture_13.pdf | 24-Jan-2019 13:09 | 52K | ||

lecture_12.pdf | 20-Jan-2019 11:12 | 52K | ||

lecture_11.pdf | 31-Dec-2018 15:18 | 50K | ||

lecture_10.pdf | 10-Dec-2018 15:09 | 44K | ||

lecture_09.pdf | 05-Feb-2019 15:09 | 67K | ||

lecture_08.pdf | 24-Nov-2018 18:16 | 56K | ||

lecture_07.pdf | 07-Jan-2019 08:28 | 55K | ||

lecture_06.pdf | 07-Dec-2018 21:12 | 55K | ||

lecture_05.pdf | 01-Nov-2018 17:41 | 55K | ||

lecture_04.pdf | 23-Oct-2018 14:29 | 51K | ||

lecture_03.pdf | 23-Oct-2018 12:37 | 44K | ||

lecture_02.pdf | 23-Oct-2018 12:38 | 45K | ||

lecture_01.pdf | 04-Feb-2019 11:27 | 53K | ||

compiled_exercises.pdf | 05-Feb-2019 14:26 | 45K | ||