Algorithmic Number Theory
WS2018 Special Topic Lecture in : Algorithmic Number Theory
Time and Place:
Every Mon. 16:15-18:00 (starts Oct. 1, 2018)
Note: We can adjust the regular schedule in the first meeting, depending on the needs of the registered students.
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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
Elementary Number Theory. Basic understanding of fields, rings and groups.
Open to all students with mathematical background (including computer science students).
Note: First part of the course will have more algorithms than the second part.
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).