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.
JKU S2046

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Jose Capco


Course Outline:

  1. On Rings and Groups
  2. Carmichael Numbers and Prime Recognition
  3. Wilson's Theorem and AKS Theorem
  4. AKS Theorem and AKS Algorithm
  5. Quadratic Extensions and Square Root mod p
  6. Sieving B-Smooth Numbers and Basic Quadratic Sieve
  7. Quadratic Sieves. Elliptic Curve Primer
  8. Algorithms on Elliptic Curve Group Structure
  9. Elliptic Curve Factorization Algorithm
  10. Valuation Theory
  11. Computing Heights
  12. Elliptic Curve Rank Conjectures and Elkies Curve
  13. Birch-Swinnerton-Dyer Conjecture


Course Requirement:

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).

[ICO]NameLast modifiedSizeDescription

[DIR]Parent Directory  -
[DIR]codes/23-Oct-2018 13:02 -
[   ]compiled_exercises.pdf05-Feb-2019 14:26 45K
[   ]lecture_01.pdf04-Feb-2019 11:27 53K
[   ]lecture_02.pdf23-Oct-2018 12:38 45K
[   ]lecture_03.pdf23-Oct-2018 12:37 44K
[   ]lecture_04.pdf23-Oct-2018 14:29 51K
[   ]lecture_05.pdf01-Nov-2018 17:41 55K
[   ]lecture_06.pdf07-Dec-2018 21:12 55K
[   ]lecture_07.pdf07-Jan-2019 08:28 55K
[   ]lecture_08.pdf24-Nov-2018 18:16 56K
[   ]lecture_09.pdf05-Feb-2019 15:09 67K
[   ]lecture_10.pdf10-Dec-2018 15:09 44K
[   ]lecture_11.pdf31-Dec-2018 15:18 50K
[   ]lecture_12.pdf20-Jan-2019 11:12 52K
[   ]lecture_13.pdf24-Jan-2019 13:09 52K
[   ]lecture_14.pdf24-Jan-2019 13:19 47K
[   ]lecture_15.pdf03-Feb-2019 13:48 64K