Number Theory

Syllabus

Final Presentations:

Beamer slides due Wednesday, March 7 by midnight

Friday, March 9 from 1:50-3 pm (Miller-Rabin witnesses, AKS primality test)

Wednesday, March 14 from 3-5 pm (Quadratic Reciprocity, AES symmetric key cryptosystem, Elliptic curves and cryptography)

Details (adapted from a document by Professor Rana)

Topics and papers:

  • AES symmetric key cryptosystem (Landau) [MATH 545: Rings and Fields would be helpful]
  • Elliptic curves and cryptography (Koblitz)
  • Miller-Rabin witnesses (Conrad)
  • AKS primality test (Granville, original AKS paper)
  • Factoring algorithms (Bimpikis and Jaiswal) [MATH 545: Rings and Fields would be helpful]
  • Quadratic Reciprocity (Goldmakher, Cox [access Jstor with LU login])

Readings:

  • 6.5.1-6.5.2 [first edition] OR 7.5.1-7.5.2 [second edition] (for Friday, February 23)
  • 6.4 [first edition] OR 7.4 [second edition] (for Monday, February 19)
  • 6.3 [first edition] OR 7.3 [second edition] (for Friday, February 16)
  • 6.1-6.2 [first edition] OR 7.1-7.2 [second edition] (for Wednesday, February 14)
  • 3.10 (for Wednesday, February 7)
  • 3.9 (for Friday, February 2)
  • 3.5 (for Wednesday, January 31)
  • 3.3-3.4 (for Monday, January 29)
  • 3.1-3.2 (for Friday, January 26)
  • 2.6-2.7 (for Wednesday, January 24)
  • 2.3-2.5 (for Monday, January 22)
  • 2.1-2.2 (for Friday, January 19)
  • 1.6-1.7 (for Wednesday, January 17)
  • 1.4-1.5 (for Wednesday, January 10)
  • 1.3 (for Monday, January 8)
  • Sections 1.1-1.2 (for Friday, January 5)

Problem Sets:

  • PS7 (due in class on Friday, February 23)
  • PS6 (due in class on Friday, February 16)
  • PS5 (due by 2pm on Friday, February 9)
  • PS4 (due in class on Wednesday, January 31)
  • PS3 (due in class on Wednesday, January 24)
  • PS2 (due in class on Wednesday, January 17)
  • PS1 (due in class on Wednesday, January 10)

Sage:

Resources for LaTeX: