This course is an introduction to number theory and some of its applications:
o Mathematical induction, integer representations and operations.
o Primes and greates common divisors, Euclidean algorithm, Fundamental Theorem of Arithmetic,
linear Diophantine equations.
o Congruences and modular arithmetic, Fermat's and Euler's theorems, Wilson's theorem.
o Multiplicative functions such as Euler's phi function, Mobius function and Mobius inversion.
o Some applictions in cryptography, RSA, primitive roots, discrete logarithm and index arithmetic.
o Quadratic residues and Gauss's quadratic reciprocity.
Approximate schedule of the course:
Week of:
Aug. 29: 1.1, 1.2, 1.3
Sep. 5: 1.4, 1.5
Sep. 12: 2.1, 2.2, 2.3
Sep. 19: 3.1, 3.2, 3.3
Sep. 26: 3.4, 3.5, 3.7
Oct. 3: 4.1, 4.2
Oct. 10: 4.3, 6.1
Oct. 17: 6.3, 7.1
Oct. 24: 7.2, 7.3, 7.4
Oct. 31: 8.1, 8.3
Nov. 7: 9.1, 9.2
Nov. 14: 9.4, 11.1
Nov. 21: Thanksgiving
Nov. 28: 11.2
Dec. 5: Review