Syllabus


Lectures Sections in Text Brief Description
9/11 1.1, 1.2 Introduction, Division and Euclidean Algorithms
9/13 1.2, 1.3 Bezout's identity, least common multiples
9/15 1.3, 1.4 LCMs, Linear Diophantine Equations
9/18 2.1, 2.2 Fundamental Theorem of Arithmetic, Distribution of primes
9/20 2.2, 2.4 Distribution of primes, primality testing
9/22 3.1 Modular arithmetic
9/25 3.2 Linear Congruences
9/27 3.3, 3.4 Chinese remainer theorem
9/29 3.4, 4.1 Polynomials and polynomial congruences
10/2 4.1 The Arithmetic of ${\mathbb Z}_p$
10/3
(x-hour)
4.2 Pseudoprimes and Carmichael Numbers
10/4 Midterm I In class part; all material through $\S3.4$; takehome part due 10/6
10/6 class notes Strong pseudprimes and Miller's test
10/9 5.1, 8.1 Euler's function
10/11 5.2, class notes Multiplicative functions; Euler's function, General remarks about
cryptography and public key cryptosystems, signatures, authentication
10/13 class notes Cryptography review, RSA
10/16 6.1, 6.2 $U_n$ and primitive roots
10/18 6.3-6.5 Primitive roots for composite moduli, indices
10/20 6.6+supplement, 7.1 Indices, applications of primitive roots, discrete logs, quadratic residues
10/23 7.1, 7.2 Quadratic residues
10/24
(xhour)
7.3 The Legendre symbol and properties
10/25 Midterm II In class part; all material through $\S6.6$; takehome part due 10/27
10/27 7.3 Gauss's Lemma
10/30 7.4 Quadratic Reciproicity
11/1 7.4 Road Trip (Connections)
11/3 7.4, 8.2, 8.3 Mersenne numbers, Pepins' test, Perfect numbers, Dirichlet convolution
11/6 8.2-8.6 Mobius inversion; Dirichlet convolution
11/8 8.6, class notes Congruent Numbers, Pythagorean Triples, Rational Points on the unit circle
11/10 Chapter 11.5, class notes Congruent Numbers, Pythagorean Triples, Rational Points on the unit circle
11/13 Class notes Congruent Numbers, Pythagorean Triples, Rational Points on the unit circle
11/17 Final Exam 8-11am, 007 Kemeny


T. R. Shemanske
Last updated November 05, 2017