Math 406 Syllabus, Fall 2018

Month	Date	Topic	Sections
August	27	Introduction: course overview / Divisibility	1
	29	The division algorithm / The gcd / the Euclidean algorithm	2.5-2.7
	31	The extended Euclidean algorithm / Other bases	2.7-2.8
September	5	Other bases / The extended Euclidean algorithm / Fermat & Mersenne Primes	2.7-2.9
	7	Fermat & Mersenne Primes / Review / Theorem 3.1	3.1-3.2
	10	Theorem 3.1	3.1-3.2
	12	The exact change problem / postage stamp problem	3.2
	14	Fundamental Theorem of Arithmetic	4.1-4.2
	17	Rational Root Theorem (with proof) / Pythagorean triples (no proof)	5.1-5.4
	21	Riemann zeta function	5.7
	24	Divergence of the sum of reciprocals of primes	5.7.1
	26	Congruences - definitions and basic properties	6.1
	28	Quizterm 1
October	1	Modular exponentiation / divisibility tests / Linear congruences	6.2-6.4
	3	Linear congruences	6.4
	5	The Chinese remainder theorem	6.5
	8	Simple ciphers	7.2-7.4
	10	Stream and block ciphers	7.5-7.6
	12	Review	Ch. 2-6
	15	Quizterm 2
	17	Modular polynomials information sharing / Fermat's little theorem	7.7, 8.1
	19	Euler's theorem	8.2
	22	Euler's theorem / Euler's phi function	8.2
	24	Euler's phi function / RSA	8.4, 9.1
	26	RSA / digital signatures	9.1-9.2
	29	Order / application to Fermat numbers / Primitive roots	11.1-11.2
	31	Primitive roots / Decimal criterion for rationality	11.2-11.3
November	2	Quizterm 3
	5	The discrete log problem / Diffie-Helman / ElGamal	11.5, 12.1, 12.4
	7	Squares mod p	13.1
	9	Squares mod p / Statement of Quadratic Reciprocity / Primality testing and Carmichael numbers	13.1, 14.2
	12	Statement of Minkowski's theorem / volume computations	15.1
	14	Fermat's theorem on sums of squares	15.2
	16	Conclusion of the proof of Minkowski's theorem	15.1
	19	Quizterm 4
	26	Elliptic curves mod p
	28	Elliptic curve addition law
	30	Elliptic curve addition law, discrete log problem, Diffie-Helman, ElGamal
December	3	Quizterm 5
	5	Associativity of the group law
	7	Review - part 1
	10	Review - part 2
	17	Final exam