Lecture Notes PDF

Date	Lecture	Topics
Wed 08/24	1	Integers in other bases
Fri 08/26	2	Digits in other bases, Fibonacci sequence
Mon 08/29	3	Prime numbers 1.2.1, unique factorization 1.1.20, Bezout
Wed 08/31	4	Bezout's formula via linear algebra
Fri 09/02	5	Linear equations
Mon 09/05	6	Gcd, lcm, unique factorization
Wed 09/07	7	Modular arithmetic 2.1 and 2.3.2, Solving diophantine equations using congruences
Fri 09/09	8	Divisibility criteria, Exponentiation 2.3.2
Mon 09/12	9	Invertible mod n 2.1.13, Chinese Remainder Theorem 2.2.2
Wed 09/14	10	Chinese Remainder Theorem 2.2.2, Explicit CRT 2.2.3
Fri 09/16	11	Euler function 2.2.1, Fermat's little theorem, Euler's theorem 2.1.2, exponentials with Euler and CRT
Mon 09/19	12	Multiplicative orders, fractions in base b, primitive roots mod p 2.5
Wed 09/21	13	Wilson's theorem and setup for the proof of the existence of primitive roots mod p
Fri 09/23	14	Counting primitive roots mod p
Mon 09/26	15	Quadratic residues, Legendre symbol
Wed 09/28	16	CRT example, solving monomial equations mod primes
Fri 09/30	17	Solving monomial equations mod primes and discrete logarithm
Mon 10/03	18	Square roots mod primes, Gauss' lemma	Mod 1601 Notes
Wed 10/05	19	Gauss' lemma, quadratic reciprocity
Fri 10/07	20	Applications of quadratic reciprocity
Mon 10/10	21	Valuations, factorials
Wed 10/12	22	Valuations of factorials and of binomial coefficients
Fri 10/14	23	Valuations of binomial coefficients, counting primes
Mon 10/24	24	Lucas' Theorem on binomials mod p
Wed 10/26	25	Asymptotics of integer functions and the Prime Number Theorem
Fri 10/28	26	Asymptotics of integer functions and the Prime Number Theorem
Mon 10/31	27	Lifting the exponent, Fibonacci
Wed 11/02	28	Primitive roots mod prime powers
Fri 11/04	29	Continued fractions intro
Mon 11/07	30	Continued fractions and Mobius transformations
Wed 11/09	31	Continued fractions convergence
Fri 11/11	32	Continued fractions and rational approximations
Mon 11/14	33	Continued fractions recognizing rationals
Wed 11/16	34	Continued fractions and quadratics
Fri 11/18	35	Hensel's Lemma
Mon 11/21	36	Hensel's Lemma examples
Mon 11/28	37	Hasse-Minkowski and rational points on conics
Wed 11/30	38	The Riemann zeta function
Fri 12/02	39	Dirichlet density and the Riemann zeta function, primes in arithmetic progressions	Proportion of integers that start with 1
Mon 12/05	40	Primality testing
Wed 12/07	41	Probabilistic models for primes

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