# Math 350 Fall schedule

Monday Wednesday Friday
August 25

No Class!
August 27

In Lecture:

August 29

In Lecture:
• Induction on the positive integers, continued
• Well ordered sets and transfinite induction
• Countable sets

Sept. 1

No Class!
Sept. 3

In Lecture:
• Infinite descent, continued.
• Cardinality of sets
• Order types of ordered sets
• Cantor's diagonal argument showing the reals are not countable.

Sept. 5

In Lecture:
• Subsets of countable sets are countable
• The countable union of countable sets is countable
• Power sets and the general case of Cantor's Theorem.
• Cardinalities of increasing size

Sept. 8

In Lecture:
• Definition of ordinal numbers
• Statement of Von Neumann's theorem about the ordinal associated to a well ordered set

Sept. 10

In Lecture:
• Proof of Von Neumann's theorem about the ordinal associated to a well ordered set
• Multiplication of ordinals

Sept. 12

In Lecture:

Sept. 15

In Lecture:
• Divisibility and the division algorithm, gcd's
• Computational complexity and polynomial time problems

• Rosen, Sects. 3.3 , 3.4

Sept. 17

In Lecture:
• The Euclidean algorithm

• Rosen, Sects. 3.3, 3.4, 3.5

Sept. 19

In Lecture:
• Fibonacci numbers
• Lame's theorem on the complexity of the Euclidean algorithm

• Rosen, Sects. 3.3, 3.4, 3.5

Sept. 22

In Lecture:
• The extended Euclidean algorithm
• The fundamental theorem of arithmetic

• Rosen, Sects. 3.3 , 3.4

Sept. 24

In Lecture:

• Rosen, Sections 4.1, 4.2, 4.3

Sept. 26

In Lecture:
• Chinese Remainder Theorem
• Hensel's Lemma

Sept. 29

In Lecture:
• Hensel's Lemma (continued)

Oct. 1

In Lecture:
• Mid term exam
Oct. 3

In Lecture:

• Rosen, Sections 4.1, 4.2, 4.3, 4.4, 8.4

Oct. 6

In Lecture:
• The primes p for which -1 has a square root and the primes congruent to 1 mod 4
• Start of RSA cryptography

• Rosen, Sections 8.4

Oct. 8

In Lecture:
• Existence of primitive roots modulo a prime

• Rosen, Chapter 9

Oct. 10

In Lecture:
• No class - Fall Break!
Oct. 13

In Lecture:
• Integers n for which there is a primitive root mod n

• Rosen, Chapter 9

Oct. 15

In Lecture:
• discrete logarithms and applications

• Rosen, Chapter 9

Oct. 17

In Lecture:

• Rosen, Chapter 10

Oct. 20

In Lecture:
• The proof of quadratic reciprocity, continued

• Rosen, Chapter 10

Oct. 22

In Lecture:
• End of the proof of quadratic reciprocity

• Rosen, Chapter 10

Oct. 24

In Lecture:
• Algebraic numbers
• Transcendental numbers
• Liouville's Theorem

Oct. 27

In Lecture:
• Finite Continued fractions

• Rosen, Chapter 12.2

Oct. 29

In Lecture:
• Infinite continued fractions

• Rosen, Chapter 12.3

Oct. 31

In Lecture:

• Roseh, chapter 12.3

Nov. 3

In Lecture:
• Infinite continued fractions, contined

• Rosen, Chapter 12.3

Nov. 5

In Lecture:
• Periodic infinite continued fractions and quadratic numbers

• Rosen, Chapter 12.3

Nov. 7

No class: Skype sessions TBA
Nov. 10

In Lecture:
• Discrete Fourier Transform

Nov. 12

In Lecture:
• Fast Fourier transform
• Application to multiplication of integers

Nov. 14

In Lecture:
• Application of Fourier transforms to multiplication of integers, continued
• Application of Fourier transforms to factoring

Nov. 17

In Lecture:

Nov. 19

In Lecture:
• Start of probability theory

Nov. 21

In Lecture:
• Probability theory, continued

Nov. 24

No Lecture - Skype sessions with project groups TBA
Nov. 26

In Lecture:
• Probability theory, continued

Nov. 28

No class - Thanksgiving break!
Dec. 1

In Lecture:
• Error correcting codes

Dec. 3

In Lecture:
• Finite fields and polynomial rings over fields

Dec. 5

In Lecture:
• Finite multiplicative groups of fields are cyclic
• Constructing splitting fields of polynomials

Dec. 8

In Lecture:
• Simultaneous diophantine approximation
• Droste Music and Two-Note number theory

Dec. 10

No class
Dec. 12

No class

Last updated: 11/20/14