Math 350 Fall schedule

Monday Wednesday Friday
August 25

No Class!
August 27

In Lecture:
Associated Reading:
Video of class (downloadable)
August 29

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

Associated Reading:
Video of class (downloadable)
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.

Associated Reading:
Video of class (downloadable)
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

Associated Reading:
Video of class (downloadable)
Sept. 8

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

Associated Reading:
Video of class (downloadable)
Sept. 10

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

Associated Reading:
Video of class (downloadable)
Sept. 12

In Lecture:
Associated Reading:
Video of class (downloadable)
Sept. 15

In Lecture:
  • Comments about homework concerning ordinals
  • Divisibility and the division algorithm, gcd's
  • Computational complexity and polynomial time problems

Associated Reading:
  • Rosen, Sects. 3.3 , 3.4

Video of class (downloadable)
Sept. 17

In Lecture:
  • The Euclidean algorithm

Associated Reading:
  • Rosen, Sects. 3.3, 3.4, 3.5

Video of class (downloadable)
Sept. 19

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

Associated Reading:
  • Rosen, Sects. 3.3, 3.4, 3.5

Video of class (downloadable)
Sept. 22

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

Associated Reading:
  • Rosen, Sects. 3.3 , 3.4

Video of class (downloadable)
Sept. 24

In Lecture:
Associated Reading:
  • Rosen, Sections 4.1, 4.2, 4.3

Video of class (downloadable)
Sept. 26

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

Associated Reading:
Video of class (downloadable)
Sept. 29

In Lecture:
  • p-adic numbers
  • Hensel's Lemma (continued)

Associated Reading:
Video of class (downloadable)
Oct. 1

In Lecture:
  • Mid term exam
Oct. 3

In Lecture:
Associated Reading:
  • Rosen, Sections 4.1, 4.2, 4.3, 4.4, 8.4

Video of class (downloadable)
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

Associated Reading:
  • Rosen, Sections 8.4

Video of class (downloadable)
Oct. 8

In Lecture:
  • Existence of primitive roots modulo a prime

Associated Reading:
  • Rosen, Chapter 9

Video of class (downloadable)
Oct. 10

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

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

Associated Reading:
  • Rosen, Chapter 9

Video of class (downloadable)
Oct. 15

In Lecture:
  • discrete logarithms and applications
  • Quadratic residues and non-residues

Associated Reading:
  • Rosen, Chapter 9

Video of class (downloadable)
Oct. 17

In Lecture:
Associated Reading:
  • Rosen, Chapter 10

Video of class (downloadable)
Oct. 20

In Lecture:
  • The proof of quadratic reciprocity, continued

Associated Reading:
  • Rosen, Chapter 10

Video of class (downloadable)
Oct. 22

In Lecture:
  • End of the proof of quadratic reciprocity

Associated Reading:
  • Rosen, Chapter 10

Video of class (downloadable)
Oct. 24

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

Associated Reading:
Video of class (downloadable)
Oct. 27

In Lecture:
  • Finite Continued fractions

Associated Reading:
  • Rosen, Chapter 12.2

Video of class (downloadable)
Oct. 29

In Lecture:
  • Infinite continued fractions

Associated Reading:
  • Rosen, Chapter 12.3

Video of class (downloadable)
Oct. 31

In Lecture:
Associated Reading:
  • Roseh, chapter 12.3

Video of class (downloadable)
Nov. 3

In Lecture:
  • Infinite continued fractions, contined

Associated Reading:
  • Rosen, Chapter 12.3

Video of class (downloadable)
Nov. 5

In Lecture:
  • Periodic infinite continued fractions and quadratic numbers

Associated Reading:
  • Rosen, Chapter 12.3

Video of class (downloadable)
Nov. 7

No class: Skype sessions TBA
Nov. 10

In Lecture:
  • Discrete Fourier Transform

Associated Reading:
Video of class (downloadable)
Nov. 12

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

Associated Reading:
Video of class (downloadable)
Nov. 14

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

Associated Reading:
Video of class (downloadable)
Nov. 17

In Lecture:
Associated Reading:
Video of class (downloadable)
Nov. 19

In Lecture:
  • Start of probability theory

Associated Reading:
Video of class (downloadable)
Nov. 21

In Lecture:
  • Probability theory, continued

Associated Reading:
Video of class (downloadable)
Nov. 24

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

In Lecture:
  • Probability theory, continued

Associated Reading:
Video of class (downloadable)d
Nov. 28

No class - Thanksgiving break!
Dec. 1

In Lecture:
  • Error correcting codes

Associated Reading:
Video of class (downloadable)
Dec. 3

In Lecture:
  • Finite fields and polynomial rings over fields

Associated Reading:
Video of class (downloadable)
Dec. 5

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

Associated Reading:
Video of class (downloadable)
Dec. 8

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

Associated Reading (and listening):
Video of class (downloadable)
Dec. 10

No class
Dec. 12

No class

Last updated: 11/20/14
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