Math 371 schedule

Monday Wednesday Friday
August 25

No class
August 27

In Lecture:
  • Recap of the definition of a group
  • Basic examples
  • Subgroups, homomorphisms
  • The subgroup generated by a subset

Associated Reading:
  • Dummit and Foote: 1.1, 1.4, 1.6, 2.1, 2.4
  • Lang: 1.1 - 1.2

Video of class (downloadable)
August 29

In Lecture:
Associated Reading:
  • D-F: 1.2, 1.3, 1.6, 1.7, 2.1, 3.1, 3.2

Video of class (downloadable)
September 1

No class
September 3

In Lecture:
  • Isometry groups
  • the isometry group of R^n

Associated Reading:
Video of class (downloadable)
September 5

In Lecture:
  • The dihedral group and isometries of an n-gon
  • Group actions

Associated Reading:
Video of class (downloadable)
September 8

In Lecture:
  • Group actions, continued
  • Orbits and stabilizers

Associated Reading:
  • D-F: 1.2, 1.7, 1.3, 4.1, 4.2

Video of class (downloadable)
September 10

In Lecture:
  • Cycle decompositions of elements of a symmetric group
  • The orbit formula, and applications

Associated Reading:
  • D-F: 1.2, 1.7, 1.3, 4.1, 4.2, 4.3

Video of class (downloadable
September 12

In Lecture:
Associated Reading:
  • D-F: 1.2, 1.7, 1.3, 4.1, 4.2, 4.3

Video of class (downloadable)
September 15

In Lecture:
  • Automorphisms and Inner automorphisms
  • Kernels of group homomorphisms

Associated Reading:
  • D-F: 4.3, 3.3

Video of class (downloadable)
September 17

In Lecture:
  • The class equation and applications
  • Statement of Sylow's Theorem

Associated Reading:
  • D-F: 4.3, 4.5

Video of class (downloadable)
September 19

In Lecture:
  • Examples of the Sylow Theorem
  • Beginning of the proof of the Sylow Theorem

Associated Reading:
  • D-F: 4.3, 4.5

Video of class (downloadable)
September 22

In Lecture:
  • Completion of the proof that p-Sylow subgroups exist

Associated Reading:
  • D-F: 4.3, 4.5

Video of class (downloadable)
September 24

In Lecture:
Associated Reading:
  • D-F: 4.3, 4.5

Video of class (downloadable)
September 26

In Lecture:
  • Direct and Semidirect products

Associated Reading:
  • D-F: Chapter 5

Video of class (downloadable)
September 29

In Lecture:
  • Semidirect products, continued

Associated Reading:
  • D-F: Chapter 5

Video of class (downloadable)
Oct. 1

In Lecture:
  • Mid term exam
Oct. 3

In Lecture:
Associated Reading:
  • D-F: Chapter 5

Video of class (downloadable)
Oct. 6

In Lecture:
  • The fundamental theorem of finitely generated abelian groups
  • Start of ring theory

Associated Reading:
  • D-F: Chapters 5 and 7

Video of class (downloadable)
Oct. 8

In Lecture:
  • Ring theory, continued
  • Ideals

Associated Reading:
  • D-F: Chapter 7

Video of class (downloadable)
Oct. 10

No class - Fall Break!
Oct. 13

In Lecture:
  • Centers of rings
  • Quotient rings

Associated Reading:
  • D-F: Chapters 7 and 8

Video of class (downloadable)
Oct. 15

In Lecture:
  • Chinese remainder Theorem

Associated Reading:
  • D-F: Chapter 8

Video of class (downloadable)
Oct. 17

In Lecture:
Associated Reading:
  • Dummit and Foote, Chapter 7.4

Video of class (downloadable) - to be posted
Oct. 20

In Lecture:
  • Euclidean rings
  • Principal ideal domains

Associated Reading:
  • D-F: Chapters 7 and 8

Video of class (downloadable)
Oct. 22

In Lecture:
  • Principal ideal domains (continued)

Associated Reading:
  • D-F: Chapter 8

Video of class (downloadable)
Oct. 24

In Lecture:
  • Irreducible elements and prime elements

Associated Reading:
  • D.F: Chapter 8

Video of class (downloadable)
Oct. 27

In Lecture:
  • Unique factorization domains (UFD's)
  • Euclidean rings are Principal ideal domains, and Principal ideal domains are UFD's

Associated Reading:
  • D-F: Chapter 8.3

Video of class (downloadable)
Oct. 29

In Lecture:
  • End of the proof that PID's are UFD's
  • Beginning of module theory

Associated Reading:
  • D-F: Chapter 83
  • D-F.: Chapter 10.1, 10.2, 10.3

Video of class (downloadable)
Oct. 31

In Lecture:
Associated Reading:
  • D-F.: Chapter 10.1, 10.2, 10.3

Video of class (downloadable)
Nov. 3

In Lecture:
  • Fraction fields
  • Localization of modules

Associated Reading:
  • D-F: Chapter 10

Video of class (downloadable)
Nov. 5

In Lecture:
  • Beginning of classification of finitely generated modules over a PID

Associated Reading:
  • D-F: Chapter 12

Video of class (downloadable)
Nov. 7

No lecture, but see the video below:
  • Proof of the fundamental theorem about tinitely generated modules over a PID

Associated Reading:
  • D-F.: Chapter 12

Video of class (downloadable)
Nov. 3

In Lecture:
  • Fraction fields
  • Localization of modules

Associated Reading:
  • D-F: Chapter 10

Video of class (downloadable)
Nov. 5

In Lecture:
  • Beginning of classification of finitely generated modules over a PID

Associated Reading:
  • D-F: Chapter 12

Video of class (downloadable)
Nov. 7

No lecture, but see the video below:
  • Proof of the fundamental theorem about tinitely generated modules over a PID

Associated Reading:
  • D-F.: Chapter 12

Video of class (downloadable)
  • At 10:02 minutes into the video, I meant to define \phi(N) = R a_\phi, rather than \phi(T) = R a_\phi.
  • Similarly, at 13:36 in the video, I meant to say \nu(N) = R a_\nu, rather than \nu(T) = R a_\nu, and I should have said that y is an element of N rather than just that y is an element of T.
Nov. 10

In Lecture:
  • Rational canonical forms of matrices

Associated Reading:
  • D-F: Chapter 12.2

Video of class (downloadable)
Nov. 12

In Lecture:
  • Rational Canonical form, continued

Associated Reading:
  • D-F: Chapter 12.2, 12.3

Video of class (downloadable)
Nov. 14

In Lecture:
  • Jordan canonical form

Associated Reading:
  • D-F: Chapter 12.2, 12.3

Video of class (downloadable)
Nov. 17

In Lecture:
Associated Reading:
  • D-F: Chapter 12.3
  • D-F.: Chapters 13.1, 13.2

Video of class (downloadable)
Nov. 19

In Lecture:
  • Algebraic extensions
  • Irreducible polynomials of elements of a field which are algebraic over a subfield.

Associated Reading:
  • D-F: Chapter 13.1, 13.2

Video of class (downloadable)
Nov. 21

In Lecture:
  • Straightedge and compass constructions - summary of results
  • Splitting fields and algebraic closures
  • Separable extensions

Associated Reading:
  • D-F: Chapter 13.3, 13.4, 13.5

Video of class (downloadable)
Nov. 24

No class, but look at the video posted below about straightedge and compass constructions

Associated Reading:
  • D-F: Chapter 12.3

Video of class (downloadable)
Nov. 26

In Lecture:
  • Normal, separable and Galois extensions

Associated Reading:
  • D-F: Chapter 13.4, 13.5

Video of class (downloadable)
Nov. 28

No class - Thanksgiving Break!
Dec. 1

In Lecture:
  • Normal extensions
  • Algebraically closed fields and algebraic closures of fields
  • Separable extensions

Associated Reading:
  • D-F: Chapter 13.4, 13.5

Video of class (downloadable)
Dec. 3

In Lecture:
Associated Reading:
  • D-F: Chapter 14.1, 14.2

Video of class (downloadable)
Dec. 5

In Lecture:
  • A resume of Galois Theory

Associated Reading:
  • D.-F.: Chapter 14

Video of class (downloadable)
Dec. 8

In Lecture:
  • Finite fields
  • Finite subgroups of the multiplicative group of a field
  • Extensions of fields generated by roots of unity
  • Review of the course

Associated Reading:
  • D.F.: Chapter 14.3, 14.4, 14.5, 14.6
  • See the course schedule to review material since the mid-term.

Video of class (downloadable)
Dec. 10

No class
Dec. 12

No class

Last updated: 12/5/14
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