Algebra Notes

• 6300 Lecture 1
• 6300 Lecture 2
• 6300 Lecture 3
• 6300 Lecture 4
• 6300 Lecture 5
• 6300 Lecture 6
• Handout on Burnside's Lemma/Pólya Enumeration
• Solution's to problems on Burnside's Lemma
• 6300 Lecture 7/8
• 6300 Lecture 9
• 6300 Lecture 10
• 6300 Lecture 11
• 6300 Lecture 12
• 6300 Lecture 13
• 6300 Lecture 14
• 6300 Lecture 15
• 6300 Lecture on Rings of Fractions
• 6300 Lecture on the Chinese Remainder Theorem
• 6300 Lecture on Euclidean Domains and Principal Ideal Domains
• 6300 Lecture on UFDs and Polynomial Rings
• 6300 Lecture on Polynomial Rings that are UFDs and Gauss' Lemma
• 6300 Lecture on Fields (13.1)
• 6300 Lecture on Algebraic Extensions
• 6300 Final Lecture (More on algebraic extensions, geometric constructions with straightedge and compass)
• 6301 Lecture on Splitting Fields and Finite Fields
• 6301 Lecture on Algebraic Closures and Separable Extensions
• 6301 Lecture on Cyclotomic Fields
• 6301 Lecture on Automorphism Groups and Fixed Fields
6301 Lecture on counting automorphisms, an exmaple of a cyclotomic field, and Galois groups of finite fields
• 6301 Extra examples before starting Fund. Theorem of Galois Theory
• 6301 Extra example full picture
• 6301 Lecture on characters and fixed fields
• 6301 Lecture on the Fundamental Theorem of Galois theory
• 6301 Lecture on Composite Extensions and Simple Extensions (Primitive Element Theorem)
• Notes on example of primitive elelment theorem and Fundamental Theorem of Algebra
• Lecture on cyclotomic extensions and their Galois groups, as well as their application to the constructibility of regular n-gons
• Lecture on Galois groups of polynomials
• Lecture on Galois groups over nice fields
• Supplemental notes with more details on separable extensions
• Supplemental notes on discriminants of polynomials
• Notes on basic module theory
• Notes on modules over PIDs
• Notes on modules over PIDs (cont.)
Notes on modules over PIDs: Uniqueness in the Fundamental Theorem and the Fundamental Theorem for abelian groups
• Notes on Rational Canonical Form
• Extra example of computing invariant factors
• Notes on Jordan Canonical Form
• Further applications of Jordan Canoncial Form
• Review of groups and rings
• Review of fields, Galois theory, and modules