MAT 535 Syllabus Algebra II Spring 2026

• January 27th
  Appendix II: Category Theory
  
• January 29th
  Section 10.4 Tensor Products of Modules
  
• February 3rd
  Section 10.5 Exact Sequences — Projective, Injective and Flat Modules
  
• February 5th
  Section 17.1 Introduction to Homological Algebra — Ext and Tor
  Problem Set 1 due in lecture.
  
• February 10th
  Section 17.1 continued
  
• February 12th
  Universal delta functors.
  Problem Set 2 due in lecture.
  
• February 17th
  Sections 12.2 — 12.3 Rational Normal Form; Jordan Normal Form
  
• February 19th
  Section 13.1 Basic Theory of Field Extensions
  Problem Set 3 due in lecture.
  
• February 24th
  Section 13.2 Algebraic Extensions
  
• February 26th
  MIDTERM 1 in lecture.
  
• March 3rd
  Section 13.4 Splitting Fields and Algebraic Closures
  
• March 5th
  Section 13.5 Separable and Inseparable Extensions
  Problem Set 4 due in lecture.
  
• March 10th
  Section 14.1 Galois Theory — Basic Definitions
  
• March 12th
  Section 14.2 The Fundamental Theorem of Galois Theory
  Problem Set 5 due in lecture.
  
• March 24th
  Section 14.4 Composite Fields
  
• March 26th
  Section 14.4 continued
  Problem Set 6 due in lecture.
  
• March 31st
  Section 13.6 Cyclotomic Polynomials and Extensions
  
• April 2nd
  Section 14.5 Cyclotomic Extensions and Abelian Extensions over Q
  Problem Set 7 due in lecture.
  
• April 7th
  Section 14.6 Galois Groups of Polynomials, and Section 13.1 Classical Straightedge and Compass Constructions
  
• April 9th
  MIDTERM 2 in lecture.
  
• April 14th
  Section 14.7 Solvable and Radical Extensions: Insolvability of the Quintic, and Section 14.8 Compuation of Galois Groups over Q
  
• April 16th
  Section 18.1 Linear Actions and Modules over Group Rings and Section 18.2 Wedderburn's Theorem and Some Consequences
  Problem Set 8 due in lecture.
  
• April 21st
  Section 18.3 Character Theory and the Orthogonality Relations
  
• April 23rd
  Section 19.1 Characters of Groups of Small Order and Section 19.2 Theorems of Burnside and Hall
  Problem Set 9 due in lecture.
  
• April 28th
  Section 19.3 Introduction to the Theory of Induced Characters
  
• April 30th
  Irreducible representations of the symmetric and alternating groups
  Problem Set 10 due in lecture.
  
• May 5th
  Schur Functors and Schur-Weyl Duality
  
• May 7th
  Final exam review (Final Exam is Monday, May 18th, from 11:15 am to 1:45 pm.)

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