Math 649 SPRING 2018, List of lectures

  • On this page I will post content of all lectures with reference to the book. All handouts also will be posted here.
  • Monday, April 2: Constructions of representations. Section 22.1. Here is homework!
  • Wednesday, April 4: Wedderburn decomposition of group algebras. Section 22.2.
  • Friday, April 6: Characters. Section 22.3.
  • Monday, April 9: Character tables. Section 22.3.
  • Wednesday, April 11: Orthogonality relations for characters. Section 22.3. New homework!
  • Friday, April 13: Characters and algebraic numbers. Section 22.4.
  • Monday, April 16: Burnside theorem. Recollections on factorization in domains. Sections 22.4, 10.1.
  • Reading assignment: look at problems on representation theory in Chapter 25.
  • Wednesday, April 18: More on factorizations. Field extensions. Sections 10.2, 11.1. New homework!
  • Friday, April 20: More on field extensions. Galois group. Sections 11.2, 12.1.
  • Monday, April 23: Field of invariants under finite group action. Section 12.1.
  • Wednesday, April 25: Splitting fields and normal extensions. Sections 12.2-12.3. New homework!
  • Friday, April 27: Separable extensions. Section 12.4.
  • Monday, April 30: Fundamental Theorem of Galois Theory. Sections 12.5-12.6.
  • Wednesday, May 2: Discriminant, radical extensions, primitive element theorem, algebraic closure and absolute Galois group. Sections 13.1, 13.4, 14.1, 14.4. New homework (due on 05/16)!
  • Reading assignment: read Chapter 13.
  • Friday, May 4: Finite fields and cyclotomic fields. Sections 14.2-14.3.
  • Monday, May 7: Transcendence bases. Section 14.5. We will have MIDTERM on Friday!
  • Wednesday, May 9: Properties of transcendence degree. Symmetric functions. Sections 14.5-14.6.
  • Reading assignment: look at problems about fields in Chapter 15.
  • Friday, May 11: Midterm. Here are the solutions.
  • Monday, May 14: Prime ideals, multiplicative sets, localization. Sections 26.1-26.2.
  • Wednesday, May 16: More on localization. Integral ring extensions. Sections 26.2-26.3. New homework!
  • Friday, May 18: More on integral extensions. Sections 26.3-26.4.
  • Monday, May 21: Noether Normalization Lemma. Section 26.4.
  • Wednesday, May 23: Hilbert basis theorem. Primary ideals. Sections 27.1-27.2. New homework!
  • Friday, May 25: Primary decomposition of ideals. Section 27.2.
  • Reading assignment: look at problems on commutative algebra in Chapter 28.
  • Monday, May 28: Memorial Day, no classes
  • Wednesday, May 30: Nullstellensatz. Section 29.1.
  • Friday, June 1: Zariski topology. Section 29.2. Last homework!
  • Monday, June 4: Regular functions and regular maps. Category of algebraic sets is equivalent to (opposite) category of affine algebras. Sections 29.3-29.4.
  • Wednesday, June 6: Products of algebraic sets. Rational functions. Sections 29.5-29.6.
  • Friday, June 8: Sheaf of regular functions. Dimension. Sections 29.6-29.7.
  • Reading assignment: look at problems on algebraic geometry in Chapter 32.
  • Wednesday, June 13: FINAL EXAM. Here are solutions.
  • Please find here old qual problems with solutions: qual1, qual2.
  • THE END.