Math 446/546 SPRING 2016, List of lectures

  • On this page I will post content of all lectures. All handouts also will be posted here.
  • Monday, March 28: Cubic equation and Cardano‚Äôs formula. Section 7.2.
  • Wednesday, March 30: Properties of field extensions. Section 7.3. Please find your homework.
  • Friday, April 1: Extension by finitely many algebraic elements is finite (and hence algebraic). Section 7.3.
  • Monday, April 4: Splitting field of cubic polynomial and its automorphisms. Section 7.4.
  • Wednesday, April 6: Intermediate fields in the splitting field of cubic polynomial. Section 7.4. New homework.
  • Friday, April 8: Splitting fields of general polynomials. Section 7.5.
  • Monday, April 11: First look at Galois extensions. Section 7.5.
  • Wednesday, April 13: Splitting fields, abstractly. Sections 9.1-9.2. New homework.
  • Friday, April 15: The splitting field. Section 9.2.
  • Monday, April 18: Separable and inseparable extensions. Section 9.3. We will have MIDTERM on Friday!!! Please find practice problems!
  • Wednesday, April 20: Transitive subgroups of symmetric groups; splitting fields of separable polynomials are Galois extensions. Sections 5.5 and 9.4. Please find solutions for the practice problems. New homework.
  • Friday, April 22: MIDTERM. The solutions are here.
  • Monday, April 25: Degree of Galois extension and the order of Galois group. Section 9.4.
  • Wednesday, April 27: Primitive element theorem and applications. Section 9.5. There will be no homework for this week.
  • Friday, April 29: Galois correspondence. Section 9.5.
  • Monday, May 2: Symmetric polynomials and symmetric rational functions. Section 9.6.
  • Wednesday, May 4: Fundamental theorem of symmetric functions. Section 9.6. New homework.
  • Friday, May 6: Generic equation of degree n. Section 9.7.
  • Monday, May 9: Galois groups of quartic polynomials. Section 9.8
  • Wednesday, May 11: Galois groups of higher degree polynomials. Section 9.9. New homework.
  • Friday, May 13: Finite fields and Frobenius element. Reduction modulo p. Section 9.9. and Gallian, Section 22.
  • Monday, May 16: Chebotarev density theorem (statement). We will have MIDTERM on Friday!!! Please find practice problems!
  • Wednesday, May 18: Constructible numbers. Gallian, Section 23. Please find solutions for the practice problems. New homework.
  • Friday, May 20: MIDTERM. The solutions are here.
  • Monday, May 23: Solvable groups. Sections 10.1-10.2.
  • Wednesday, May 25: Alternating groups are simple (and hence non solvable). Section 10.3. Last homework.
  • Friday, May 27: Cyclotomic polynomials. Section 10.4.
  • Monday, May 30: Memorial Day.
  • Wednesday, June 1: Radical extensions and solvable Galois groups Sections 10.5-10.6. Please find practice problems for the final!
  • Friday, June 3: Solvable extensions are radical. Section 10.7. Please find solutions for the practice problems.
  • THE END.