John Jones - MAT 543

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MAT 543

  • Final exams have been graded, and (unofficial) course grades are available through current grade below. I will not be posting solutions for the final, but you are welcome to come by and ask about the problems.
  • Current Grade. Enter the last 4 digits of your affiliate id:

  • Homework assignments
  • Extra programs to help with matrix operations in gp: matrixops.gp. Loading the file causes it to print a help message. In fact, the majority of the file itself is the help message. The programs let you do most row/column operations - enough to put a matrix in Smith normal form where you guide the process, but you don't have to do real nitty-gritty work. For example, once you have the gcd of the rest of the matrix in the (i,i) entry, you can use one command to clear out the rest of the ith row and the ith column.
  • To experiment with factoring a given polynomial modulo several primes $p$, there are a couple of programs below. You will need access to the algebra/number theory program gp, so you may need to install it. It should already be on mathpost. If you do need to install it, gp is free, and very good at computations.

    The extra files to load are

    • frobs.gp which contains gp programs for tabulating factorizations of a polynomial modulo several primes p. Try commands such as
      read("frobs.gp")
      read("auts.gp")
      seefrobs(x^5+x+1,10)
      frobs(x^5+x+1,1000)
      f=randpoly(9,20)
      frobs(f, 1000)
    • auts.gp which contains some gp programs we aren't using (yet), but also has lots of interesting polynomials in it. The polynomials a4 and v4 are irreducible over Q, but factor modulo p for every prime p.
  • Solutions for midterm.
  • Example of the permutation representation coming from $GL_2({\bf F}_2)$ acting on non-zero vectors. (pdf)
  • Sketch of the classification of actions of a group G on sets A. (pdf)
  • Solution for an unassigned homework problem on subgroup indecies. (pdf)
  • Description of projective space $ {\bf P}^n(F)$, especially the real projective plane $ {\bf P}^2({\bf R})$. (pdf)
  • Classifying groups of orders 6 and 8. (pdf)
  • Dates for test: October 26-27
  • Course syllabus (pdf)
Last Update: December 9, 2005