The course is over! Thanks to everyone for a great semester, and enjoy your summer.
- Prof. Graham Leuschke
- Time & Place
- MWF 9:30–10:25 in Carn 115
- Joseph A Gallian, Contemporary Abstract Algebra, 8th ed.
- Office Hours
- MW 11-12, TR 2-3; by appointment; and any time my door is open (317G Carnegie)
- Important documents
- The third midterm exam will be in class on Friday, April 25. It will cover Chapters 10 through 14 (up through ideals and factor rings).
- The second midterm exam was in class on Friday, March 28. It covered up through Chapter 9 (normal subgroups and factor groups).
- The first midterm exam was Friday, February 21, as in the syllabus. The exam covered up through Chapter 6 (Isomorphisms).
- Why all rings should have a 1, by Bjorn Poonen
- Solutions to some of the homework: hw03, hw04, hw05
- Keeler’s theorem and products of distinct transpositions: An episode of Futurama features a two-body mind-switching machine which will not work more than once on the same pair of bodies. After the Futurama community engages in a mind-switching spree, the question is asked, “Can the switching be undone so as to restore all minds to their original bodies?” Ken Keeler found an algorithm that undoes any mind-scrambling permutation with the aid of two “outsiders.” We refine Keeler’s result by providing a more efficient algorithm that uses the smallest possible number of switches.
- Permutations and the 15-puzzle from class on 3 Feb. Skip to Section 5 for the good stuff, then come back to Section 4 for the details.
- Group theory and Rubik’s Cube from class on 3 Feb. Skip to Section 3. There are about 519 quintillion conceivable configurations for the Rubik’s Cube, but only 1/12 of them are “valid”.
- MAT534-spring2014-hw01 posted 13 Jan 2014 (updated 14 Jan 2014; #4 was completely backwards)
- MAT534-spring2014-hw02 posted 17 Jan 2014
- MAT534-spring2014-hw03 posted 24 Jan 2014
- MAT534-spring2014-hw04 posted 3 Feb 2014
- MAT534-spring2014-hw05 posted 6 Feb 2014 (updated 7 Feb, replaced one problem with another)
- MAT534-spring2014-hw06 posted 18 Feb 2014 (Caution: typo on #4, should be mod 7)
- MAT534-spring2014-hw07 posted 26 Feb 2014
- MAT534-spring2014-hw08 posted 6 March 2014
- MAT534-spring2014-hw09 posted 21 March 2014, due Monday 31 March.
- MAT534-spring2014-hw10 posted 8 April 2014, due 7 April (oops)
- MAT534-spring2014-hw11 posted 8 April 2014, due 16 April
- MAT534-spring2014-hw12 posted 23 April 2014