This is where handouts and links will go, plus the list of project ideas that I’ll develop over the course of the term.
Materials to help you study
Quiz 1, Quiz 2, Quiz3 from earlier this semester
You asked for materials from previous years. Here are some quizzes (Quiz 1/sols, Quiz 2/sols, Quiz 3/sols) and the midterm. Caveat: the emphasis was different that time– more number theory and arithmetic, less group theory! (We hadn’t even covered normal subgroups yet by the time of the midterm.) Notation: o(a) means the order of a.
Book problems to try from chapter 3 for more practice include 3.1)9,16, 3.2)5,14, 3.3)6,10. Here are solutions to those problems and more.
Practice problems on Cayley graphs, cosets, quotient groups.
Quiz 4 and Quiz 5 from this semester, plus older Quiz 4/sols and the final exam.
Book problems to try from chapter 4 include 4.2)7,9,13,15,20, 4.3)6,9,14,24. Here are solutions. From chapter 5, try 5.1)19, 5.2)4,9,14,16, 5.3)7,8,13,25.
Practice problems for final exam. Overview of entire course.
Project
Signup form: here (Signup deadline Friday Nov 1.)
Project Ideas (non-coding)
- fundamental groups for genus 1,2,3
- normal forms
- factorization tests (sec 4.4 from the book)
- Heisenberg geometry
- what is a Baumslag-Solitar group?
- Rubik’s cube as a group problem
Project Ideas (coding)
- growth of groups
- Dehn’s algorithm
- asymptotic densities