Meets: MWF 9:00-9:50am in CR 141.
Instructor: Eric Moorhouse, Ross 63=216.
HW4 is due 5:00pm, Wed Dec 4 on WyoCourses. Our Exam is scheduled for 8-10am, Wed Dec 11 in our usual classroom CR 141.
Handouts/Links
- Students frequently ask me ...
- Students and Teachers Working Together (UW policy on the rights and responsibilities of students and teachers)
- UW Policy on Academic Honesty
- Syllabus / Policies
- Recordings from Lectures—pdf slides, video recordings, and computer sessions (if any)
- Instructional Videos
- Review: some basics on learning to read and write proofs
- Review of mathematical induction
- Review: some basics on numbers and polynomials
- Review of integers
- Review of linear algebra
- Review of cardinality of sets. If this is mysterious, you may want to start with a discussion of infinity in which we explain the practical necessity of distinguishing between countable and uncountable sets.
- Complex numbers
- Introduction to Fields
- HW1 due 5pm Fri Sept 27, 2024. Solutions. Average: 75/80
- HW2 due 5pm Mon Oct 21, 2024. Solutions. Average: 89/100
- Galois Theory. On first reading, you should ignore all mention of separability. The characteristic of a field was defined in our earlier handout Introduction to Fields (above). In characteristic zero (but also over finite fields), finite extensions are separable.
- In preparation for the Test on Mon Nov 4
- Practice Problems 1. (Do not read the solutions until after you have worked on the practice problems for yourself.)
- Sample Test. I have corrected #5(i) (note that Q[x] is a ring, not a field; so as originally stated, the problem did not make sense).
- Do not read the solutions to the Sample Test until after you have worked on the Sample Test for yourself. These solutions include a correction on #3.
- This handout includes a fuller discussion of finite extensions of fields (i.e. extensions of finite degree), including (Example 5) the discussion of straightedge and compass constructions.
- Test (Mon Nov 4) and solutions. Average: 81/100
- HW3 due 5pm Fri Nov 22, 2024 on WyoCourses. Solutions. Average: 63/75.
- HW4 due 5pm Wed Dec 4, 2024 on WyoCourses. Solutions. Average: 66/75.
- Sample Exam in preparation for the final exam. (Do not read the solutions until after you have worked through the sample exam for yourself.)
- Solutions to the exam. The exam itself will appear in WyoCourses
/ revised November, 2024