Email: szchebol@ilstu.eduz (with the two "z"'s removed)
Office Hours: Open door and also by appointment
Class meeting time:
Tuesdays and Thursdays in STV 126
Text: Galois Theory (3rd Edition) by Ian Stewart.
Announcements:
Welcome to MAT 407! You first job is to get a physical copy of the text book either from an online bookstore or from a library. Make sure you get the
3rd edition. I heard that the earlier editions of this book are significantly different from the 3rd edition.
A soft copy is available below.
SAGE: This is the link to main Sage math website. It has everything you need to know about Sage: setting up an account, lots of useful
documentation, download instructions, videos, help etc.
Projects: I will collect here some ideas for inclass
projects. These will be
assigned to students on a first-come-first-serve basis.
Lagrange's method for solving polynomial equations of degree less than 5 which is based on some general
principle about the symmetric functions of the roots.
An in-depth analysis of cubic and quartic equations.
Gauss's work on the 17-gon
Hilbert's theorem 90.
Extra Credit Problems: There are no due dates for these problems. You can hand them in whenever you want.
3.16 (you may use Sage to find the answer here)
6.11
Homework
Nov 13 (due Nov 25th)
Read Chapter 15.
Nov 8 (due Nov. 13th)
Read Chapters 13 and 14
Oct 24 (due Nov. 6th)
Read Chapter 12.
Turn in problems 11.1, 11.6, and do parts (a) and (e) for 11.2, 11.3, and 11.4
Start working on your final projects.
Oct 15 (due Oct. 23rd)
Read Chapter 11
Work on the take-home midterm
Oct 4 (due Oct. 14th)
Do all problems. Turn in 9.1, 9.2, 9.6, and 9.7.
Read Chapter 10.
Sep 25 (due Oct. 2nd)
Prepare for your presentations (on Chapter 7) to given on October 7th.
Read Chapter 8 (Section 8.1 -- 8.6). Skip the rest of this chapter for now.
Turn in problems 8.1, 8.12 (parts a--d)
Turn in the proofs of the inclusions in (8.2).
Read Chapter 9.
Sep 18 (due Sep. 25th)
Complete reading all chapters up to 6.
Do all problems of Chapter 6 except 6.5, 6.11, 6.15, and 6.16.
Turn in the following problems: 6.1 (c),(d), 6.3, 6.6, 6.8, and 6.9
Sep 9 (due Sep. 18th)
Read Chapter 6.
Do all problems of Chapter 5.
TBA
Sep 2 (due Sep. 9th)
I made one mathematical mistake in my lecture today. Read your notes carefully and find it.
Try to fix that mistake if you can.
Read Chapter 5
Sage: Given a non-zero element in the field \(K = \mathbb{Q}(2^{1/3})\) find an explicit formula for its inverse.
Do the following problems: 4.2, 4.5 (this involves some basic facts about infinite cardinals), 4.10
Turn in the following problems: 4.3, 4.4, and 4.8
Aug 28 (due Sep. 2nd)
Read Chapter 4.
Sage: Input a polynomial \(f(x) \) in \(\mathbb{Z}[x]\) and get all primes \(p < 1000\) for which \(f(x) \mod p \) is irreducible. (What happens when you take \(f(x) = x^4+1? \))
Aug 27 (due Sep. 2nd)
3.1 a, 3.2 (find hcf for the polynomials in 3.1 (a)), 3.4 (use theory and then check your answers using sage), 3.5 a, 3.17 (give proper justification) [Turn these for grading]