Math 4010 Section 102 & 5530 Section 102 Homepage
News & Announcements
XX/XX Future use:
Transcendental Functions [Source: (.tex)]
12/06 Done! Grades are posted on AsULearn with final letter grades posted as a comment on final course averages.
Just because this class is over doesn't mean I hope help anymore. If you every have any questions mathematical
or otherwise, don't hesistate to ask. I'm happy to help if I can!
For the record:
(1) Corrine - Boolean algebras
(2) Halley - Unsolvability of General Polynomial
(3) Tanner - Sylow Theorems
(4) Dee - Origami Constructability
(5) Lindsey - Dedekind Fields and Valuations
11/22 Differential Algebra and Liouville's Theorem (.pdf) [Source: (.tex)]
Some differential Galois Theory (.pdf) [Source: (.tex)]
11/08 The Conjugate Trick: (.pdf) [Maple source: (.mw)]
11/01 An example of the Galois correspondence (.pdf) [Source: (.tex)]
10/30 A handout so I can skip some proofs: Characters (.pdf) [Source: (.tex)]
10/28 A handout for Monday's class (I'll bring copies)...
The Alternating Group (.pdf) [source (.tex)]
10/16 Homework #5 (.pdf) [Source: (.tex)] is due Wednesday, October 23rd.
10/04 Homework #4 (.pdf) [Source: (.tex)] is due Friday, October 11th.
09/27 Test review materials...
Rutgers Exams:
Exam #1 (.pdf) and Answer Key (.pdf)
Exam #2 (.pdf) and Answer Key (.pdf)
Most of Exam #1 looks like good review. Of course, some of the material is a little off topic.
Also, be aware that some definitions (e.g. gcd is slightly different) & notations (e.g. M(F)
for 2x2 matrices over F) may be a little different from ours. Exam #2 looks good as well.
Generally I would down-play problems about matrices and Exam #2 8(b) is outside the scope
of what we've done.
Math 4720 & 5210 (Abstract Algebra):
Test #2 (.pdf)
Final Exam (.pdf)
Test #2 is great stuff to look at. Although there's no answer key - but you can ask me.
Ignore stuff about fields of fractions. Final Exam: 1,2(a)-(f),3,4,5(a),6,9 are relevant.
Again, there's no key - but you can ask me. :-)
09/12 Homework #3 (.pdf) [Source: (.tex)] is due Wednesday, September 18th.
09/04 Homework #2 (.pdf) [Source: (.tex)] is due Wednesday, September 11th.
08/23 Homework #1 (.pdf) [Source: (.tex)] is due Wednesday, September 4th.
08/12 Now posted...
4010 and 5530 syllabi, tentative schedule, worthless homework page, and empty asULearn gradebook.
Handouts for a class coming soon!
Ring Definitions
Ring Examples
Factorization Theory (.pdf) [Source: (.tex)] and related Maple examples (.mw)
Chinese Remaindering (.pdf) [Source: (.tex)]
Partial Fraction Decompositions (.pdf)
For some questionable history about Galois: Stefanie (The Ballad of Galois).
Course Data
MAT 4010 Section 102 & MAT 5530 Section 102
Title: INTRO TO GALOIS THEORY
Meetings: MWF 11:00am-11:50am
Room: WA 308
Course Title & Description:
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MAT 4010-102 & 5530-102 "Introduction to Galois Theory" 3 credits
Prerequisite: MAT 3110
Title: "Introduction to Galois Theory"
Everyone knows how to solve the quadratic equation. Although much more
involved, there are also corresponding cubic and quartic equations.
However, it turns out that no such "quintic formula" exists! This was
first shown in the 1800's by Abel (and sort of by Ruffini in 1800). In the
1820's Galois developed a complete theory which explains exactly when a
polynomial equation is "solvable".
This course will include a review of basic group and ring theory. We will
cover some of the theory of vector spaces (linear algebra) and then study
field extensions. This will then allow us to show the impossibility of
obtaining certain compass-straightedge geometric constructions (eg.
trisecting angles, doubling cubes, squaring circles). Next, we will
develop the Galois correspondence relating field extensions to (Galois)
groups of automorphisms and then show the impossibility of solving certain
quintic equations.
If there is time, I also plan on sketching out some of "differential Galois
theory" and discuss solvability of differential equations.
Prerequisite details: MAT 3110. Although I will assume everyone has had an
introductory course in modern algebra and linear algebra, I will take time to
review necessary background material. I will assume that students are familiar
with the definition of a ring, but not that they know any ring theory.
Our main text will be "Galois Theory" (2nd edition) by Joseph Rotman
For more details about "What is Galois theory?" I recommend the wikipedia
article... https://en.wikipedia.org/wiki/Galois_theory ...or come talk to me!
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