• 4010 Syllabus and 5530 Syllabus
• Schedule
• Homework
• asULearn (Online gradebook, chatroom, etc.)

News & Announcements

05/09 Final presentations went well. Thanks to all!

      I posted final grades on AsULearn. Your letter grade can be found in a comment on 
      your final course average. Great job everybody! I hope you all enjoyed this course
      a tenth as much as I did! 
      
      If you ever need anything, don't hesitate to ask. I'm happy to help in any way I
      can. Also, if you still have one of my books -- give it back! Don't make me change
      your grade. :)
      
      [Note to self: UPDATE schedule to reflect what was covered when. Get a copy of 
       notes from Josh.]

05/03 Some differential Galois Theory (.pdf) [Source: (.tex)]

05/02 Differential Algebra and Liouville's Theorem (.pdf) [Source: (.tex)]

04/21 Test #2 (.pdf) [Source: (.tex)]

04/19 The Conjugate Trick: (.pdf) [Maple source: (.mw)]

04/01 A handout for Monday's class (I'll bring copies)...
      The Alternating Group (.pdf) [source (.tex)]

03/30 Homework Set #5 [Source: (.tex)] is due Wednesday, April 6th.

03/16 Homework Set #4 [Source: (.tex)] is due Wednesday, March 23rd.

02/24 Test #1 (.pdf) [Source: (.tex)]

02/17 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. :-)
      
      I'll try to dredge up my old Rutger's test review sheets...  

02/09 Homework Set #3 [Source: (.tex)] is due Wednesday, February 17th Friday.

      Chinese Remaindering (.pdf) [Source: (.tex)]

02/05 For some questionable history about Galois: Stefanie (The Ballad of Galois).

02/03 I just fixed the latest round of typos for Homework #2 and the Factorization Theory handout...Yay!

01/29 Factorization Theory (.pdf) [Source: (.tex)] and related Maple examples (.mw) 

      Homework Set #2 [Source: (.tex)] is due Friday, February 5th.

01/27 Partial Fractions in Euclidean Domains (.pdf) -- a paper written with former ASU student Tyler Bradley.

01/15 Homework Set #1 [Source: (.tex)] is due Friday, January 22nd.
      Please turn in problems 5,8,13,16, & 19 [see pages 12,16-17]

01/11 Ring Definitions
      Ring Examples

01/08 Both the 4010 and 5530 syllabi are posted along with a very very inaccurate 
      tentative schedule, worthless homework page, and empty asULearn gradebook.

10/09 Course Data
      MAT 4010 Section 101 & MAT 5530 Section 102 
      Title: GALOIS THEORY	
      Meetings: MWF 11:00am-11:50am
      Room: WA 105	
      
      Course Title & Description:
      -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
      MAT 4010-101 & 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 around 1800 by Abel (and independently by Ruffini). A few 
      decades later 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!
      -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-