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  MATH 4321           END-SEMESTER INFORMATION SHEET            SPRING 2009
            _____________________________________________________
  
         FINAL EXAM will be in PKH 304, 2:00-4:30 pm on Tues May 12.
	   REVIEW will be in PKH 304, 4:00-5:00 pm on Mon May 11.
            _____________________________________________________
  
  
  * The sections covered on the test = all those covered in the homework
    assignments: http://www.uta.edu/math/vancliff/T/S09/hwk4321.html .
  
  * See above for the date/time of a review session.
  
  * When I write a test, I look over the lecture notes & homework for that 
    test, & previous tests, & use them to model at least 60% of the test 
    problems (& most of them are fair game).  You should expect an assortment 
    of different types of questions: a few asking for definitions or to state 
    a certain theorem, a few asking you to solve a homework question, & a few 
    asking you to solve a problem similar to one on the homework.
  
  * Thus, a good (& usually effective) way to review is to go over the 
    homework problems you have not already done & make sure you understand 
    all the homework well, by 24 hours prior to the test.  Also, go over 
    Tests 1-3 and the study questions for Test 2.  In the last 24 hours, 
    reread ALL the homework problems & skim through the lecture notes. 
  
  * Only calculators specified on the first-day handout will be permitted in 
    the test.  If you bring one, make sure the batteries are working. Also 
    bring some form of photo ID.
  
  * If you wish to leave the room during the test, you should ask permission 
    first & turn in your test to me. Only in exceptional circumstances will 
    I let you continue the test should you return. (So it is better to be 
    3 minutes late to the test, rather than ask to go to the bathroom during 
    the test.) If you finish early but prefer to stay in the room, then you 
    should NOT get out any work, book or item, no matter what the subject 
    matter is.  Should you wish to leave the test early, then you may.
    Try to keep your eyes on your own work during the test.
    It is your responsibility to be on time.
  
  * If you wish to know your grade early, turn in to me a STAMPED ADDRESSED 
    postcard (or a postcard inside a stamped addressed envelope) with the 
    following listed on the back (OR send me an e-mail that includes the 
    following):
    (a) Math 4321
    (b) Your full name written clearly
    (c) Your MAV ID number
    (d) Grade on Final =      
    (e) Grade in course =
    I will not know your course grade until Thurs May 14 at the earliest.

                                      OVER





                       SUMMARY OF COURSE MATERIAL


1. Rings, integral domains, domains, fields, division rings (= skew fields), 
   non-commutative examples.

2. Integral domains embed in field of quotients.

3. Polynomials, factoring, homomorphisms, factor rings, 
   1st isomorphism theorem, ideals (left, right, 2-sided), 
   prime/maximal ideals and related theorems.

4. Field F inside field E (including viewpoint of E = vector space over F), 
   algebraic/transcendental extensions, finite fields.

5. Automorphisms of fields, extension theorem, splitting fields,
   separable extensions (summary of results on pg 448 of book).

6. Topics in #5 for Galois theory = correspondence between field extensions 
   and groups of automorphisms.

7. Application of Galois Theory: insolvability of the quintic ( = deg-5 poly).


#6 + #7 = the punchline for the course.




 

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