(last revision 4/17/12 9:00 pm)

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  MATH 4321             INFORMATION SHEET FOR TEST FOUR           SPRING 2012


  * Test 4 will be in class on Thurs April 26. Test 4 will last 20 minutes.
  
  * The relevant sections for the test are 
              Sections 18-24, 26, 27, 29-31, 33, 48-50 inclusive. 
    The homework for that material is posted online at my website 
    https://vancliff.utasites.cloud/T/S12/hwk4321.html . 
  
  * My office hours are Tues and Thurs 4:00-4:50 pm. In addition, some class 
    time before the test starts will be available for asking me questions.  
    Ph: 817-272-3932, e-mail: vancliff@uta.edu .
  
  * You should learn definitions such as ring, subring, division ring, field,
    unit, zero divisor, integral domain, homomorphism, isomorphism, 
    characteristic, automorphism, field of quotients/fractions, (ir)reducible 
    polynomial, (left/right) ideal, factor ring, kernel, coset, maximal ideal, 
    prime ideal, prime field, linear (in)dependence, dimension/degree, basis, 
    algebraic/transcendental element/extension, finite extension, algebraic 
    closure, algebraically closed, (primitive) n'th root of unity. 
    
  * You should know the statement of any theorem with a title, such as the 
    first isomorphism theorem (pg 242) & the theorems summarized on page 248 
    (in the box) and how to use such a theorem (but not its proof).  You 
    should be ready to present examples like those occurring in the homework, 
    and to show that a certain subset of a ring is a subring or an ideal 
    (1-sided or 2-sided).  You should know examples of commutative rings, 
    noncommutative rings and elements with only a left inverse but not a 
    right inverse.  Moreover, any question in the homework is game for the 
    test, & so is any question occurring on Tests 1-3. 
    
  * As part of your study, I suggest you look over all the homework problems
    and your solutions to them, skim through the lecture notes, and look over 
    Tests 1-3 and their solutions; see  
    vancliff.utasites.cloud/T/S12/4321t1s.pdf   and 
    vancliff.utasites.cloud/T/S12/4321t2s.pdf   and
    vancliff.utasites.cloud/T/S12/4321t3s.pdf 
    for the solutions to Tests 1-3 (use password  math4321  to open the 
    files).   I also suggest looking through the table of contents in your 
    book, since that gives a brief summary of the material that we have 
    covered.

  * No calculators are allowed; no notes are allowed. Bring some form of 
    photo ID.
  
  * Try to keep your eyes on your own work during the test.
  
  * 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 nor item, no matter what the subject 
    matter is, without first checking with me.  Should you wish to leave 
    the test early, then you may.
  
  * It is your responsibility to be on time.
  
  * I plan to return the graded test to you on Tues May 1 with a solution 
    sheet.
  
  
For your mathematical edification, I recommend the link at my website to 
a 19-minute movie on abstract algebra!   See 
    https://vancliff.utasites.cloud/T/S12/#4321

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