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MATH 4321    INFORMATION SHEET FOR FINAL TEST    SPRING 2015

(scroll down to see a summary of the course material)

• The Final Test will be 5:30-8:00 pm on Tues May 12 in PKH 311; it is worth 38% of your course grade.

• The relevant sections for the Final Test are all the sections covered on the homework website throughout the semester.

• I will have an office hour in my office, PKH 462,

  • Sat May 9, 2:30-3:30 pm and

  • Tues May 12, 1:10-2:30 pm and

  • Tues May 12, 4:00-4:50 pm.

  Also, see my website for my usual office hours through Friday May 8 and the GTA's office hours through that date.

• As per the course information sheet, any student not obtaining a positive score on the Final Test for this class will not pass this class.

• 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, extension field, prime field, vector space, linear (in)dependence, dimension/degree, basis, algebraic/transcendental element/extension, finite extension, algebraic closure, algebraically closed, (primitive) n'th root of unity, normal extension, separable extension, perfect field, Galois field/group, etc. You should be ready to present examples like those occurring in the homework, and be able to show that a subset of a ring is a subring or a (left/right) ideal. You should know examples of commutative rings, noncommutative rings and elements with only a left inverse but not a right inverse (or vice versa). 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 know the Galois correspondence discussed in lecture on Tuesday April 28, and know how to go from the diagram of fields to the diagram of groups, and vice versa, as demonstrated in the examples on the handout of Tuesday April 28.

• Moreover, any question in the homework or from the Quiz or from Tests 1-3 is game for the test. Work through all previous tests from this class; see the homework website for the links. The ratio of old material (that tested already) to new material (that not tested yet) will likely be 70:30.

• No calculators are allowed; no notes are allowed; no phones, no tablets. You will need to put your belongings (including cell phones and tablets) by the side walls and possibly move seats in order to spread out in the room (if there are enough chairs & tables) - noncompliance will result in a score of 0 on the test.

• Bring some form of photo ID.

• It is your responsibility to be on time.

• 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.

• See below for a summary of the course material.