Math 503, METU, Fall semester, 2009
Added March 31, 2010: My own notes from the course
We meet Wednesdays, 8.40–11.30, in M-214. The main reference for the course is Thomas W. Hungerford, Algebra (New York: Springer, 1974).
The class of November 25 December 2
December 9 will consist
only of an examination, starting at 9.40 (an hour later than usual).
Exercises
I think it is worthwhile for every mathematician to be familiar with the axiomatic development of the natural numbers. An account by me of this development can be found in § 2.1 of my notes, “Non-standard Analysis”:
I suggest satisfying yourself that you can prove all of the unproved propositions in that section.
Please submit solutions to the following exercises in Hungerford's Algebra. Note that, in his exercises, Hungerford often writes a statement A when he really means, “Prove that A”; so you should prove it.
Write so that others can read. Use ordinary language, as published writers of mathematics do. For example, do not write “A ≟ B,” but say instead, “We want to show that A = B.” It is occasionally useful to write “A ⇒ B” instead of “If A, then B”; but one must note well that this by itself does not mean that A or B is true. Suppose you know, or have assumed, that A is true, and you have said so. If you can conclude that B is true, and you want to say so, then just say it: say, “Hence, B,” or “Therefore, B”; don't write “⇒ B.”
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- I.1: 2, 3, 9, 11, 12, 13, 15
- I.2: 2, 3, 11
- I.3: 1, 2, 5, 9, 10
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- I.4: 3, 5, 6, 7, 8, 13
- I.5: 1, 2, 6, 13(a), 19
- I.6: 8, 11
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- I.7: 5
- I.8: 1, 4, 7, 9, 13
- I.9: 3, 4, 6, 13
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- II.1: 8, 10
- II.2: 8, 9, 14, 15
- II.4: 3, 8, 9, 10, 13
- II.5: 2, 3, 11
