Monthly Archives: October 2008

Office Hour

I had initially announced my intention to hold office hour (Fridays, 3-4) in the 5th floor common room. But because demand isn’t very high these days, I’m changing locations back to my office in KLB. Remember to look at the directions on my webpage.

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Gauss’ Lemma

In the online lecture notes on page 10, number 25 [now Lecture 4, Example 29] uses Gauss’ Lemma for a polynomial of degree 4, however the corallary of Gauss’s Lemma states that the polynomial must be of degree 2 or 3. Would you please explain why we were able to use it in this case.

Reply:

Thanks very much for your question. I see now that the notes were rather misleading in that regard. I’ve rewritten Lecture 1 now with your question in mind. In particular, look at the `refined’ Gauss’ Lemma and its corollaries.

Unique factorization

After receiving many questions from students, I recalled that I was myself quite unhappy with the proof that I presented of the unique factorization theorem as well as the theorem on infinitude of primes. As a general principle, it’s good to avoid proofs by contradiction. In fact, in my own research papers, I don’t think I’ve ever given a proof by contradiction.

In Monday’s lecture, I’ll present a more straightforward proof by induction of both theorems.