Wednesday & Friday May 7 & 9
Wednesday:
Subrings of the complex numbers.
Irreducible vs. prime.
In {a + b sqrt(-5)}, 2 is irreducible but not prime.
Prime => irreducible.
Friday:
In Z, irreducible => prime.
Unique factorization.
We did unique factorization by weak induction on the number of primes being multiplied together; maybe it would have been more intuitive to do it by strong induction on n. (We found two factorizations of n/pk, and could have said "since n/pk < n, by induction we know that...")
Subrings of the complex numbers.
Irreducible vs. prime.
In {a + b sqrt(-5)}, 2 is irreducible but not prime.
Prime => irreducible.
Friday:
In Z, irreducible => prime.
Unique factorization.
We did unique factorization by weak induction on the number of primes being multiplied together; maybe it would have been more intuitive to do it by strong induction on n. (We found two factorizations of n/pk, and could have said "since n/pk < n, by induction we know that...")
posted by Allen Knutson @ 2:12 PM
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