MAT 215Problem Set 4Notes
Rudin #2
Let F be a field. Let f (z) be a polynomial in z of degree n with coefficients
in F . This means f (z) = an z n + an1 z n1 + + a1 z + a0 , with ai F for
all i and with an 6= 0. Compare these two theorems.
Theorem 1. f (z
MAT 215Problem Set 3
Due Thursday, Oct. 6, 2016
Reading
Rudin, 1.201.38.
Problems
1
The following theorem gives an important property of N, described by saying N
is well ordered.
Theorem. Let S be a non-empty subset of N. Then S has a least element;
that
MAT 215Problem Set 4
Due Thursday, Oct. 13, 2016
Reading
Rudin, 2.12.14. Review 1.241.38.
Problems from Rudin
pp. 2223: 8, 9, 12, 15.
p. 43: 2, 3, 4.
Other Problems
Problems 1 and 2 are for 2.22.3. If f : A B and C A, we define f (C),
the image of C under
MAT 215Problem Set 2
Due Thursday, Sept. 29, 2016
Reading
Rudin, pp. 18.
Problems
Problems from Rudin
pp. 2122: 1, 2, 31 , 4, 5.
Other Problems
1
In this problem, x and y are real numbers. Here are six statements.
(a) (x)(y) x < y < x + 1.
(b1 ) (x)(y) x
MAT 215Problem Set 5
Due Thursday, Oct. 20, 2016
Reading
Rudin, 2.152.30.
Problems from Rudin
pp. 4344: 5, 6, 7, 9, 10 (omit the part about compactness).
Other Problems
1
This problem will prove that every non-empty open set in R is a disjoint union
of co