Math 100C - Schedule.
Approximate Lecture Schedule (Beachy and
Blair text)
It is IMPORTANT to read the material BEFORE
the lecture.
| Week |
ending
on |
Monday |
Wednesday |
Friday |
| 1 |
Apr 1
|
9.1 & 9.2
|
9.1 & 9.2
|
Vector Spaces
|
| 2 |
Apr 8
|
Vector Spaces
|
6.1
|
6.1
|
| 3 |
Apr 15
|
6.2
|
6.2
|
6.2
|
| 4 |
Apr 22
|
Review
|
Exam 1
|
6.3
|
| 5 |
Apr 29
|
6.3
|
6.3
|
6.3
|
| 6 |
May 6
|
6.4
|
6.4
|
6.4
|
| 7 |
May 13
|
6.5
|
6.5
|
6.5
|
| 8 |
May 20
|
Review
|
Exam 2
|
8.1
|
| 9 |
May 27
|
8.1
|
8.2
|
8.2
|
| 10 |
June 3
|
Holiday
|
Final Exam
|
8.3
|
11
|
June 10
|
|
|
|
Math 100C - Homework Assignments.
-
Homework assignments are due to your TA's box on the 6th floor
of AP&M at 5:00pm on Fridays. Late HW will not be accepted.
The homework assignments have to be
written up neatly on letter size paper. The pages have to be stapled
together.
Students are allowed
to discuss the homework among themselves, but are expected to turn in
their
own work — copying someone else's is not acceptable. Homework scores
will
contribute 20% to the final grade.
- Although you are required to turn in only
the HW problems listed below, you are strongly advised to attempt solving as many problems from each section as
possible.
HW 1, due on Friday, April 8.
Section 9.1: 11, 13, 14;
Section 9.2: 4, 8, 9. Read the proof of Theorem 9.2.8.
HW 2, due on
Friday, April 15.
Section 6.1: 2, 3, 8b, 9, 11, 12.
Section 9.2: 2.
HW 3, due on
Friday, April 22.
Section 6.2: 1e, 1f, 2c, 5, 6,
7, 9, 10, 11.
HW 4, due on Friday, April 29.
* Let K be a field and f, g be two
polynomials in K[X], such that
gcd(f,g)=1 and deg(f)=m and
deg(g)=n. Assume that max(m,n) > 0.
Prove that the field extension K(X)/K(f/g) is finite.
What is its degree ?
6.2: 2a), 3.
** Let p be a prime number and let
\zeta:=cos(2\pi/p) + i sin(2\pi/p)
be the usual primitive root of unity of order p.
Show that the extension
Q(\zeta)/Q is finite, of degree (p-1).
HW 5, due on
Friday, May 8.
Section
6.3: 1, 2, 3, 4.
HW 6, due on
Friday, May 15.
Section 6.4: 1c), 5, 6, 8, 9, 10, 12, 14, 15.
HW 7, due on
Wednesday, May 27.
Section 6.5: 4, 5, 7, 9, 10, 11.
Question (not to be turned in): Is it true
that if q is a power of a prime p, then every
generator of F_q as a field extension of F_p
must be a generator of the multiplicative group
F_q* ? Justify your answer.
HW 8, due on
Friday, May 29.
HW 9, due on
Friday, June 3.