# 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