Professor:
Dr. Janet Vassilev
Office: SMLC 324
Office
Hours: MWF 23 pm and by appointment.
Telephone: (505)
2772214
email: jvassil@math.unm.edu
webpage: http://www.math.unm.edu/~jvassil
Date

Section

Topic

Homework

1/19

23

Review of factoring polynomials^{} 

1/21

23

Factoring
polynomials

Quiz 2: What is an irreducible polynomial in F[x]?

1/24

27

Ideals in F[x]

Quiz 3: What is the content of a polynomial f(x) in
Q[x]?

1/26

27, 26

Unique
Factorization and Factor Rings

Homework
1: Section 23: 3, 9, 12, 21, 27, 28;
Section 27: 5, 8, 32
Quiz 4: Is 4x^2+12x+15 in Z[x] irreducible?

1/28

29

Extension
Fields

Quiz 5: What is
the property of ideals that is important in making R/I a ring when R is a
ring and I is an ideal?

1/31

29

Extension
Fields

Quiz 6: What is
an extension field of a field K?

2/2



Class canceled
due to snow closure

2/4


_{ } 
Class canceled
due to natural gas closure

2/7

30

Vector Spaces

Quiz 7: Give an
example of an algebraic extension of Q.

2/9

31

Algebraic
Extensions

Homework 2:
Section 29: 4, 8, 10, 14, 23, 25, 30, 31, 33; Section 30: 4, 9, 15
Quiz 8: Is a
spanning set of a vector space necessarily linearly independent?

2/11

31

Algebraic
Extensions

Quiz 9: Is a
finite field extension always algebraic?

2/14

31

Zorn’s Lemma
and Algebraic Closure

Quiz 10: If E is
an algebraic extension, what is \overline{F}_{E}?

2/16

33

Finite Fields

Homework 3:
Section 31: 4, 10, 19, 23, 27, 29, 30, 32, 36

2/18

33

Finite Fields

Quiz 11: If [E:F]=n and F
has q elements, how many elements does E have?

2/21

34

Isomorphism
Theorems

Quiz 12: F_{p^n} is contstructed
inside what field?

2/23

35

Series of
Groups

Quiz 13: State
the 2^{nd} Isomorphism Theorem.

2/25


Review

Quiz 14: Is {e}
< {e,f_1} <S_3 a subnormal series?

2/28


Midterm 1


3/2

35

Series of
groups

Homework 4:
Section 33: 2,8,9,12; Section 34: 4, 9; Section 35
4,5

3/4

35

Series of
groups

Quiz 16: Give
isomorphic refinements of the normal series (0) < (5) <Z_20 and (0)<(4)<(2)<Z_20.

3/7

35

Sylow Theorems

Quiz 17: Give
an example of a composition series.

3/9

36

Sylow Theorems

Homework 5:
Section 35: 8, 12, 13, 17, 18, 28, 29; Section 36: 2, 4, 6, 10, 12, 13, 16
Quiz 18: In a group
of order 18, what is the size of the Sylow
3subgroup?

3/11

36

Sylow Theorems

Quiz 19: In a
group of order 50, what does the First Sylow
Theorem tell you about the orders of some of the subgroups?

3/21

37

Sylow Theorems

Quiz 20: What are the possible number of Sylow
5subgroups in a group of order 20?

3/23

39

Free Groups

Homework 6:
Section 37: 3, 4, 6, 7; Section 39 1, 2, 4, 10
Quiz 21: Is a
group of order 21 necessarily abelian?

3/25

39

Free groups

Quiz 22: Is
there a homomorphism f from F[{x,y}]
to Z_6 with f(x)=2 and f(y)=3?

3/28

40, 48

Group
Presentations, Automorphisms of Fields

Quiz 23: If N
is a normal subgroup in G and H_i form a
composition series for G, what is a composition series for G/N?

3/30


Review

Homework 7:
Section 40 1, 2, 4, 8, 13
Quiz 24:

4/1


Midterm 2


4/4

48

Automorphisms of Fields


4/6

48

Automorphisms of Fields

Homework 8: Section
48 4, 8, 10, 12, 20, 29, 34, 36, 37
Quiz 26: What
is the fixed field of \sigma mapping Q(\sqrt{26}) to itself via \sigma(\sqrt{26})=\sqrt{26}?

4/8

49

Isomorphism
Extension Theorem

Quiz 27:

4/11

49

Isomorphism
Extension Theorem

Quiz 28: What
is the partially ordered set that we used in proving the Isomorphism
extension theorem?

4/13

50

Splitting
Fields

Homework 9:
Section 49: 2, 4, 6, 8, 9, 11, 12, 13
Quiz 29: What
is the splitting field of x^px over Z_p?

4/15

50

Splitting
Fields

Quiz 30: Does
x^230 split over Q(\sqrt{2},
\sqrt{3}, \sqrt{5})

4/18

51

Separable
Extensions

Quiz 31: Tell
me something special about Z_p(y) and Z_p(y^p)

4/20

51

Separable
Extensions

Homework 10: Section 50: 2, 4, 10, 14, 15, 18, 20, 24;
Section 51 8, 9, 11, 15, 17, 18
Quiz 32: Is a
field with 32 elements perfect?

4/22

52

Totally
Inseparable Extensions

Quiz 33: What
is the primitive element theorem?

4/25

53

Galois Theory

Quiz 34: Give
an example of a normal field extension.

4/27

53

Galois Theory

Homework 11:
Section 52: 1, 2, 5, 7; Section 53 2, 8, 14, 15, 16, 17, 19, 23

4/29

56

Insolvability
of the Quintic


5/2


Review


5/4


Review


5/6


Review


5/13


Final exam

