### MATH 421, ALGEBRA II

```Summer, 1995                   MATH 421
Prof. John Beachy            Information sheet

COURSE OBJECTIVES:
The student is expected to continue learning
basic results about groups, rings, and fields.
The concepts of homomorphism and quotient structure
(using an appropriate equivalence relation)
are of particular importance,
both for groups and for rings,
and will be used in particular to construct extension fields.
The course will end with a proof
that certain geometric constructions
(trisecting an angle, doubling the cube, and ``squaring the circle'')
are impossible using only a compass and straightedge.

These ideas represent developments in algebra since the early 1800's,
and although they go beyond what is taught in high school algebra,
they are important for prospective secondary teachers.
Work with rings and extension fields
is also an important prerequisite for studying algebra

COURSE PREREQUISITE:  Math 420

TEXT: Abstract Algebra with a Concrete Introduction,
by Beachy and Blair, Prentice Hall, 1990.

SYLLABUS:  Chapter Three, Groups, sections 3.6--3.8
Chapter Four, Polynomials, sections 4.1--4.4
Chapter Five, Rings, sections 5.1--5.3
Chapter Six, Fields, sections 6.1--6.3

REFERENCES:  Herstein: Abstract Algebra
Artin: Algebra
Fraleigh: A First Course in Abstract Algebra
Gallian: Contemporary Abstract Algebra
Hillman and Alexanderson

4 tests (400), and homework (100).
The second test will be a takehome test.

OFFICE HOURS:  Monday-Thursday, 9:30--10:30, or by appointment.
Watson 355, Phone: 753-6753

June, 1995             July, 1995             August, 1995
S  M Tu  W Th  F  S    S  M Tu  W Th  F  S    S  M Tu  W Th  F  S
1  2  3                      1          1  2  3  4  5
4  5  6  7  8  9 10    2  3  4  5  6  7  8    6  7  8  9 10 11 12
11 12 13 14 15 16 17    9 10 11 12 13 14 15   13 14 15 16 17 18 19
18 19 20 21 22 23 24   16 17 18 19 20 21 22   20 21 22 23 24 25 26
25 26 27 28 29 30      23 24 25 26 27 28 29   27 28 29 30 31
30 31

Classes begin: 6/19    Holiday: Tue, 7/4      Classes end: 8/10

LECTURES:
Monday         Tuesday        Wednesday      Thursday
Week of
6/19    Review         Review         3.6            3.6
6/26    3.7            3.7            3.7            3.8
7/3     3.8            Holiday        3.8            TEST I
7/10    4.1            4.2            4.3            4.4
7/17    5.1            5.1            5.2, TEST II   5.2
7/24    5.3            5.3            5.3            TEST III
7/31    6.1            6.1            6.2            6.2
8/7     6.2            6.3            6.3            TEST IV

ASSIGNMENTS:

6/26   p99 #20  p109 #5,14  p117 #7  p124 #4,8,14  p130 #9
6/28  p138 #1,5,6,7  p147 #1,3,4,5
7/5   p157 #6,7,9,12,13,16
7/12  p171 #13,14,16,17  p180 #1b,2c,7c,11
7/17  p180 #9  p186 #2f,2g,3a,6  p192 #9,10
7/27  p223 #17-20  p231 #6-9
8/8   p243 #1d,e,2,4  p247 #1b,c,2,5
```