(864) 656-3434 (Dept)

** Email: ** kevja@clemson.edu

** Web: **
http://www.ces.clemson.edu/~kevja/

### Office Hours

Office hours are by appointment. Please email me to set up an appointment
or simply drop by my office.

### Required Text

``Abstract Algebra An Intorduction'', 2nd ed. by Thomas W Hungerford

### Goals and Objectives.

To introduce students to topics and techniques from modern algebra.
In particular we will cover material from the theory of groups rings
and fields.

### Course Contents.

We will cover parts of Chapters 1-7, 9, 11 of the text, with most sections
indicated ``optional'' omitted. Time permitting, we will cover other
sections of interest.

### Learning Outcomes

Upon successful completion of this course, a student will be able to:
- Employ the well-ordering principle to write a proof.
- Employ the principle of mathematical induction to write a proof.
- Be able to prove basic properties of the integers from the basic
axioms.
- Apply the Euclidean algorithm to compute the greatest
common divisor of two integers and
write it as an integral linear combination of the given numbers.
- Understand modular arithmetic.
- Be able to perform basic computations (addition, subtraction,
multiplication, inversion and division) in modular arithmetic.
- Deduce elementary properties of rings from the
defining axioms.
- Be able to perform basic arithmetic operations with polynominals.
- Understand congruence in polynomial rings.
- Understand irreducibility of polynomials.
- Understand arithmetic in polynomial quotient rings.
- Be able to perform basic computations (addition, subtraction,
multiplication, inversion and division) in polynomial quotent rings.
- Be able to detect reducibility of polynomials over polynomial
quotent rings.
- Construct and identify ring homomorphisms
- Define subrings and ideals of a ring and list their elements.
- Understand the general quotient ring constrution.
- Be able to perfrom basic arithmetic operations in quotient rings.
- Understand the concept of homomorphism of rings.
- Be able to check if a given ring map is a homomorphism.
- Understand the fundamental theorem of ring homomorphisms.
- Understand basic group theory.
- Be able to deduce elementary properties of groups from the
defining axioms.
- Understand the construction of quotient groups.
- Calculate the order of a group element and its powers.
- Define subgroups and normal subgroups of a group and list
their elements.
- Understand the concept of group homomorphisms.
- Be able to check if a given map of groups is a homomorpjhism.
- Construct and identify group homomorphisms.
- Understand quotient groups and the fundamental theorem of
group homomorphisms.
- Give particular examples and explain the properties of abstract
objects, such as groups, rings, and fields

### Time Requirements.

Please be sure to devote at least six hours per week outside of class
to this course. This will include reading the text as well as working
homework problems.

### Grading Policies

The grading in this class will be as follows:

- 3 In-class Exams 45%
- Homework and Quizes 30%
- Cumulative Final Exam 25%

All exams will be cumulative. Click here for
a schedule of examination times.
The following grading scale will be used:

A |
90-100 |
B |
80-89 |
C |
70-79 |
D |
60-69 |
F |
0-59 |

All grading will be on the basis of your work shown and not on the
answer alone.

### Make-up Policy

Absolutely ** NO ** late homework will be accepted and there will
be
**No** make-ups for missed quizes or exams. In the event, that a
student
misses an exam due to a documented excused absence, that student's
final exam
score will be substituted for the missing exam score. Any student who
misses
an exam and cannot provide documentation indicating that the absence
was excused will recieve a 0 for the exam.

### Attendance Policy.

Regular and punctual attendance is expected. If the instructor is not
present 25 minutes after class is scheduled to begin then you may leave.

### Academic Integrity

As members of the Clemson University community, we have inherited
Thomas Green Clemson's vision of this institution as a high seminary
of learning. Fundamental to this vision is a mutual commitment to
truthfulness, honor, and responsibility, without which we cannot earn
the trust and respect of others. Furthermore, we recognize that
academic dishonesty detracts from the value of a Clemson degree.
Therefore, we shall not tolerate lying, cheating, or stealing in any
form.

### Disability Access

It is University policy to provide, on a flexible and individualized basis,
reasonable accommodations to students who have disabilities. Students are
encouraged to contact Student Disability Services to discuss their
individual needs for accommodation.