# MTHSC 412 Syllabus Fall Semester 2012

Time: 11:15 - 12:05; M,W,F.
Location: M103 Martin Hall.
Instructor: Kevin James
Office: O-21 Martin Hall
Phone:
• (864) 656-6766 (office)
• (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.

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.