Math 01 MATH 01524 1 Abstract Algebra I, Fall 2013
Dr Abdul Hassen, Robinson 229E, (856) 256-4500 Ext. 3888, hassen@rowan.edu
Office Hours: TR 11 - 12pm (you are also welcome to just email me questions that you have, make an appointment outside of office hours, or else stop by my office whenever I'm around).
Textbook: Abstract Algebra, David S. Dummit and Richard M. Foote
Course description: Topics will include the construction of number systems, theory of groups, rings, integral domains and fields. Other than on recommendation of the advisor, this course should not be chosen if a corresponding similar course has been part of the student's undergraduate study.
Objectives: Secondary school algebra is today marked by much greater attention to mathematical structure and proof. Instructional competence in algebra may thus be seriously handicapped by a lack of formal background in the content and concepts of modern algebra. It is the purpose of this course to provide opportunity to acquire this background. The course is, however, in general inappropriate for recent graduates.
Content: The following topics will be covered.
1. Introduction: Sets, relations, functions; Equivalence relations, partitions; Cardinal numbers; Integers
2. Groups: Definitions and examples; Basic group theorems; Cyclic groups; Subgroups, normal subgroups; Quotient groups; Homeomorphism, automorphism
3. Rings: Definitions and examples; Ring theorems; Homeomorphisms; Ideals; Euclidean rings; Polynomial rings; Integral domains; Ordered integral domains
4. Fields: Definition and examples; Extension fields; Polynomial fields; Rational and Real numbers; Finite fields; Splitting fields; Field Isomorphism; Galois theory
Grading policy: Grading is based on midterm (30%), final exam (40%) and homework assignments (30%)
Letter Grade: A(-) 85 - 100, B(-,+) 70 - 84, C(-,+) 60 - 69, D(-,+) 50 - 59, F < 49
Homework Policy: There will be three homework assignments (posted on the Backboard page of the course website). Each problem of the assignment requires proof. You will be expected to give a clear and logical reasoning of your work.
References: