Markus Schmidmeier
Mathematical Sciences
Florida Atlantic UniversityWelcome to my Algebra class! We meet MWF 3:00 - 3:50 p.m. in BU 112. Graduate students, this course has course number MAS 5311, Intro Abstract Algebra I. Undergraduate students can take this course as MAT 4906-004, Directed Independent Study, with permission from the instructor. Introductory Abstract Algebra I
Prerequisites
A solid background in the following two courses will be required: MAS 4301, Modern Algebra, and MAS 4107, Linear Algebra 2. It is possible to take MAS 4107 in parallel to this course.
Textbook
I. N. Herstein, Topics in Algebra, 2nd edition, Wiley 1975, ISBN 0-471-01090-1.
Topics
There is so much time and opportunity to become abstract. Why rush it at the beginning? In this introduction we will focus on two algebraic structures, groups and rings. In each case we will start with generalities about the particular structure and then proceed to a detailed study of key examples.
We introduce groups and homomorphisms between them, and study groups defined by homomorphisms. Famous are the Sylow theorems which often deliver enough structural insight to recognize a given finite group as a known one. (Herstein, Chapter 2)
In the case of rings, homomorphisms define subrings and ideals, and conditions on ideals in turn characterize classes of rings. You are already familiar with the ring of integers; in this course we will meet further rings, in particular polynomial rings, whose elements and ideals have similar factorization properties. (Herstein, Chapter 3)
In a follow-up to this course, Introductory Abstract Algebra II, I plan to cover vector spaces and fields. (Herstein, Chapters 4 and 5, with selected topics from Chapters 6 and 7)
Credit
Homework: There will be 10 homework assignments, together they count for 40% of the grade.
Midterm Exam: The midterm exam on Monday, October 9, will count for 20% of the grade.
Final Exam: The final exam on December 4, 1:15 - 3:45 p.m., is comprehensive and counts for 40% of the grade.
Contact Me
Office hours: MWF, 11-12 a.m. in SE 230, or after class
Course Web Page: http://www.math.fau.edu/schmidme/iaa06.html
E-mail: markus@math.fau.edu.
Last modified: by Markus Schmidmeier