Markus Schmidmeier • Mathematical Sciences • Florida Atlantic University
Welcome to my course! We meet Wednesday and Friday, 2:00 - 3:20 p.m. in ED 125. I will be absent for a conference on September 26 and 28. To make up for lost class time, we will meet for an extra 30 minutes on September 19, 21, and October 3, 5, 10 (on those days we meet 2:00 to 3:50 in ED 125). Course numbers are MAS 5311 (CRN: 10895) for graduate credit or MAS 4304 (CRN: 11517) for undergraduate credit. Introductory Abstract Algebra I
Prerequisites
Good knowledge of Modern Algebra (MAS 4301) and linear algebra. Note that the course MAS 4107 (Linear Algebra 2) is offered in parallel to this course.
Textbook
I. N. Herstein, Topics in Algebra, 2nd edition, Wiley 1975, ISBN-10: 0471010901, ISBN-13: 978-0471010906.
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 weekly homework assignments. In the odd weeks, I will collect and grade the assignment, the best 6 count for 20% of the grade.
Quizzes: In the even weeks, there will be a quiz related to the homework assignment. The best 6 quizzes count for 30% of the grade.
Presentations: One oral presentations of about 10 minutes during September or October about a problem from the book will count for 10% of the grade.
Final Exam: The final exam is on Wednesday, December 12, 1:15 - 3:45 p.m. It is comprehensive and counts for 40% of the grade.
Further Information For the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale and Financial Assistance Opportunities please visit Infos for all my courses.
Contact Me
Office hours: Monday, 2:00 - 4:00 p.m. and Wednesday, 3:30 - 5:00 p.m. in SE 272
Course Web Page: http://math.fau.edu/schmidme/courses/iaa18.html
E-mail: markus@math.fau.edu.
Last modified: by Markus Schmidmeier