Markus Schmidmeier • Mathematical Sciences • Florida Atlantic University

# Introductory Abstract Algebra I

Welcome to my course! We meet MWF 9:00 - 9:50 a.m. in BU 308. Course numbers are MAS 5311 for graduate credit or MAS 4304 for undergraduate credit.

Prerequisites

Good knowledge of Modern Algebra (MAS 4301) and linear algebra. Note that the courses MAS 5145 (Graduate Linear Algebra) and MAS 4107 (Linear Algebra 2) are 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, the 10 best count for 30% of the grade.

Presentations:  Two oral presentations of about 5 minutes, one before the midterm, will count for 10% of the grade.

Midterm Exam:   The midterm exam on October 9 (not 10/11) will count for 20% of the grade.

Final Exam:   The final exam is on Friday, December 6, 7:45am (sic!) - 10:15am 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:   MWF, 11 a.m. - noon in SE 230

Course Web Page:   http://math.fau.edu/schmidme/iaa13.html

E-mail:   markus@math.fau.edu.