Markus Schmidmeier • Mathematical Sciences • Florida Atlantic University
Welcome to my course! We meet MWF 10:00 - 10:50 a.m. in SC 179. Course numbers are MAS 5312 for graduate credit or MAS 4306 for undergraduate credit.
Introductory Abstract Algebra II
Linear algebra and introductory abstract algebra.
I. N. Herstein, Topics in Algebra, 2nd edition, Wiley 1975, ISBN-10: 0471010901, ISBN-13: 978-0471010906.
Fields play a central role in algebra and its applications. Results about them have impact on the theory of numbers. Field theory encompasses the theory of equations which treats questions about the roots of polynomials. And the study of certain field extensions yields the answers to problems left open in greek mathematics about the doubling of the cube, the trisection of the angle, the constructability of regular polygons, and last but not least, the transcendence of π.
Key topic of this course are the beautiful ideas, due to the brilliant French mathematician Evariste Galois, which have served as a guiding inspiration for algebra as it is today (Herstein, Chapter 5.6).
In this course, we will resume our study of rings in Chapter 3.6ff (Euclidean rings). Prime examples are the ring of integers and the polynomial ring. Nomen est omen: It is the Euclidean Algorithm which provides access to ring theoretic properties like principal ideal ring, or unique factorization domain.
Last semester we have seen that finite abelian groups are direct sums of cyclic groups. But abelian groups are just modules over the integers! We generalize the result just mentioned to finitely generated modules over a Euclidean ring. (Chapter 4.5)
Key topic in this course is the theory of field extensions a.k.a. Galois Theory (Chapter 5), with its application to constructions with ruler and compass.
As time permits, we will study finite fields (Chapter 7.1).
Homework: There will be weekly homework assignments, the 10 best count for 30% of the grade.
Presentations: Two oral presentations of at most 10 minutes each, one before the midterm, will count for 20% of the grade.
Midterm Exam: The midterm exam on February 21 will count for 10% of the grade.
Final Exam: The final exam on Monday, April 28, 7:45 a.m. - 10:15 a.m. in SC 179 is comprehensive and counts for 40% of the grade.
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.
Office hours: MWF, 11 a.m. - noon in SE 230
Course Web Page: http://math.fau.edu/schmidme/iaa14.html
Last modified: by Markus Schmidmeier