Algebra is one of the fundamental areas of mathematics and will almost certainly play an important role in whatever research area you choose to pursue during your time in graduate school. The goal of the Math 230 sequence is to provide a broad overview of algebra and to give you with a strong foundation that prepares you to pursue more advanced topics in the future. You will develop your algebraic intuition by working with many examples, solving lots of problems, and doing many proofs. Another key goal of this course is to prepare students for success on the Qualifying Exam in Algebra.
In 230 a we will begin with a review of group theory and then move on to more advanced topics in the subject. In the latter part of the course we will focus on ring theory. The plan is to cover Chapters 1-9 of Dummit and Foote, but not every section.
Math 230b will study modules and field theory, and Math 230c will focus on Galois theory and representation theory.
We assume that you have already taken a standard undergraduate course in abstract algebra and proof-based linear algebra. You will have seen some of the course material before, so we plan to review the basics quickly in order to move on to new and challenging topics. We will definitely not have enough time to cover everything in detail in lecture so you will be expected to do a significant amount of reading outside of class.
I will post mandatory homework, which should be handed by everybody and which will cover the fundamental concepts will learn in the class and supplemental homework, with more challenging problems, that are meant to expand and enrich your knowledge about the subject.
The first midterm exam (solutions will be posted sometime next week): Midterm1
Classifying semi-direct products: http://math.stanford.edu/~conrad/210BPage/handouts/math210b-remarks-on-semidirect.pdf
I will also try to spend most of the time in class working on examples and problems and I highly recommend that you read them before the corresponding class.
The grade breakdown is the following:
The pacing for sections in Dummit and Foote will be roughly the following:
Week 10 Sections 7.6, 8.1, 8.2 , 8.3, 9.1, 9.2, 9.3, 9.4- This is postponed for next quarter.