Meetings: MWF 10:00-10:50 AM, Math Science. Building 3106, and Tu 10:00-10:50AM, MSB 2112.
Attendance to all meetings will be assumed, but it is not required!
Instructor: Prof. Jesús A. De Loera.
Phone: (530)-554 97 02
Office hours: MW 11-12pm or by appointment.
My office is 3228 Mathematical Sciences Building.
TA info: The TA for the class Ms. Lily Silverstein, her office hours will be Tu and Th from 12:30-1:30pm, at her office 2141.
Text and References:
This quarter I will use 2 main sources. None of them is required to be
purchased and can be obtained online or the library.
First, the book by Rotman Advance Modern Algebra which you used in 250A. Second, I will often use the book ``Algebra'' (Springer Graduate Texts
in Mathematics, vol. 73), by Thomas W. Hungerford. In addition, I will supplement the course with my own emphasis, notes, and exercises.
E.g., there is a good chance you will have to learn a bit of SAGE or MAPLE to help with your homework!
Description: This is course is the second part of our graduate-level algebra sequence.
In close coordination with Prof. Vazirani, who taught 250A, I will cover:
- Fields and Galois Theory: Fields structure, classification of finite fields, algebraic and Galois field extensions, fundamental theorem of Galois theory, geometry applications and equation solvability by radicals, algebraic closure, transcendence degree, Calculation of Galois groups (about 12 lectures, in first MIDTERM).
- Commutative Rings and Modules: Prime and maximal ideals, unique factorization domains, generalized Chinese remainder theorem, Artinian and Noetherian rings, quotients of polynomial rings, Hilbert basis theorem, localization of rings, Hilbert Nullstellensatz, basic algebraic geometry, Groebner bases (about 12 lectures, in second MIDTERM).
- Advanced Linear Algebra: Finitely generated modules over a PID, Jordan canonical form, and Smith normal form (about 4 lectures, in FINAL exam).
Grading policy and Rules:
New homework exercises will be posted on my web page weekly (see the end of this web page) and announced in class too. Please NO late homework, NO make-up exams either. This is a graduate class!
There will be 7 or 8 homework sets. Each worth 4 points. We will drop the lowest 2 or 3 scores (depending on final number), thus we have 20 points from homework.
Homework will be assigned each week, due about a week and half later.
Each set will consist of 12 to 15 problems will come in each homework, but we will not grade all problems!
Here is how the homework will be graded: A student will receive 1 point for submitting at least a half of the homework set, 1 point more for submitting at least 3/4 of the problems.
Finally, up to 2 points from carefully grading of one randomly-chosen problem.
To motivate people to do the homework entirely. The midterm exams will be partly composed of those homework problems! It should also be fairly clear nobody can get more than a B if they do not submit homeworks.
Final Exam (comprehensive)