There are three qualifying exams for students working in algebra.
Groups and Rings: PhD qualifying exam in algebra (based on MTH 571)
Field and Galois Theory: PhD qualifying exam in algebra (based on MTH 572)
One of the following:
Computational Algebra (MTH 577)
Commutative Algebra (MTH 671-672)
Coding Theory and Cryptography (MTH 673)
The exam is graded Pass/Fail and is administered by the Algebra Committee which contains three faculty members of the Department from the area of research in Algebra/Algebraic geometry. The student can take each exam only twice.
The PhD exams in algebra are offered every year, during the second half of the months of May and August. Students who intend to take the exam should register with the graduate committee.
June 2: MTH 571
June 9: MTH 572
August 18: MTH 571
August 25: MTH 572
The exam is based on the contents of the sequence MTH 571. However, topics that are not covered in the course can also be on the exam. As textbooks recommended for the study among others are
An introduction to the theory of groups, J. Rotman
Finite Group Theory, I. Martin Isaacs
Algebra, Lang
Algebra, Hungerford
This examination will cover topics listed as below
Group Theory
Sylow theorems
Solvable and nilpotent groups
Abelian groups
p-groups
nilpotent groups
Linear Groups
Rings
Basics on rings
Polynomial Rings
Localization
Notherian rings; the Hilbert Basis Theorem
The exam is based on the contents of the sequence MTH 671. However, topics that are not covered in the course can also be on the exam. As textbooks recommended for the study are
Books
Introduction to Commutative Algebra, Atyah & MacDonald.
Algebra, Lang
Algebra, Hungerford
Topics
Categories and functors
Products and coproducts
Equilazers, pushbacks, pushouts
Limits and colimits
Inverse limits
Module theory
Modules
Modules over PID's
Direct sums and free modules
Exact sequences
Free modules; Projective and Injective modules
Tensor Products
Linear algebra
Canonical forms
Artinian Rings; the Wedderburn-Artin Theorem
The exam is based on the contents of the sequence MTH 572. However, topics that are not covered in the course can also be on the exam. As textbooks recommended for the study are
Books
Algebra, S. Lang
Field Theory, Roman
Field and Galois Theory, Morandi
Topics
Field Extensions
Algebraic Extensions
Separable Extensions
Norms and Traces
Galois Theory
Galois grous of polynomials
Abelian Extensions
Finite Fields
Transcendental Extensions
This Exam will be first offered in the Summer 2013. The list of topics is subject to change
Topics
Computational Group Theory
Algebraic Equations
Invariant Theory
Commutative algebra and Algebraic Geometry
A more detailed list will be available soon.
The coding theory Exam will first be offered in the Summer 2013. The exam is based on the following book
Books
Fundamental of Error Correcting Codes, C. Huffman and V. Pless
Topics
All basic topics of the book might be covered in the exam.