### Groups and Rings. 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
### TopicsThis examination will cover topics listed as below - Sylow theorems
- Solvable and nilpotent groups
- Abelian groups
- p-groups
- nilpotent groups
- Linear Groups
- Basics on rings
- Polynomial Rings
- Localization
- Notherian rings; the Hilbert Basis Theorem
### Commutative Algebra#### 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 ### Homological Algebra
- Categories and functors
- Products and coproducts
- Equilazers, pushbacks, pushouts
- Limits and colimits
- Inverse limits
- 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
| ### Fields and Galois Theory. #### 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
### Computational AlgebraThis 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
#### TopicsAll basic topics of the book might be covered in the exam. |