MAT 535: Algebra II Fall 2016 | |

Home General Information Syllabus Homeworks Exams |
## General Information
- Vector spaces: Cayley-Hamilton Theorem, Jordan normal form, bilinear forms, signature, tensor products, symmetric and exterior algebras.
- Homological algebra: categories and functors, universal and free objects, exact sequences, extensions.
- Representation theory for finite groups: irreducible representations and Shur's Lemma, characters, orthogonality.
- Galois theory: splitting fields, finite fields, extension fields of various types, Galois polynomial and group, fundamental theorem of Galois theory, symmetric functions.
Please be aware that there is a number of misprints in the book; you can find the errata here. Additional references: - D. Cox,
*Galois Theory*, Wiley-Interscience, 2004. - M. Artin,
*Algebra*, Prentice Hall, 1991. - S. Lang,
*Algebra*, 3rd ed., Springer-Verlag, 2002. - Jacobson,
*Basic Algebra,*, 2nd ed, W.H. Freeman, New York, 1985, 1989. - S. Roman,
*Advanced Linear Algebra*, 3rd ed., Springer-Verlag, 2007. - B. L. van der Waerden,
*Algebra*, Springer-Verlag, 1994. - Blyth,
*Module Theory*, Oxford University Press, 1990. - J.-P. Serre,
*Linear Representations of Finite Groups*, Prentice Hall, 1991.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.sunysb.edu/ehs/fire/disabilities.shtml |

Copyright 2016 Stony Brook University |