MAT 535: Algebra II Spring 2019 | |

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## 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.
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