# Course

## M551 - Algebraic Computation

Course No:
M551
Credit:
4
Prerequisites:
M205, M307
Approval:
2014
UG-Elective
Syllabus:
Linear algebra and lattices: Asymptotically fast matrix multiplication algorithms, linear algebra algorithms, normal forms over fields, Lattice reduction; Solving system of non-linear equations: Gr ̈obner basis, Buchberger’s algorithms, Complexity of Gr ̈obner basis computation; Algorithms on polynomials: GCD, Barlekamp-Massey algorithm, factorization of polynomials over finite field, factorization of polynomials over Z and Q; Algorithms for algebraic number theory: Representation and operations on algebraic numbers, trace, norm, characteristic polynomial, discriminant, integral bases, polynomial reduction, computing maximal order, algorithms for quadratic fields; Elliptic curves: Implementation of elliptic curve, algorithms for elliptic curves.
Reference Books:
1. A. V. Aho, J. E. Hopcroft, J. D. Ullman, “The Design and Analysis of Computer Algorithms”, Addison-Wesley Publishing Co., 1975.
2. H. Cohen, “A Course in Computational Algebraic Number Theory”, Graduate Texts in Mathematics 138, Springer-Verlag, 1993.
3. D. Cox, J. Little, D. O’shea, “Ideals, Varieties and Algorithms: An introduction to computational algebraic geometry and commutative algebra”, Undergraduate Texts in Mathematics, Springer-verlag, 2007.