E0 231 Algorithmic Algebra (Jan-Apr 2011)

Lectures | Seminars

Lectures

• 6 JAN (Th): Organizational Lecture
• 11 JAN (Tu): Introduction-Division algorithms and multivariate division algorithms; Applications of algorithmic algebra for 3-coloring of Graphs and integer programming
• 13 Jan (Th): Power products, multivariate polynomials
• 18 Jan (Tu): Affine space and algebraic sets, algebraic sets of ideals generated by set of polynomials
• 20 Jan (Th): Rings and ideals and their representations
• 25 Jan (Tu): Monomial orders and characterization of well orders
• 3 Feb (Th): Axiom of choice, natural numbers, induction priciple and well ordering of natural numbers
• 5 Feb (Sat): Examples of monomial orders
• 8 Feb (Tu): Structure of monomials and polynomials in monomial ideals
• 10 Feb (Th): Dicksons lemma (without proof; we are going to prove much general result) and its consequences
• 15 Feb (Tu): HBT, Grobner Bases
• 17 Feb (Th): HBT, ACC, Algebraic sets
• 19 Feb (Sat): Characterization of Grobner bases, S-Polynomials Buchberger Criterion (without proof; I will give proof once we cover syzygies)
• 21 Feb (Tu): Buchberger Algorithm
• 24 Feb (Th): Reduced Grobner Bases
• 28 Feb (Mon): (Extra Lecture by Aswin: On Equivalence relations)
• 1 Mar (Tu): Elimination Theorem and Applications
• 2 Mar (Wed): (Extra Lecture by Maria: Basic Group theory)
• 21 Feb (Th): Abstract orders, Noetherian and well founded relations
• 15 Mar (Tu): Dicksons Lemma
• 17 Mar (Th): Dicksons Lemma
• 19 Mar (Sat): Basic Ring theory
• 22 Mar (Tu): Basic ring theory
• 24 Mar (Th): Basic Ring Theory: Isomorphism theorems and Correspondence theorem
• 29 Mar (Tu): Ideal Member ship problem and keeping track
• 31 Mar (Th): k-vector space basis of residue class rings
• 7 Apr (Th): (Lecture by Prashant) Modules, Noetherian Modules, Syzygies, Proof of Buchberger Criterion
• 12 Apr(Tu): (Lecture by Prashant) Modules, Noetherian Modules, Syzygies, Proof of Buchberger Criterion
• 14 Apr (Th): (Lecture by Prashant) Modules, Noetherian Modules, Syzygies, Proof of Buchberger Criterion ***I will give a written notes for this topics****

Seminars

• Computing the Radical of an Ideal in Positive Characteristic by Vineeth Kumar T
• Invariant Theory of Finite Groups and Subalgebra Bases by Maria Francis
• A Treatise A Treatise on the Algorithms in Real Algebraic Geometry by Hari Krishna Malladi
• Course Report on Involutive Basis and Toric Ideals by Ashwin Guha
• Projective Algebraic Geometry by Chintan Rao H
• The Dimension of a Variety by Anirban Sinha
• A New Algorithm for Discussing Grobner Bases with Parmeters by Chitrang Patel
• Automatic Geometric Theorem Proving by Rony Thomas P Roy
• Application of norm equations to elliptic curve by Jyoti Ranjan Adhikary
• Integer Programming Using Grobner Basis by Ratul Ray
• Grobner Bases In Graph Colouring by Sourav Medya

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