Christian Eder: Introduction to Computer Algebra
- Lecturer: Christian Eder
- Date and Room:
- Wednesday 13:15 - 14:45, Leipzig University, Hörsaalgebäude, room HS-19
- Thursday 9:15 - 10:45, Leipzig University, Seminargebäude, room SG 3-20
- Language: English
- Target audience: MSc students, PhD students, Postdocs
- Keywords: Arithmetics, Systems of (non-)linear equations, lattices, resultants, Gröbner bases, factorization
- Prerequisites: Basic knowledge about algebra and the usage of computer algebra systems
- Remarks: Literature and up to date infos
Abstract
The lecture gives an introduction to basic concepts of Computer algebra. In more detail, we will discuss the following topics:
- Integer and polynomial arithmetics, fast multiplication, gcd computations, complexity of algorithms.
- Systems of equations, Hermite- and Smith-normal form, p-adic approximation, lattices, LLL algorithm.
- Resultants and extended gcd computations.
- Multivariate polynomials, Gröbner bases for ideals and modules, modular methods, Faugère's F4 and F5 algorithm, syzygies, free resolutions.
- (Squarefree) Factorization, Hensel lifting, factorization with LLL, primality tests, factorization over algebraic number fields.
Regular Lectures (Summer 2019)
- Artificial Neural Networks and Machine Learning: Theoretical Foundations II
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- Thursday, 11:15 - 12:45, MPI MiS A3 01
- Embedding theorems in complex geometry
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- Tuesday, 11:15 - 12:45, University Augusteum A-314
- Continuum Mechanics
- Jan Burczak
- Wednesday, 9:15 - 10:45 and Friday, 9:15 - 10:45, University Augusteum A-314
- Modern Algebraic Geometry
- Claus Diem
- Monday, 11:15 - 12:45, University SG 3-13 and Friday, 13:15 - 14.45, University Augusteum A-314
- Introduction to Computer Algebra
- Christian Eder
- Wednesday 13:15 - 14:45, University HS-19 and Thursday 9:15 - 10:45, University SG 3-20
- Enumerative geometry
- Francesco Galuppi
- Wednesday, 09:30 - 11:00, and Thursday, 13:30 - 15:00, MPI MiS G3 10
- Stochastic variational inequalities
- Benjamin Gess
- Monday, 16:15 - 17:45, MPI MiS A3 01
- Schemes and Sheaves
- Jürgen Jost
- Monday, 13:30 - 15:00, MPI MiS A3 01
- Information and Complexity
- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 02
- Randomness in PDE–selected topics
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- Thursday, 9:15 - 10:45, MPI MiS A3 01, starting May 16
- Category theory and applications
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- Wednesday, 11:00 - 12:30, MPI MiS A3 02
- Introduction to Microlocal Analysis
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- Thursday, 11:15 - 12:45, University, SG 311
- Introduction to percolation theory
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- Hodge Theory and Periods of Varieties
- Emre Sertöz
- May 6 - 10, MPI MiS G3 10, details see extra page
- Introduction to D-modules
- Christian Sevenheck
- Friday, 11:00 - 12:30, MPI MiS G3 10
- Invitation to Nonlinear Algebra
- Mateusz Michałek, Bernd Sturmfels
- June 4 - 14, MPI MiS, details see extra page
- Population Dynamics
- Florian Völlering
- Wednesday and Friday 9:00 - 11:00, University, SG 3-13
- IMPRS-Ringvorlesung
- Felix Otto, Peter Stadler (lectures), Tobias Ried (exercises)
- Lectures: Tuesday, 10:15 - 11:45, MPI MiS G3 10
- Exercises: Thursday, 15:30 - 17:00 (at 04.04.: 13:00 - 14:00), MPI MiS G3 10