Applied linear algebra

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Applied linear algebra

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 2	2 + 3	exam + term grade	applied math.	mm1c1la4e mm1c2la4e	4	recommended

Course coordinator

Gyula Károlyi
Department of Algebra and Number Theory
Institute of Mathematics

Strong	Weak	Prerequisites
Practice class
		Strong: Algebra2L (mm1c1al2)
		Strong: Discrete matematics1L (mm1c1vm1)
Lecture
Lecture		Weak: practice class

Remarks

Syllabus designed by:

Gyula Károlyi, Department of Algebra and Number Theory, Institute of Mathematics.

Prerequisites

Classical and linear algebra, discrete mathematics, geometry.

Literature

M. Aigner, G. M. Ziegler: Proofs from the Book. Springer, 2009.
P. D. Lax: Linear algebra and its applications. Wiley, 2007.

Syllabus

Algebraic applications. Generalized inverses, application of generalized inverses to solutions of systems of linear equations (exact solution and best approximation). Jordan normal form, taking the power of matrices, solving linear recurrences, Markov chains. Positive matrices, stochastic matrices, the Perron-Frobenius theorem. Fast matrix multiplication.
Applications in graph theory. Graphs and associated matrices. The Cauchy-Binet formula. The number of spanning trees, Cayley's theorem about the number of labelled trees. Catalan numbers. Shannon capacity.
Geometric and combinatorial applications. Volume and determinants. Applications of Vandermonde's determinant. The solution of Hilbert's third problem: Dehn's theorem about equidecomposability. Points sets with a small number of distances. Extremal set theory, block systems.