Operations research 2

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

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

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 2	2 + 3	exam + term grade	pure math.	mm1c1op4m mm1c2op4m	4	optional
2 + 2	2 + 3	exam + term grade	applied math.	mm1c1op4a mm1c2op4a	4	compulsory

Course coordinator

András Frank
Department of Operations Research
Institute of Mathematics

Strong	Weak	Prerequisites
Practice class
Practice class		Strong: Operations Research1L-p (mm1c1op3m) or Operations Research1L-a (mm1c1op3a)
Lecture
Lecture		Weak: practice class

Remarks

Syllabus designed by:

Tibor Illés, Department of Operations Research, Institute of Mathematics.

Literature

J. Matousek and B. Gärtner: Understanding and Using Linear Programming. Springer, 2006.
Y. Peres: Game Theory, Alive. Online lecture note.
M. S. Bazaraa, H. D. Sherali and C. M. Shetty: Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, Inc., New York, 1993.
A. Ruszczynski: Nonlinear Optimization. Princeton University Press, 2006.

Syllabus

The simplex method and sensitivity analysis. Preflow-push and Network simplex algorithms. Introduction to integer programming and approximation algorithms. Basic concepts of game theory: dominant strategies, Nash equilibrium, 0-sum games, Lemke-Howson algorithm. Elements of convex optimization: convex cones, separation theorems, system of convex inequalities, Karush-Kuhn-Tucker theorems, Lagrangean dual problem.

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