MathMods :: Joint MSc

Sem3 UAB Stochastic

Sem3 UAB Stochastic

Applications  @  UAB  30 ECTS credits

Stochastic modelling and optimisation

From the curriculum of the Barcelona (UAB) partner, "Stochastic Modelling and Optimisation", students will learn how to model real systems in which randomness plays a significant role, and how to deal with situations in which a best alternative is sought among many feasible possibilities. Sometimes, both these features are present. Frequently, the best solution of a complex optimisation problem is impossible to be found exactly, and the realistic goal is to seek a suboptimal solution that can be attained in a reasonable time. Also, the random elements of a system are often introduced intentionally so as to disregard features which would make the model too complicated. One of the main objectives is to highlight this sort of compromise when it comes to solving a real world problem. Competence in designing algorithms and using existing standard software in these fields is essential. But at the same time we will try to ensure that the students get as solid as possible a theoretical background. After this semester, the students should be able to: join industrial R+D departments or laboratories, where the modelling of experimental data or the improvement of products and processes are the goal; enrol in general engineering consulting enterprises; or pursue studies in mathematics applied to finance, econometrics, networking, logistics, etc.

 

Below you can find information about the subjects for this semester.

  • Combinatorial optimisation [6 credits]

    Combinatorial optimisation

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      This course is an introduction to Combinatorial Optimisation at the first-year graduate level. We will also cover and review some important aspects of Linear and Integer Optimisation at the start

    • Topics

       

      Linear Optimisation, Integer Optimisation, Graph and Network Optimisation, Complexity Theory and Heuristics

    • Books

       

      G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, M. Protasi, "Complexity and Approximation".
      Springer Verlag, 1999.

      Sniedovich, M. (2006), "Dijkstra’s algorithm revisited: the dynamic
      programming connexion Journal of Control and Cybernetics/ *35* (3): 599–620.

      Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L,
      "Introduction to Algorithms" (first edition ed.). MIT Press and McGraw-Hill.

      Judea Pearl, "Heuristics: Intelligent Search Strategies for Computer
      Problem Solving", Addison-Wesley Pub (Sd) 1984.


    Open this tab in a window
  • Probability and Stochastic Processes [6 credits]

    Probability and Stochastic Processes

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      This is a course in basic stochastic processes. Many systems evolve over time with an inherent amount of randomness. The purpose of this course is to develope and analyse probability models that capture the features of the system under study to predict the short and long term effects that this randomness will have on the system under consideration.

    • Topics

       

      Bernoulli Processess, random walks; Discrete-time Markov chains; Reneval theory; Poisson point processes; Brownian motion

    • Prerequisites

       

      Basic properties of measures, the integral with respect to Lebesgue measure, Lebesgue measure, sigma-algebras.

    • Books

       

      [1] R.M. Dudley. Real Analysis and Probability. Cambridge studies in advanced mathematics 74, 2002.
      [2] E. Hewitt and K. Stromberg, Real and Abstract Analysis. 1991. Springer.
      [3] W. Feller. An Introduction to Probability Theory and Its Applications. John Wiley & Sons, Inc, 1968.
      [4] P.G. Hoel, S.C. Port and C.J. Stone. Introduction to Probability Theory. Houghton Miin Company, 1971.
      [5] H.-H. Kuo. Introduction to Stochastic Integration. Springer, 2006.
      [6] D.C. Montgomery and G.C. Runger. Applied Statistics and Probability for Engineers. John Wiley & Sons, Inc., 2003.
      [7] S.H. Ross. Introduction to Probability Models. Academic Press, 2007.
      [8] H.L. Royden. Real Analysis. Third Edition. 1988. Prentice-Hall. Inc.
      [9] M. Sanz i Solé. Probabilitats. 1999. Universitat de Barcelona.
      [10] A.N. Shiryaev. Probability. 2000. Springer.
      [11] D. Williams. Probability with Martingales. Cambridge Mathematical Textbooks, 1991.


    Open this tab in a window
  • Workshop of Mathematical Modelling [6 credits]

    Workshop of Mathematical Modelling

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      The Mathematical Modelling Workshop is aimed and analyzing and solving real-world problems by means of mathematics. It has a very practical and interdisciplinary character

    • Topics

       

      The main part of the workshop is a project to be developed by the students, organised in teams. Besides, the workshop will include also a few lessons about general ideas and techniques, as well as about illustartive examples.


    Open this tab in a window

Pick 2 units from

  • Data visualisation and modelling [6 credits]

    Data visualisation and modelling

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      To learn the methodologies of data simulation, bootstrapping and permutation testing, that allow a fast solution to complex statistical models without deep knowledge of classical statistical topics. Introduce Bayesian networks as graphical structures for representing probabilistic relationships among many variables and for doing inference.

    • Topics

       

      Introduction to the R language. Permutation tests. Jackknife. Parametric and non-parametric bootstrap. Causal networks and inference in Bayesian networks. Learning Bayesian network parameters.


    Open this tab in a window
  • Parallel programming [6 credits]

    Parallel programming

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      To identify the difficulties related to parallel programming. To apply an adequate methodology for the development of parallel applications. To understand the different approaches: shared memory, message passing. To evaluate parallel application performance and tune for performance improving.

    • Topics

       

      Introduction to parallelisation. Programming in the C language. OpenMP programming. CUDA. MPI programming.


    Open this tab in a window
  • Research and innovation [6 credits]

    Research and innovation

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona

    Open this tab in a window
  • Simulation of Logistic Systems [6 credits]

    Simulation of Logistic Systems

    • ECTS credits 6
    • Semester 3
    • University Autonomous University of Barcelona
    • Objectives

       

      This subject seeks to introduce the decision making activity in the production and logistic field. This subject will introduce the students to analyze the cause-effect relationship between the elements that determine system behavior, and design mechanism to avoid the propagation of perturbation through the whole system.

    • Topics

       

      Introduction to Flexible manufacturing systems; Discrete event system modeling; Statistic models in simulation; Discrete event system simulation and decision making in the logistic field.

    • Books

      N.Viswanadham,Y. Narahari. Performance Modeling of Automated Manufacturing Systems. Prentice Hall, 1992.


      Merkuryev, Merkureva, Guasch, Piera: Simulation-Based Case Studies in Logistics: Education and AppliedResearch. Springer London. 2009.


      M.A. Piera, T.Guasch, J. Casanovas, J.J. Ramos. Cómo Mejorar la Logística de su Empresa Mediante la Simulación. Ed. Diaz De Santos. 2006.


    Open this tab in a window

Home Program structure Semester 3 UAB Stochastic modelling and optimization

Connect with us

Our partners' addresses

University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

Autonomous University of Barcelona, Catalonia - Spain (UAB)

Departament de Matemàtiques, Edifici Cc - Campus UAB 08193 Bellaterra – Catalonia

University of Hamburg, Germany (UHH)

Department of Mathematics
Bundesstr. 55 20146 Hamburg - Germany

University of Nice - Sophia Antipolis, France (UNS)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2

Vienna Univ. of Technology, Austria (TUW)

Technische Universität Wien
Institute of Analysis & Scientific Computing
Wiedner Hauptstr. 8, 1040 Vienna - Austria

This web-site reflects the views only of the author, and the EU Commission cannot be held responsible for any use which may be made of the information contained therein.