MSE Master of Science in Engineering

The Swiss engineering master's degree

Jedes Modul umfasst 3 ECTS. Sie wählen insgesamt 10 Module/30 ECTS in den folgenden Modulkategorien:

  • ​​​​12-15 ECTS in Technisch-wissenschaftlichen Modulen (TSM)
    TSM-Module vermitteln Ihnen profilspezifische Fachkompetenz und ergänzen die dezentralen Vertiefungsmodule.
  • 9-12 ECTS in Erweiterten theoretischen Grundlagen (FTP)
    FTP-Module behandeln theoretische Grundlagen wie die höhere Mathematik, Physik, Informationstheorie, Chemie usw. Sie erweitern Ihre abstrakte, wissenschaftliche Tiefe und tragen dazu bei, den für die Innovation wichtigen Bogen zwischen Abstraktion und Anwendung spannen zu können.
  • 6-9 ECTS in Kontextmodulen (CM)
    CM-Module vermitteln Ihnen Zusatzkompetenzen aus Bereichen wie Technologiemanagement, Betriebswirtschaft, Kommunikation, Projektmanagement, Patentrecht, Vertragsrecht usw.

In der Modulbeschreibung (siehe: Herunterladen der vollständigen Modulbeschreibung) finden Sie die kompletten Sprachangaben je Modul, unterteilt in die folgenden Kategorien:

  • Unterricht
  • Dokumentation
  • Prüfung
Stochastic Modeling (FTP_StochMod)

The ubiquitous presence of uncertainty and noise in the engineering sciences and the importance of randomized algorithms in computer and data science make it mandatory to understand and quantify random phenomena. To achieve this goal the course will provide a solid review of probability theory and an introduction to the theory of stochastic processes. Special attention is given to applications, including examples from various fields such as communications and vision, signal processing and control, queuing theory or physics of small systems (Brownian motion).

Eintrittskompetenzen

  1. Basis calculus (integration, differentiation, ordinary differential equations, complex numbers, Fourier transform)
  2. Basic probability theory (probability, conditional probability, Bayes' theorem, expectation, variance, random variables)
  3. Linear algebra (matrix algebra, system of linear equations, eigenvectors, eigenvalues)

Lernziele

The student is familiar with the main working tools and concepts of stochastic modeling (expectation, variance, covariance, autocorrelation, power spectral density). He/She is able to explain properties and limitations of stochastic processes as a modeling tool for noisy systems. He/She will be able to model and analyze simple random phenomena through adaptation of proposed stochastic models.

Modulinhalt

  • Probability review: random variables, conditional probabilities, theorem of large numbers, central limit theorem.
  • General introduction to discrete and continuous stochastic processes. Applications, e.g., communications, Kalman filtering.
  • Discrete, continuous and hidden Markov chains. Applications, e.g., page rank algorithm, queuing systems, pattern recognition, speech recognition.
  • Bernoulli, Poisson, Gaussian processes, Brownian motion, white and colored noise.

Lehr- und Lernmethoden

Ex cathedra teaching
Presentation of simulation results and case studies

Bibliografie

The script is, in principle, sufficient. Further readings are:

  1. Sheldon M. Ross, Probability Models, Elsevier.
  2. John A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press.
  3. Mario Lefebvre, Applied Stochastic Processes, Springer.
  4. Bassel Solaiman, Processus stochastiques pour l’ingénieur, PPUR.

Vollständige Modulbeschreibung herunterladen

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