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Modelling and Simulation

Code: 104410
Credits: 6
2026/2027
Degree programme Type Course
Computational Mathematics and Data Analytics OB 3

Contact lecturer

Name :
David Rojas Perez
Email :
david.rojas@uab.cat

Group languages

You can consult this information at the end of the document.

Prerequisites

The contents of calculus, probability, and linear algebra given in the 1st year should be known. A fair command of programming in Python is also necessary. It is advised to have followed the subjects Ordinary Differential Equations (2nd year) and Partial Differential Equations (3rd year).

 

Objectives

One of the aims of data analysis is to describe the real world and foresee its behavior.This requires a modeling task that involves different competencies such as problem analysis, simplification hypotheses, contrasting model results with empirical facts, progressive model refining, and simulation of modeled system components.

The main aim of this subject is that students achieve the ability to formulate models suitable for solving actual problems and to analyze them either formally or computationally, as best suits.

This subject has an important practical component, setting it as a bridge between mathematics and the real world and aiming to cross it in both directions.

Learning outcomes

  • CM25 (Assess the difficulty of doing an analytical probability calculation in complex situations.) Assess the difficulty of doing an analytical probability calculation in complex situations.
  • CM27 (Create reality simulation models to establish and verify hypotheses in the study of more complex problems or situations.) Create reality simulation models to establish and verify hypotheses in the study of more complex problems or situations.
  • KM22 (Identify the basics of logistics and other fields in which operations research is applied in the technological and industrial field.) Identify the basics of logistics and other fields in which operations research is applied in the technological and industrial field.
  • SM20 (Distinguish, in a problem, what is important for the construction of the mathematical model and its solution from what is not.) Distinguish, in a problem, what is important for the construction of the mathematical model and its solution from what is not.
  • SM21 (Distinguish when analytical probability calculations can be performed and when stochastic simulation should be used.) Distinguish when analytical probability calculations can be performed and when stochastic simulation should be used.
  • SM22 (Select models of the scientific or technological reality related to a decision-making problem, expressing them in the mathematical language of optimisation problems with dynamic programming or stochastic queueing.) Select models of the scientific or technological reality related to a decision-making problem, expressing them in the mathematical language of optimisation problems with dynamic programming or stochastic queueing.
  • SM23 (Use computer applications for statistical analysis, numerical and symbolic calculation, graph visualisation, optimisation and others to experiment with and solve problems.) Use computer applications for statistical analysis, numerical and symbolic calculation, graph visualisation, optimisation and others to experiment with and solve problems.

Contents

  • The mathematical modelling cycle and dimensional analysis.
  • Modelling with one-dimensional discrete dynamical systems.
  • States and classes: High-dimensional discrete dynamical systems.
  • Stochastic processes and Markov chains.
  • Discrete-event simulation.
  • Model validation and verification.


Learning activities and methodology

Title Hours ECTS Learning outcomes
Project 14 0.56 CM25, CM27, KM22, SM20, SM21, SM22, SM23
Theoretical lessons 35 1.4 CM25, CM27, SM20, SM21
Project development and personal study 95 3.8 CM25, CM27, KM22, SM20, SM21, SM22, SM23

This course will combine theory and Challenge-Based Learning (CBL) through a project that will be carried out in teams.

The project problem is different for each team and will have to be validated by the teacher. Optionally, one can choose a project from the Aprenentatge Servei (ApS) office.

The project must be developed by each team as autonomously as possible.

The development of the project must lead to a final report.

In addition to the written work, the results will be the subject of an oral presentation.

 

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Second Midterm Exam 35% 3 0.12 CM27, KM22, SM20, SM21
Written Project Report and Presentation 30% 0 0 CM25, CM27, KM22, SM20, SM21, SM22, SM23
First Midterm Exam 35% 3 0.12 CM27, KM22, SM20, SM21

The assessment of the course will be based on:

  • First Midterm Exam: 35%
  • Second Midterm Exam: 35%
  • Project: 30%

To pass the course, students must:

  • Obtain a minimum score of 4.0 out of 10 in the weighted average (50%-50%) of the two midterm exams.
  • Obtain an overall average grade of at least 5.0 out of 10, which will be the final course grade.

If the minimum threshold in the midterm exams is not met, the final course grade will be the average of the midterm exam grades, provided that this average is below 4.0.

Students will have the opportunity to take a Resit Examination for the midterm exams. Attendance at this examination will automatically replace the grades obtained in the midterm exams. The resit examination grade will account for 70% of the final course grade and will be capped at a maximum of 6.0 out of 10.

This course does not provide for a single-assessment system.

The remaining 30% of the grade is based on a project developed throughout the second part of the course. This assessment is continuous in nature, and its final grade is not recoverable through a resit examination.

Although a substantial part of the work will be carried out in teams, assessment is individual. If deemed necessary, individual interviews and/or written examinations related to the project may be conducted to verify authorship.

For the possible award of Honors Distinction (Matrícula d'Honor), grades obtained in the resit examination will not be taken into account.

A student will receive a grade of Not Assessed if they do not sit either of the two midterm exams or the resit examination.

The use of Artificial Intelligence (AI) technologies is permitted in this course exclusively for the Project and only for support tasks, such as literature or information searches, text proofreading, and translations.

Students must clearly identify any parts generated using AI technologies, specify the tools employed, and include a critical reflection on how these tools influenced both the process and the final outcome of the activity.

Failure to disclose the use of AI in this assessed activity will be considered a breach of academic integrity, in the same way as copying, plagiarism, or cheating in an examination, and will result in an automatic fail grade for the course or more severe disciplinary sanctions in serious cases.

Bibliography

- Edwards, D. & Hamson, M. (2001) Guide to mathematical modelling. 2nd ed. Houndmills; Palgrave.

- Dym, C. L. (2004) Principles of mathematical modeling. 2nd ed. Amsterdam; Elsevier Academic Press.

- Olinick, M. (2014) Mathematical modeling in the social and life sciences. Hoboken, New Jersey; John Wiley & Sons.

- Giordano, F. R. et al. (2014) A first course in mathematical modeling. 5th ed. International ed. Australia; Brooks/Cole, Cengage Learning.

- Coleman, H. W. & Steele, W. G. (2018) Experimentation and uncertainty analysis for engineers. 4Th ed. Hoboken, NJ, USA; Wiley.

- Law, A. M. (2015) Simulation modeling and analysis. 5th ed. International edition. New York; Mcgraw-Hill.

- Kroese, D. P. et al. (2011) Handbook of Monte Carlo methods. Hoboken, N.J; Wiley.

- Ortega, R. (2013) Modelos Matemáticos. Editorial Universidad de Granada.

Software

During the course, the software will be specified, and instructions to install it will be given if necessary.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan second semester morning-mixed
(PLAB) Practical laboratories 1 Catalan second semester morning-mixed
(SEM) Seminars 1 Catalan second semester morning-mixed