As an assistant professor, I teach university courses. Here, you will find information about the university courses that I teach.

# Eindhoven University of Technology

The upcoming years, I will be involved in the following courses at TU Eindhoven:

- 2MMR10 – Professional Portfolio: Modelling Week (academic year 2019-20)
- 2WH10 – Effectiveness of Mathematics (academic years 2019-21)
- 2WH20 – Programming and Modeling (academic years 2019-20)
- 2MMS50 – Stochastic Decision Theory (academic years 2019-21)
- 2WB50 – Stochastic Simulation (academic year 2020-21)

Here is more information about these courses and on my involvement.

## MSc courses

### 2MMR10 – Professional Portfolio: Modelling Week

At the end of this first year MSc course, there is a modelling week. During this week, the students work in groups on real problems posed by problem owners from industry. The week starts with presentations by the problem owners, and concludes with presentations of the solutions by the students. The students:

- Gain experience in solving real-life problems
- Report back their findings to the problem owner
- Work in groups/team
- Learn how to capture the essence of a practical problem in terms of a mathematical model
- Learn how to extract value from mathematical modelling
- Learn to have a professional attitude when dealing with problems coming from the public/industrial sector
- Become aware of the diversity in culture, attitude and character of the members of the work team.

I am involved as a supervisor for one of these teams.

### 2MMS50 – Stochastic Decision Theory

The goal of the course is to familiarize students with the basic mathematical concepts and computational techniques for stochastic decision and optimization problems, and illustrate the application of these methods in various scenarios. The methodological framework of Markov decision processes and stochastic dynamic programming models will play a central role, and the students are expected to obtain knowledge of the main problem formulations and be able to apply the the main computational approaches in that domain to stylized problems. The use of these problem formulations and computational techniques will be illustrated in the context of various specific examples. The students will also gain familiarity with so-called multi-armed bandit models and Gittins indices for stochastic optimization in scenarios with unknown parameter values, and learn how to apply these approaches to specific problem instances. In addition, the students are expected to acquaint themselves with several miscellaneous topics, such as newsboy problems, achievable performance regions, optimal stopping problems, and stochastic approximation methods.

## BSc courses

### 2WH10 – Effectiveness of Mathematics

This first year BSc course is an umbrella course that covers all fields of mathematics studied in our department. I am one of two responsible teachers for the

- grasp the concept chance, probability and events
- describe chance experiments with discrete random variables
- perform simple calculations with events and discrete random variables
- compute expectations of discrete random variables
- apply the Law of Large Numbers
- apply the Central Limit Theorem
- model chance experiments with Markov chains
- compute the probability of reaching an absorbing state of a Markov chain
- grasp the concept of parameter estimation and confidence intervals
- compute required sample size for simple simulations
- describe how simple chance experiments can be simulated using a random number generator that produces uniform random numbers on the unit interval

### 2WH20 – Programming and Modelling

Modeling is the translation of a problem set in natural or technical context into a formal mathematical description, in terms of concepts, attributes and relations. These are used to further evaluate, analyze, simulate, or optimize the problem characteristics. Programming enables us to build the formal model, execute it, and visualize the results. Structured programming typically emphasizes the use of concepts, attributes and relations. In this course, the student will tackle a modelling assignment, and learn to:

- Programming:
- The student has knowledge and skills of programming constructs and techniques.
- By applying this knowledge the student is able to set up well structured Python programmes, both with existing libraries and with creating self defined functions.
- Modelling:
- Students learn to handle a concrete real-life problem in the context of Analysis, Discrete Structures or Stochastics. They are able to make an analysis, translate subproblems into formal mathematical problems, analyze these and devise a methodology and appropriate bookkeeping to solve these problems. The can then interprete the mathematical results in the original problem context.
- Professional skills:
- The student learns to participate in projects where coorperation is important. The student is able to find relevant literature in the library and on the internet, and to cite it correctly.

### 2WB50 – Stochastic Simulation

Many real-life processes are too difficult or too complex to analyse in an exact, theoretical way. Throughout this course we discuss a variety of real-life processes that exhibit a stochastic behaviour, ranging from financial models, manufacturing networks, to models for particle systems in chemistry or physics. The course is very practical, in the sense that emphasis will be placed on developing simulation models for these processes. Many of the lectures will be interactive, with the lecturer and the students writing a simulation together, step by step. The main goal of the course is that the students not only learn and understand the required simulation techniques, but are also forced to actually write the simulation.

## Delft University of Technology

As an assistance professor at TU Delft, I was involved in the following courses:

- EE2T21 – Data Communications Networking (academic years 2017-2019)
- Reading Seminar (academic year 2018-2019)

Here is more information regarding these courses.

### EE2T21 – Data Communications Networking

Data Communications Networking is an introductory course to telecommunication networks. Telecommunication networks include local area networks, the Internet, and telephone networks. This is an obligatory course for second year students that are following the Bachelor Electrical Engineering at the faculty of Electrical Engineering, Mathematics & Computer Science.

#### Learning Objectives

In this university course, students learn to:

- Explain the functionalities with which modern end-to-end communication in data communication networks is achieved.
- Explain the architecture and design concepts that underlie the internet and its protocols.
- Perform elementary calculations and performance analyses on small networks.
- Implement basic mathematical coding and routing algorithms that have inspired error correction methods and routing protocols in networks.

#### Course material

This course covers Chapters 1 – 7.5 of the book Data Communications Networking, written by professor Piet Van Mieghem. The topics covered are therefore:

- Chapter 1. Introduction to data communication networks
- Chapter 2. Local Area Networking
- Chapter 3. Error control and retransmission protocols
- Chapter 4. Architectural principles of the internet
- Chapter 5. Flow control protocols in the internet
- Chapter 6. Routing algorithms
- Chapter 7. Routing protocols

#### Educational load

The students can earn 2 ECTS by taking this course. This is roughly equivalently to a load of 56 hours. The course is taught in just under 4 weeks. The course is therefore lecture intensive, and a high degree of self-study is expected from the students.

#### Prerequisites and dependants

No prerequisite university courses are specified for this course. Familiarity is expected with the basic courses taught in the BSc program up to that point. The reason is that this course sits within the second year of our BSc program. The relevant courses include:

- EE1M11 – Linear Algebra and Analysis A,
- EE1M12 – Linear Algebra and Analysis B, and
- EE1M31 – Probability Theory and Statistics.

Follow-up university courses that specify this course as a prerequisite include:

- EE4C06 – Networking, and
- IN4341 – Performance Analysis.

#### Sample exam

Here is the exam that students did on July 6th, 2018. This gives you an impression of the contents of the course.

### Reading Seminar (academic year 2018-2019)

In the fall of 2018, I will organize a reading seminar on part one of the book ** Graph Spectra for Complex Networks**, written by Piet Van Mieghem.

## Reading Seminar Fall 2018

Date | Topic | Location | Presenter |
---|---|---|---|

Chapter 2: Algebraic graph theory | |||

October 3rd, 2018 | 1. adjacency matrix; 2. admittance matrix, Laplacian; 7-8. line graph; 10-13. permutation matrix, isomorphism and automorphism; 14-15. partitions, quotient matrix; 17-20. walks, paths, diameter, shortest path | HB 09.120 | Albert Senen-Cerda |

Chapter 3: Eigenvalues of graphs | |||

October 10th, 2018 | 21. eigenvalues; 23. Gerschgorin’s theorem; 27-28,31. identities relating graphs properties to eigenvalues; 30. identity relating number of links in a line graph to the number of connected triplets in a graph | HB 09.120 | Qiang Liu |

October 17th, 2018 | 33-35. number of walks of length k; 43-44. lower bounding eigenvalues; 50,54. eigenvalue bounds in connected graphs; 64. random walk on a graph, relation between concentration and spectral gap | HB 09.120 | Bastian Prasse |

Chapter 5: Spectra of special types of graphs | |||

January 23rd, 2019 | 5.1. complete graph; 5.2. small-world graph; 5.3. circuit; 5.4-5.5. path; 5.6. wheel; 5.7. complete bipartite graph; | HB 09.120 | Albert Senen-Cerda |

Chapter 6: Density functions of eigenvalues | |||

121. eigenvalue density function; 123. integral form; 124. trace relation; 128. limiting density function on paths; 130. limiting density function on small world graphs; | HB 09.120 | Albert Senen-Cerda | |

January 30th, 2019 | 131-133. large sparse regular graphs, McKay’s law; 134-135. random matrices, Wigner’s Semicircle Law; 137. spectrum of the Erdos-Renyi random graph 6.5.2 Marcenko-Pastur’s law | HB 09.120 | Jaron Sanders |