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Regular version of the site
Bachelor 2023/2024

# Mathematical Modeling and Simulation

Category 'Best Course for New Knowledge and Skills'
Type: Elective course (Software Engineering)
Area of studies: Software Engineering
When: 4 year, 1-3 module
Mode of studies: offline
Open to: students of all HSE University campuses
Language: English
ECTS credits: 10
Contact hours: 60

### Course Syllabus

#### Abstract

Models are often built to answer “WHAT–IF” questions with less cost, time, and effort compared to the physical implementation of real changes or the construction of real objects. For example, “Will the traffic density on the road likely decrease by about 25% IF we add a second lane?”. To verify the hypothesis, we do not construct a lane, which is costly, time-consuming, and may not decrease the traffic density at all. Mathematical and Simulation Modeling is vital for computer science, biology, epidemiology, business, technology, network theory, economics and social sciences, management of resources, self-driving cars, physics, chemistry, Earth science. It is also used in music, linguistics, and psychology, to name a few. Mathematical and Simulation Modeling covers agent-based modeling, cellular automata, and computer simulation and includes model training, tuning, and evaluation. Mathematical and Simulation Modeling combines methods from statistics, machine learning, probability theory, automata theory, optimization, decision-making theory, and game theory, as well as a broad range of other mathematical and computational disciplines.

#### Learning Objectives

• Know the Definitions of Mathematical and Simulation Modeling
• Be able to mathematically define Predator-Prey Interactions
• Know the Components and Applications of Cellular Automata
• Know Agent-based modeling and simulation concepts and applications
• Be able to Classify Swarm Intelligence Approaches and Algorithms
• Know Ant Colony Optimization (ACO) Metaheuristics
• Be able to design and run a Mathematical/Simulation Model of Road Traffic
• Be able to design and run a Mathematical/Simulation Model of Fire Spread
• Be able to design and run a Mathematical/Simulation Model of Computer Networks
• Be able to design and run a Mathematical/Simulation Model of a Distributed System

#### Expected Learning Outcomes

• The Student Defines Mathematical and Simulation Modeling
• The Student Classifies Mathematical and Simulation Model Types
• The Student Narrates a brief history of the discipline
• The Student Lists Key Types of Mathematical and Simulation Modeling
• The Student Lists Mathematical and Simulation Modeling Applications
• The Student Defines Predator-Prey Interactions
• The Student Reproduces Classical Lotka-Volterra differential equations
• The Student Describes Population Equilibrium
• The Student Defines Cellular Automata and its Key Components
• The Student Lists Research and Business Application Domains of Cellular Automata
• The Student Reproduces Rules from the Conway's Game of Life Cellular Automaton
• The Student Defines Traffic Cellular Automata, its Simulation Goals, and Input Data
• The Student Reproduces the Nagel-Schreckenberg one-dimensional model
• The Defines Typical Traffic Cellular Automata simulation statistics
• The Student Describes the Importance of wildfire simulation
• The Student Lists the differences between Data-Driven and Physical (Mathematical)-Based Simulation Models
• The Student Lists key input data for wildfire simulation
• The Student Lists agent-based modeling and simulation concepts and applications
• The Student Defines agent, environment, autonomous actions, design objectives, and communication
• The Student Names the key benefit of the Swarm Intelligence Approach
• The Student Constructs an algorithm based on the Ant Colony Optimization (ACO) Metaheuristic
• The Student Lists the tasks that are possible to solve with Swarm Intelligence
• The Student Lists the Computer Network application areas
• The Student Defines the communication protocol in terms of computer networks
• The Student Designs a Computer Network in a specialized simulation software
• The Student Defines computer network components
• The Student Defines the OSI model and its abstraction layers
• The Student Defines cloud, grid, peer-to-peer, volunteer, and scientific computing
• The Student Describes the purpose of the What-If analysis in terms of Cloud-Based and Distributed Systems
• The Student Defines the problems solved by Mathematical and Simulation Modeling of Cloud-Based and Distributed Systems
• The student defines basic quantum computing notations
• The student narrates about the problems of quantum computing simulations
• The student applies basic quantum computing operations

#### Course Contents

• Introduction
• Predator-Prey Interactions
• Cellular Automata
• Road Traffic Simulations with Cellular Automata
• Mathematical and Simulation Modeling of Fire Spread
• Agent-Based Modeling
• Swarm Intelligence
• Mathematical and Simulation Modeling of Computer Networks
• Mathematical and Simulation Modeling of Cloud-Based and Distributed Systems
• Mathematical and Simulation Modeling: Application Domain Examples
• Fundamental Problems and Applications: Examples

• EX1
• CW2
• HW1
• HW2
• PPT
• EX2

#### Interim Assessment

• 2023/2024 1st module
1 * EX1
• 2023/2024 3rd module
0.15 * CW2 + 0.2 * EX2 + 0.2 * HW1 + 0.2 * HW2 + 0.25 * PPT

#### Recommended Core Bibliography

• An introduction to agent-based modeling: Modeling natural, social, and engineered complex systems..., Wilensky, U., 2015
• Klein, D., Marx, J., & Fischbach, K. (2018). Agent-Based Modeling in Social Science, History, and Philosophy. An Introduction. Historical Social Research, 43(1), 7–27. https://doi.org/10.12759/hsr.43.2018.1.7-27