Game theory
What do a prime minister, a general, an athlete, a lawyer, a businessman, a psychologist, a spouse and a biologist have in common? Game Theory deals with the study of the behavior of rational beings (those who decide and act on the basis of their logic and “interest”), in situations where they compete or cooperate with others.  Therefore, all of us are faced daily with difficult problems that are at the core of Game Theory, which in conjunction with Mathematics, is indispensable in the understanding of social sciences, including economics, sociology, environmental studies, and psychology.

Probability
Uncertainty is prevalent in our lives. Everyday questions, such as what’s the weather going to be this weekend and whether it’s worth playing a game of chance, or larger-scale questions like how the global climate changes, and how an epidemic develops, or even more exotic ones, such as what is the possibility of life on other planets or the risk of the earth being hit by a celestial body, cannot be answered with complete certainty. Through mathematics and probability theory we can study uncertainty and analyze these situations. 

In this course, we deal with the fundamental concepts of theory and harness its power to study games between people, companies, states and other entities when faced with situations of uncertainty. Students play games, study and analyze them and are led to the most innovative scientific ideas, to make strategic decisions, thereby increasing their profit and/or reducing their damage!

Learning Objectives

• Review and apply the fundamentals of probability to solve mathematical problems, develop an understanding of the theoretical foundations for fundamental models in game theory and model certain types of human behavior in competitive decision-making situations.
• Examine and find the balance (solution) in zero-sum, non-zero sum, signaling, cooperative games, simultaneous and sequential games and utilize real-life and computer simulations to test theories and justify conclusions.
• Share ideas and solutions to problems, both written and orally through individual exercises and collaborative projects or tournaments.

Are robots smarter than humans? Will automated control systems eventually become clever enough to control us? In this course, students embark on a journey into the world of technology, engineering, algorithmic thinking and programming. They learn how to design, build, and program their own robots and clever control systems using LEGO EV3 Mindstorms and Arduino UNO.

In the course’s robotics segment, students delve into the capabilities of LEGO EV3 Mindstorms, a versatile robotics kit renowned for its ease of use. Through engaging activities and challenges, students learn to assemble robots, utilize sensors, and program behaviors using a Scratch 3-based programming environment tailored for EV3. They discover how to navigate obstacles, follow lines, and complete tasks, all while honing their problem-solving and critical-thinking skills.

In the course’s automation segment, students explore the world of electronics and clever control systems using Arduino UNO, a popular microcontroller platform. With Arduino, students learn to interface sensors, motors, and other peripherals, enabling them to automate processes and create clever control systems like an automated plant watering system or a home security system. Using a Scratch 3-based programming environment adapted for Arduino, students write code to control inputs and outputs, create responsive behaviors, and bring their projects to life.

By the end of the course, students emerge with a deeper understanding of robotics, automation, and programming, equipped with the skills and knowledge to tackle real-world challenges in the ever-evolving field of technology.

Learning Objectives

• Develop construction skills for building robots using LEGO technic pieces, including structural stability, gear mechanisms and attachment methods, and assimilate the basic features of the Arduino UNO board including digital and analog input/output pins, power supply options, and communication interfaces.
• Understand the use and different types of sensors (e.g. touch, color, ultrasonic, and gyro sensors) to gather and use sensor data to create responsive behaviors in robots, such as obstacle avoidance, line following, and object detection.
• Learn basic principles of electronics, including voltage, current, resistance, circuits, and components such as resistors, LEDs, and how to connect and use various sensors with Arduino boards, including temperature, light, motion sensors and ultrasonic sensors.
• Develop problem-solving skills to diagnose issues, troubleshoot hardware or software problems, and debug Arduino or robot projects effectively, utilizing the basic safety practices when working with electronics.

Chance plays an important part in all aspects of life.

We take chances every day: will a shot at goal land in the goal or miss? Will we be caught in a sudden shower or not? How long do we need to wait to be served in our favourite burger house?

Chance or random variation is also a central feature of all working systems: a scientist taking measurements in a lab; a disease spreading through a population; an economist studying price fluctuation. In all these processes some element of chance or randomness are present.  Is it possible to understand and therefore model and analyse such phenomena? If so, what are the tools we need to achieve that? Do we live in a world of randomness, or, as Einstein famously claimed, no one plays dice with the universe?

During this course, we will attempt to “tame randomness” using mathematics as our compass. 

Learning objectives:

• Develop a robust theoretical understanding of the basics of probability theory. 
• Develop the capability to identify the underlying randomness in real life problems, and decide how to model and quantify it.
• Gain an in-depth understanding of the basic technical tools needed in applied probability.
• Make use of random variables and theoretical probability distributions to model simple random processes (Η).