Mathematics is more than just numbers and symbols on a page. Applications of mathematics are indispensable in the modern world. Math can be used to determine whether a meteor will impact Earth, predict the spread of an infectious disease, or analyze a remarkably close presidential election. In this course, students create and evaluate mathematical models to represent and solve problems across a broad range of disciplines, including political science, economics, biology, and physics.

Students begin with a review of some of the core mathematical tools in modeling, such as linear functions, lines of best fit, and exponential and logarithmic functions. Using these tools, students examine models such as those used in population growth and decay, voting systems, or the motion of a spring. Students also learn how to use Euler and Hamilton circuits to find the optimal solutions in a variety of real-world situations, such as determining the most efficient way to schedule airline travel. A introduction to probability and statistics lead into a study of using deterministic versus stochastic models to predict the spread of an epidemic and explore classic mathematical problems such as the traveling salesman problem, birthday paradox, and light switching problem.  Students are introduced to logic proofs by induction and contradiction.  Students leave this course familiar with all steps of the modeling process, from defining the problem and making assumptions, to assessing the model for strengths and weaknesses.

So small yet so powerful … We cannot see it, but it can change our everyday life! “Nano” indicates something small, something minute, about a billion times less than a meter. In these dimensions materials can go ‘crazy’ and display unique, unprecedented properties. How does the size of a material affect its properties? How do some plants manage to repel water and clean themselves? How can I make my clothes stain resistant? How does the gecko lizard walk on the ceiling? How can a robot climb onto a glass window? How do all this relate to bio-mimicry and everyday life?

Nanotechnology is linked to many disciplines, such as physics, biology, chemistry and mathematics, to produce useful applications with innovative properties. Through a series of approaches, including problem-solving, designing and conducting experiments, games, studying natural and artificial nanomaterials, searching for information, modeling, and group activities, students are introduced to the exciting world of science and technology at a nanoscale!

What is the difference between science and engineering? What are the techniques that must be applied for successfully tackling any engineering challenge, from designing and building a bed-side table to conceptualizing and sending a shuttle to space? How can a group of engineers efficiently compartmentalize a multi-system project, allocate tasks and optimize the budget provided to solve a multifaceted constructional problem? This course explores a range of topics from physics and science and bridges the gap between pure theoretical knowledge and its practical application. Through daily doses of lectures, class discussions, problem-solving and plentiful hands-on lab activities, the students will be exposed to an array of concepts, varying from Newtonian dynamics and circuitry to fluid dynamics and thermal physics and through their application, complete engineering tasks of progressively increasing complexity. 

Learning objectives:

• Apply concepts from various topics of physics into practical constructional projects with strict requirements, aimed at tackling specific problems of varying complexity and constraints.
• Train in the engineering design process, practical problem-solving and collaborative teamwork to complete assigned engineering design and production tasks. 
• Develop and train a variety of technical skills, including detailed technical drawings of projects, precision soldering of electronic components and wood work skills. 

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.