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.

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.

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).