booklet - CUMC - Canadian Mathematical Society

INTRODUCTION TO GAME THEORYALEXANDRE LAVOIEGame Theory is widely used to explain the underlying choices of economic agents.With this angle in mind, I will present an introduction mainly focusing on the workof Von Newmann and Nash. Open to anyone (I assume no prior knowledge in Economics).WAVES IN THE SOLAR TACHOCLINEALEXEI BORISSOVIt has been observed with helioseismology that the core of the sun exhibits solidbody rotation, while the outer shell has a rotation gradient from the equator to thepoles. The tachocline is a thin layer at the interface of these two different rotation profilesand is the root of many surface phenomena of the sun. We may also examine thedynamics of the tachocline, in particular the waves that propagate through it. In thistalk we shall apply the governing equations of magnetohydrodynamics to model thetachocline and see what types of waves can exist.A BRIEF INTRODUCTION TO "SURREAL NUMBER SYSTEM" WITH FOCUS ON ITS ARITH-METICAL ASPECTALIREZA RAFIEISurreal Number system is a construction of numbers, containing Real numbers aswell as Infinitesimals and Transfinites (Numbers which their absolute value is respectivelysmaller or larger than the absolute value of any Real number) with the propertyof total order. We will discuss the fundamental construction rules of the system, thensome arithmetical operations (including the basic operators) will be defined and eventuallythe surreal form of Transfinites and Infinitesimals will be derived. By the end,One should be able to meaningfully evaluate expressions like "Square root of the numberof elements in the Natural number set" or "Smallest possible positive number timestwo" or alike. One doesn’t need to know more than set theory and logic at the levelsof secondary school and have patience for some fundamental proofs to fully comprehendthe lecture, though pre-exposure to undergraduate-level formal logic, recursiverelations and basic group theory would be beneficial.Required Background: Basic set theory and logic16