ESP Biography

We will introduce and investigate several interesting mathematical problems and games. We will look at some of the following problems: 1) Prime spirals and other regularities in their distribution 2) Fractals and how to generate them as attractors of simple systems 3) Turing's Halting problem 4) Collatz conjecture and its variants 5) Curve shortening flows 6) The Monty Hall problem 7) Infinite sums and 1+2+3+... = -1/12 8) Proofs of e^pi > pi^e 9) Proofs of irrationality of nth root of 2 for n>2 using Fermat's last theorem 10) The combinatorics of postcards in a bag and binary necklaces 11) The volume of an n-dimensional sphere 12) A proof that there are two points exactly opposite each other on Earth that have exactly the same temperature and pressure 13) A proof that an apple with two spots on it can always be divided into two halves such that both spots are on the same half. 14) A proof that a random set of lines partitioning a 2D plane can be always be colored using 2 colors 15) How to simulate a 50:50 probability using a biased coin 16) And maybe some more

We will introduce and investigate several interesting mathematical problems and games. We will look at some of the following problems: 1) Prime spirals and other regularities in their distribution 2) Fractals and how to generate them as attractors of simple systems 3) Turing's Halting problem 4) Collatz conjecture and its variants 5) Curve shortening flows 6) The Monty Hall problem 7) Infinite sums and 1+2+3+... = -1/12 8) Proofs of e^pi > pi^e 9) Proofs of irrationality of nth root of 2 for n>2 using Fermat's last theorem 10) The combinatorics of postcards in a bag and binary necklaces 11) The volume of an n-dimensional sphere 12) A proof that there are two points exactly opposite each other on Earth that have exactly the same temperature and pressure 13) A proof that an apple with two spots on it can always be divided into two halves such that both spots are on the same half. 14) And maybe some more.

I will give an introduction to objects and phenomena we can observe in the sky during day and night, their history, how people quantify them, and how they affected our understanding of the physical universe. We will discuss the coordinate systems on the celestial sphere, objects in the Solar System, artificial satellites, stellar magnitudes, types of stars, and galaxies. We will also look at tides, why the shadow of an eclipse goes from west to east rather than the other way road, and why every full moon is not a lunar eclipse and every new moon is not a solar eclipse.

This class will provide an introduction to the currently most accurate theory of gravitation - Albert Einstein's General Theory of Relativity. Using simple mathematics, we will describe the basic concepts of the theory, its applications, and consequences. Among other things, we will talk about gravitational waves, black holes, and the geometry of the Universe.

The class will give a non-mathematical introduction to our understanding of the Universe at the deepest level. We will cover quantum field theories, curved spacetime, the Big Bang and black holes, just to name a few. We will also look at unsolved problems such as the information paradox and the directionality of time.