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LECTURES AND WORKSHOPS
Exploring Planar Universes: Beyond the Geometry of Euclid
In this workshop, we shall delve into different alternatives to Euclidean plane geometry, the geometry of the flat world. We shall start with a discussion of what characterizes Euclidean geometry, and how one can modify one of its defining properties in order to create new geometries. To explore interesting properties that some of these new geometries exhibit, we shall create geometric models by folding, gluing, and sewing 2D colored paper patterns. For the gamers and gaming enthusiasts, we shall also look into how non-Euclidean geometries are exploited to create exciting and exotic worlds in video games. Finally, we shall talk about how learning non-Euclidean geometries enriches our understanding of the laws that govern the world and the universe we live in.
Binomial Asset Pricing Model
The binomial asset pricing model (BAPM) is a simple way to characterize the movement of prices of risky assets, such as stocks, indices, and foreign currency. Specifically, the BAPM assumes that the risky asset's price moves up or down at each time step (e.g. one trading day), resulting to a tree-like structure for possible values of the price after a number of time steps. Thus, under the BAPM, one can think of price movements as intimately dictated by a finite sequence of tosses of a (possibly biased) coin. The first part of this presentation introduces the basic notions of coin toss or binomial probabilities. With these prerequisites, the second part discusses basic applications of the BAPM and its relation to commonly tackled problems in finance.
Not Just Pretty Plots
Graphicacy is defined as the ability to understand and present information in the form of sketches, photographs, diagrams, maps, plans, charts, graphs and other non-textual formats [wiki]. In this workshop, we will be introduced to best practices in creating pretty and effective plots. We will cover use cases and state-of-the-art tools used in the industry for data visualization. The discussion will also include the ethics of graphicacy and how charts are dialectic tools that can be used to inform and misinform.
Tiling Puzzles
What does it take to convince a mathematician that something is possible or impossible? Let's explore this idea through a series of tiling puzzles involving dominos and a chessboard. We will use these puzzles to explore the thought process of how mathematicians approach difficult problems and come up with new ideas. Most importantly, we're going to see some fun puzzles which are interesting and aesthetically pleasing in their own right.
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