## cSplash 2016

Mathematics of Soap FilmsBlowing soap bubbles is fun, but have you ever wondered why bubbles are spherical? Why do bubbles pinch off in the first place? Soap films may seem simple, but soap film models have applications in mathematics, physics, and even in biology! Calculus Crash Course: Biology and MedicineIn this course, we will explore some fundamental concepts in single-variable calculus by considering real-life problems in biology and medicine. As we investigate these biological problems, we will introduce and analyze relevant topics in calculus and see how they can help us model and solve the problems. Neural Nets: Are They Smarter Than a 5th Grader?Ever begun a Google search, only to find it predicting exactly what you were thinking of? Surprised when Facebook recognized your friend's face without you tagging them? Heard about the AI that recently defeated the World Champion in Go? If so, then you've likely come across neural networks, an important class of algorithms within machine learning/AI. This talk will introduce neural nets from scratch, prove some interesting mathematical results about them, and give you a whirlwind tour of what they can do - from translating languages, self-driving cars to predicting cancer in patients. Mathematics and Music: A Common PursuitWhile mathematics and music are now seen as divorced, with math belonging to the left brain and music to the right, the two disciplines were actually developed and taught jointly for many centuries until extraneous factors forced them apart in the Renaissance. Intro to Probability and Its ApplicationsInto to Probability and how they are useful in real life. From basics to more important concepts, we introduce the mathematics behind randomness and uncertainty. It's a wavy world: wind, water, and quantum mechanicsWaves are everywhere, from ripples in a pond to the "boom" of supersonic aircraft to even the motion of fundamental particles. Waves in water are ubiquitous yet surprisingly complicated, and we will give a flavor of how they are described mathematically. Similar mathematical tools can be used to describe the wave-like behavior of electrons, which lies at the heart of the "weirdness" of quantum mechanics. We'll talk about some of the basic formulas that link these waves together, and also about what sets them apart. |
Fundamental building blocks of natureThis talk is an introduction to the Standard model of fundamental particles and forces in nature and theories beyond the Standard model. We will touch upon the attempts to extend the Standard model to the Grand Unified Theories (GUT) and beyond to string theory - the theory of everything.An Introduction to Communication ComplexityImagine you and a friend each have a database, and are trying to figure out if the two are equal. The catch is that the two of you are far away from each other, and communicating is expensive. So it is too expensive for you to just send the contents of your database to your friend for her to check. Surprisingly there is a way to solve this problem by just sending each other an integer from 1 through 8, no matter how large the databases are!Intro to Spatial EconomicsAbout 3.5 billion people - 50\% of the world population - currently live in urban areas. This is a lot more than the roughly 1 billion that chose to dwell in cities in 1950 (30% of the population), but considerably less than the 6 billion (68%) the United Nations project will inhabit cities by mid-century. Why is that? What's so special about cities?Mathematics on SupercomputersSome science problems are so challenging that they require massive parallel computers, so-called supercomputers for their solution. I will explain what these computers are all about, what they can be used for and why it it necessary to rethink mathematical algorithms when we use them.Swimming at small scalesWe will talk about why it is difficult to swim in molasses, how bacteria swim and how to make artificial micron-scale swimmers. We will then look at some recent experiments on artificial swimmers.Wanna Bet? Interesting Puzzles from Betting & ProbabilityAre you the type who calculates the odds of getting a particular hand when you play poker? Do you enjoy explaining the Monty Hall problem to your parents and friends? If so, this class is for you! We will examine some classic puzzles that involve betting or probability. If time permits, I'll discuss the mathematical, economic, and psychological reasons why people buy insurance policies and lottery tickets, even though they know that, on average, they will lose money in the long run (and the insurance companies and lottery commissions will earn a profit). |