## Paradoxes in Probability

Uncertainty is all around us, yet it often runs counter to our intuition. In this talk, we will be looking at some of the most famous paradoxes in probability theory and learn how to deal with them in real life.

These are the talks for cSplash 2017.

Uncertainty is all around us, yet it often runs counter to our intuition. In this talk, we will be looking at some of the most famous paradoxes in probability theory and learn how to deal with them in real life.

Prerequisites:

Knowledge of basic set operations (union, intersection, complement), previous exposure to probability is useful but not necessary.

Professor:

Yiming Zhang

Difficulty:

Easy

Room:

312

Size:

40

Enrolled:

35

The projective plane is an amazing place. Every pair of lines meets in a point. Circles, ellipses, parabolas, and hyperbolas are all the same shape; and all quadrilaterals are the same shape. You can turn all the points into lines and all the lines into points, and nobody will notice. The price you pay is that you can't compare two distances or two angles, and, if you have three points on a line, you can't say which one is in the middle.

Prerequisites:

Basic geometry and algebra.

Professor:

Ernest Davis

Difficulty:

Medium

Room:

317

Size:

40

Enrolled:

20

Spectral analysis gives us a different way of looking at the physical world and at our own brainpower as the sum of waves in space and time. When the great mathematician-physicist Isaac Newton decomposed white light into the colors of the rainbow, he enlarged our understanding of color. The mathematician Fourier led the way into representing all signals as sums of sinewaves. The unifying concept of Newton and Fourier is the frequency spectrum.

Prerequisites:

Trigonometry, basic algebra

Professor:

Robert Shapley

Difficulty:

Medium

Room:

512

Size:

40

Enrolled:

18

Why are big drops flat and small drops round? How does a bubble begin to pop? We will answer these and other questions both the “easy” way and the exact way. You will learn some basic physics relevant to how fluids work, but along the way also see how dimensional analysis can be used to understand complex problems.

Prerequisites:

Basic algebra

Professor:

Michelle Driscoll & Rodrgio Guerra

Difficulty:

Medium

Room:

312

Size:

40

Enrolled:

4

Every object has it's building blocks. For walls, that may be bricks. For Protons, that building block is quarks. For integers, those building blocks are prime numbers! In this lecture, we will dive deep into the world of number theory and discover the amazing properties of prime numbers and how they pertain to cryptography and the natural world!

Prerequisites:

There aren't really any prerequisites for this talk except maybe a little bit of modular arithmetic. Don't worry if you're not familiar with the topic though. I will explain it.

Professor:

Nick Lewis

Difficulty:

Medium

Room:

517

Size:

40

Enrolled:

28

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