Current Talks

These are the talks for cSplash 2017.

Exploring the Hidden with Maths--An Intro to Inverse Problems

Why do we know how the earth looks inside? How are we able to image
the insides of our body without surgery? How do we find oil under the
oceans? We know these things from the combination of mathematical
models with indirect observations. For instance, from combining a
model how earthquake waves travel through the earth with seismograms,
we are able to learn about the inside of our planet. Or, from a model
how hydrogen atoms react to a magnetic field, we can generate detailed
images of the human brain. These are examples of inverse problems. I

Prerequisites: 
basic understanding of physics
Professor: 
Georg Stadler
Difficulty: 
Medium
Room: 
512
Size: 
40
Enrolled: 
11

Fibonacci and the Golden Ratio in Flowers

Do you know of Vi Hart? Her YouTube videos on doodling, flowers, and the Fibonacci sequence are fun to watch! Try watching "doodling in math: spirals, fibonacci, and being a plant" at www.youtube.com/user/Vihart to see fascinating connections to plants. In our talk, we will pick some of what she mentions about the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, ... and phi (the golden ratio), examine them in depth, and provide a proof or two.

Prerequisites: 
Algebra and inequalities are needed. We will take a limit at one point, so it might be good to either know about limits or be willing to accept that sometimes sequences of fractions have limits.
Professor: 
Sam Ferguson
Difficulty: 
Medium
Room: 
317
Size: 
40
Enrolled: 
20

How to Talk to Strangers: An Introduction to Public-Key Cryptography

Public-key cryptography allows people who have never met or coordinated before to securely communicate with one another. To motivate its discussion, we set the stage with some simpler methods of clandestine communication and show what public-key cryptography brings to the table.

Prerequisites: 
Algebra 2 and/or Precalculus: not much more than basic laws of exponents and logarithms. There will be a couple of mostly self-contained proofs. A basic understanding of probability will be helpful, but we'll build up what we need in a jiffy. We may quote one or two results from number theory without proof, or with proof depending on time and interest.
Professor: 
Liam Hardiman
Difficulty: 
Medium
Room: 
317
Size: 
40
Enrolled: 
33

Introduction to Coding Theory

Coding Theory is the study of error-correcting codes. When a message is sent through a channel, noise can alter the message so that the data received is different from the data sent. This noise can be anything from human error or faulty transmission equipment to scratches on a CD. Error-correcting codes encodes the message in a way such that errors can be detected and fixed.

Prerequisites: 
Some background knowledge with permutations and combinations may be helpful but is not necessary. Otherwise there are no prerequisites! Anyone will a general high school background will be able to follow along.
Professor: 
Jenny Shan
Difficulty: 
Easy
Room: 
512
Size: 
40
Enrolled: 
20

Introduction to Proofs

The purpose of this talk is to introduce high school students to the two basic mathematical proofs needed for college-level mathematics: Proof by Contradiction and Proof by Induction. This foundational knowledge is necessary for every advanced mathematics class, but is not always formally taught. In the end, I will also introduce Cantor's Diagonalization Proof on the different sizes of infinity to show different types of elegant proofs mathematicians have constructed in the past.

Prerequisites: 
No Prerequisites Required
Professor: 
Youngbin Yoon
Difficulty: 
Easy
Room: 
312
Size: 
40
Enrolled: 
17

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