Week 4

Our last week of COSMOS - we all agree that it went by too quickly! We started off the week with one more Discovery Lecture all about dark matter - what we know so far, and what remains to be discovered!

This week in Discrete Math, we continued practicing methods of cryptography, finishing off the week by learning RSA encryption by hand! We practiced encrypting and decrypting messages, and scratched our heads over the extremely long encrypted message Joe gave us as a challenge!

In Number Theory, we spent the week discussing Quadratic Reciprocity, and finally on Thursday, we were able to prove the Law of Quadratic Reciprocity! It is a very important theorem that has many interesting ramifications in Number Theory.

On Friday, we presented our final projects to Cluster 7 (Astrophysics), and also got to see all of their projects. We learned about binary stars, star clusters, and much more! All of the presentations were amazingly awesome, and we worked hard to make them so spectacular!

Last weekend we watched (and some of us participated in) a COSMOS Talent Show! There was music, singing, dancing, and even some skits! We also participated in the COSMOlympics, with all kinds of fun activities.

On Saturday we will share our posters with our families and friends from other clusters, and get the opportunity to look at posters from all the clusters. Then it's time to pack up and head home, taking with us memories of the best summer EVER!!!

Week 3

Week 3 of COSMOS meant finishing our study of graph theory in Discrete Math, and moving on to cryptography! We are learning several methods of encryption by hand. In Number Theory, we have continued to explore quadratic reciprocity, focusing on prime numbers in particular. In both classes, we are practicing writing proofs and collaborating together in groups.

This week, we have also had time to start working on our final projects and posters. The topics range from infinity to axioms of set theory to open problems that have still not been solved! 

Our first discovery lecture this week was particularly sweet - all about chocolate! Three members of our cluster won a prize in a raffle after the lecture, including one pound of solid chocolate (it might already be gone.) Our second lecture was all about forensics, and the study of bones in particular. We learned about the differences between crime scenes on TV, and in real life (real life was a lot messier, and smellier!)

Last weekend, we spent Saturday kayaking through a kelp forest and hanging out at the beach. We saw sea lions, otters, and even a couple of shy harbor seals! On the beach, we played in the waves, laid in the sun, and remembered to put on our sunscreen (for the most part.)

Friday we showcased our skills in a COSMOS talent show, and appreciate all of our talented peers. Another awesome week with Cluster 1 (math is fun)!

Week 2

This past week in COSMOS, Cluster 1 (math is fun!) started new topics in both classes and started working on their final projects.

In Discrete Math, students finished working with set theory and moved on to graph theory. We started by thinking about the Königsberg Bridge Problem, which prompted mathematician Euler to create the field of graph theory! We left off today wondering what the chromatic for RxR was...ask your students about it!

In Number Theory, we focused on working together in groups to write original proofs using the new method of induction. We practiced presenting and explaining our reasoning to one another, and did lots and lots of modular arithmetic!

On Monday, our discovery lecturer walked us through the history of the Human Genome Project; he was involved in the project himself! On Wednesday, our discovery lecture was about Circadian cycles in the body.

On Thursday night, we had a movie/game night with our instructors, Richard, Joe, Bob, and Sisi. We watched some cool videos about infinity and turning a sphere inside out, and played cards and did logic puzzles. There were even some Super Smash Bros competitions!  

It's been another great week at COSMOS!

Week 1 

This week, Cluster 1 began their Discrete Math course by learning some basic set theory notation, definitions, and theorems. By the end of the week, we were able to prove that some infinite sets have different cardinalities! In Number Theory, we spent the week practicing modular arithmetic and proof-writing. Students presented their own original proofs for various properties after only one week of studying this advanced subject! Outside of class, we have played many games of "Contact" (a fun word-guessing game), made new friends, and got to know our way around the UCSC campus.

Click here for photos!