Category: CAMP

Time passes remarkably quickly when each day is fulfilling. It is already Day 3 at CAMP. After some anxiety over the storm yesterday, our fantastic team felt recharged and ready for some more math, CS, and our CAMPers’ inimitable creativity.

• Uniting Communities: Long before our daily start time of 9:00 AM, our coordinator, Felicia Flores, started receiving emails from parents. Many CAMP families were still experiencing power and internet outages due to Hurricane Isaias.   

Shaylen from Hopewell, NY, told us that he had to work from the passenger seat of his family’s car and from Panera, sitting outside in the heat. Nonetheless, he missed his classmates from the COT group. Several more students, such as Eamon from the SIN group, worked from their neighbors’ backyards or houses. We were impressed with CAMPer’s commitment to continue learning and felt rewarded for our decision to keep the program running online this summer. 

 Even though we managed to keep all the classes running yesterday, some students were unable to join us. They asked us for notes of the courses they missed and were eager to catch up on work. Starting on Day 2, our instructors began putting in extra hours to summarize and upload notes for classes to CAMP’s shared Google Drive. 

• Live Interactive: With the CSC group at 11:00 AM, senior instructor Frances Stern hosted her math class. Today, we discussed the period of Caesar cipher keys and the multiplication cipher with key 3. Recall that when we were studying the Caesar cipher with a shift of 13 (ROT-13), we realized that if we applied the change twice, we returned to the original plaintext. A “period” of the function thus means the numbers of repetitions we need to return to the original message. What if we try to decide the period of each of the possible Caesar cipher keys? 

When I dropped-in for Frances’ class, her students were enthusiastically raising hands. CAMPers proposed their answers for each of the Caesar cipher keys, explaining how they got their answers. Soon, the group moved to the multiplicative cipher with key 3. CAMPers encrypted the individual letters to cipher text. When Raphaela was asked how she got the answer for the letter s (18), her classmate Isa chimed in and helped her explain. 

A highly engaging classroom environment is inseparable from our instructors’ teaching philosophy. Through communicating with parents on a daily basis, CAMP wants to ensure that students keep their cameras open during class time. To increase the attention span of students, we also fit in a break period between each class. 

Frances, who has published two books on doing math with kids (please link this to: https://www.talkaboutmath.org/), wrote the following on her teaching philosophy:

“All children can learn and enjoy mathematics if they are engaged at a level appropriate to their understanding and knowledge with the purpose of helping them to build upon these. They like to know why they are learning a topic, so starting with an interesting problem – something they do not know how to solve – and allowing them to find solutions engages them creatively while demonstrating the “why.” That can be followed with practice – questions – to gain fluency and efficiency.”

• Advanced Math in Programing: Next stop is the CS classroom, students were facing some new challenges. Remember that we made a Caesar cipher with the Python language yesterday? Today, CAMP upped our game with encoding matrices as lists, performing matrix multiplication, and operating on column vectors. Since most CAMPers have not learned about matrices at school, instructor Matt Goehrig opened his class by introducing students to the mathematical concept. 

• Art and Cryptography: In the art classroom today, instructors Tiffany and Chelsea let students explore abstract art cipher in physical, or digital settings with Pixel studio. CAMPer made a pictorial alphabet using graph paper or the app. Using their unique visual alphabet, CAMPers will then create an artwork containing a secret message. 

See you again soon. 

For more updates: follow us on Facebook (https://www.facebook.com/BardMathCircle/), Instagram (https://www.instagram.com/bardmathcircle/), and Twitter (https://twitter.com/bardmathcircle)! 

Welcome to Day 2 at CAMP 2020. It is raining in most of the places where our CAMPers are. What a chilly day to stay dry, make new friends, and learn cryptography under creative settings! 

Things started coming together today. Our instructors prepared different plans for their groups. In the TAN and COT sections of Computer Science, Matt Goehrig reviewed some commands with his students. They discussed Numify and the If statement before revealing the topic of Day 2: creating your own Caesar Cipher. 

Caesar Cipher, or Caesar’s Cipher, refers to one of the most straightforward and widely known encryption techniques. It is a type of substitution cipher. Each letter in the plaintext is replaced by a letter with specific predetermined numbers of positions down the alphabet.

Although students have learned how to manually encrypt and decrypt with Caesar Cipher, programming the cipher into digital code still provides a lot of conveniences. If CAMPer wants to quickly encode a long plaintext to their friend, they can now build a computer program. This also enables the recipient to decode a complicated cipher text without hours of labor. 

To program a Caesar cipher into the Python computer language, Matt asked the students to build a flow chart of their plan, adding the functions they needed and putting each command in the right sequence.

1. Turn the message into numbers
2. Add the secret number to each number 
3. Turn that into letters 

At the COT group, Matt chose the message “BardMathCamp” and the secret number 11 as examples during his demo. CAMPers utilized the commands they learned yesterday to successfully synthesize them into a pair of encryption/decryption algorithms: a simple Caesar Cipher program. The group also modified the code to translate complete paragraphs of plaintext.

For the art class, SIN, CSC, and COS sections created Zoom backgrounds with Pixel Studio, a pixel art editor commonly used by artists and game developers.

We asked the students to install the app before our class. So that they can get to know the app and be prepared for future courses, Chelsea Cai leads CAMPers step by step through screen share on Zoom. CAMPers first created three layers and explored with the tools, including gradients, pencil, fill, etc. 

At the SEC, TAN, and COT groups of the art class, students had a hands-on experience creating abstract art ciphers with the Pigpen Code, the Red/Blue code, and the Crease code. Unlike most of the cryptographic methods we encountered, the pigpen cipher uses symbols instead of letters. Students learned to exchange letters for symbols, which are fragments of a grid. 

(example of a Pigpen Cipher)

This cipher method was used by the Freemasonry and during the American civil war. Even if our encrypted text was hacked, we could always change the key by rearranging the letters in grids. 

CAMPers also tried the Red/Blue code with our instructor Tiffany Smith. A red/blue system is created when the sender uses a light blue pencil to write their message. Then, they cover that message using red cross-hatching and a highlighter. The sender’s code can later only be revealed using a red piece of cellophane, which makes the light blue writing visible again. 

Last but not least in Tiffany’s art class, we practiced writing a Crease Code. By folding a paper multiple times and placing the secret letters or message on the creases, this technique is somewhat tricky. It requires us to fill the blank space with words that compliment the notes and constitute a complete sentence.  

In the math classroom, Erin Toliver led her class with the COS group. We practiced Modular (clock) Arithmetic, encoding, decoding of Caesar Ciphers with different shifted codes. Tomorrow, we will start pairing students for more encryption and decryption exercises. 

Hosted by our TAs: Jazmin, Olivia, Yuxuan, Tsitsi, Alex, Gigi, and CAMPers themselves, the activity periods were filled with diverse projects. Raging from games like Mastermind, Jeopardy!, Zip Zap Zop, SET, to teaching the Binary Number trick, students had a relaxing and fun ending of Day 2. 

For more updates: follow us on Facebook (https://www.facebook.com/BardMathCircle/), Instagram (https://www.instagram.com/bardmathcircle/), and Twitter (https://twitter.com/bardmathcircle)!

It is Day 1 at CAMP 2020, and the first year that we are holding the program online. Since cyberspace shortened the distance between us, the Bard Math Circle received numerous applications from around the country. We see students’ excitement over running into old friends and connecting with new CAMPers in Zoom classrooms. 

We distributed our CAMPers into the six groups: SIN, COS, TAN, SEC, CSC, and COT (trigonometry!) according to their grade level and the questions we sent out on the application form. 

For the morning groups, students and our staff members had an early start of their day during summer. This year, our Math, Computer Science, and Art classes are designed to revolve around the theme cryptography. 

After each group met their instructors, the math class introduced students to vocabularies like plaintext, ciphered or coded text, encode, decode, encrypt, decrypt, etc. The LOWERCASE stands for the plaintext, and the UPPERCASE is the cipher message. Things started to get heated when our teachers brought up a series of mathematical problems related to simple methods of cryptography: substitution, multiplication, keyword cipher, and the period problem. In a substitution cipher, each letter of the alphabet substitutes another letter (e.g., ROT-13: rotate by 13 places). On the other hand, in a multiplicative cipher, the number you multiply plays a crucial role in determining the cipher. 

If we built a times-3 cipher that multiplies the numbers by 3. As an example, we encrypted the letter c. The number for c on the cipher strip is 2, so they multiplied 2 times 3 and got 6. Since 6 is the number for g, they encrypted c as G. 

After a fifteen minute break, we resumed for the art class. The cipher wheel is a circular device using two discs. In lowercase and uppercase letters, the alphabet is recorded on both discs, creating a key to decipher coded messages. CAMP director, Japheth Wood, had mailed the material along with the CAMP t-shirts to the students beforehand. 

To generate an encoded message using their own cipher wheel, students first need to align the lowercase letter a with any number from 0 to 25 on the center of the wheel. Determining the key (the number) they are using, CAMPers encrypt the plain text according to the matching uppercase letters on the inner disc. Noah in the SIN group sent his classmates the following text:

ROVVY 10

According to his key: the number 10, we figured out that he said “HELLO.” The class also decoded a few messages pre-designed by the instructors. Chelsea, a senior instructor for the art section, shared her screen for a long encoded message. We notice that the letters K, Y, V are repeating themselves: these letters stand for “the” in her sentence: “the unicorn is the national animal of Scotland.”

During the CS class, students learned some basic necessary commands on Google Colaboratory: ord, chr, append, join, print, for/in, if/else, return, def, print, strings, lists. Further, CAMPers explored how each command works and proposed various questions on how to change the command on their copy of the shared document. 

Approaching the end of day one, our junior staff planned various activities for their group tailored to students’ interests. Some led the classroom to further explore the topic they left off, and some invited CAMPers to play the SET game as a tradition of our program. 

We had a productive first day at CAMP 2020. Stay tuned for more updates on Facebook (https://www.facebook.com/BardMathCircle/), Instagram (https://www.instagram.com/bardmathcircle/), and Twitter (https://twitter.com/bardmathcircle)! See you tomorrow. 

Welcome to CAMP 2020! Here is our list of wonderful staff.

Our last day of Camp began in a flurry of activity as Campers received their T-shirts and made the final touches on the Rubik’s Cube Mosaic.

In Math class, we learned magic tricks designed to help us understand math better using addition. We finished off our lessons and challenges from the week and prepared to present our knowledge to our parents,

After, in Art, we finished the last of our clay projects and collected all the art we had created throughout the week, including our origami creations and our playing cards. We discussed and observed how these creations connected with what we had been learning about fractals.

In Computer Science, we spent the last day finishing our project of creating a Sierpinski Gasket Triangle on the Computer and also collected all of our previous codes including our bifurcation maps to show our parents during open house.

We ended camp with an Open House for parents, where the children all presented their art pieces and projects. Camp ended with lots of amazing reviews and lots of nostalgia, ready for the school year to begin.
-Tsitsi

Day 4 of C.A.M.P. began with a flurry of activity as more campers joined the effort to complete the Mosaic and taught each other new games such as Backgammon and chess.

In Computer Science, we continued on our journey to learning and mastering NetLogo. We also continued to deepen our knowledge of computers and their systems while utilizing concepts from Math to supplement our computer science lessons.

After, in Art, we finally got to work with clay. We used it to creating amazing fractal designs and also showed how precise we could be in our measuring.

Lastly, in Math, we did advanced math using fractals and learned how to calculate the dimensions of any shape. We also learned how there are more than just 1D, 2D, and 3D figures, and sometimes the dimension can be between numbers and less than one. Math challenged us to think outside of the normal constructions of what we hear in everyday life but it also pushed us to connect what we see with what we are learning.

Our electives today included capture the flag, drawing, and the Rubik’s cubes. With our Mosaic almost finished, it’s a race against time.

Day 3 of camp began with  race to complete the Rubik’s cube mosaic! This has been a lengthy task that will require manipulating 400 Rubik’s cubes.

In Computer science, we began forming fractal images through NetLogo and utilizing the concept bifurcation from Mathematics. We managed to return the output of the function we used through code thereby demonstrating the significance of computers to calculate our functions. All of this at the press of a button!

Art gave us a creative outlet as we finished creating our very own decks of cards and moved on to creating 3D figures with fractal designs.

Finally,  in our last class, Math, we learned another way to create the Sierpinski Gasket using a large sheet of paper with an equilateral triangle on it. We marked the midpoints of this triangle, and then connected all three points to create 4 triangles inside the large triangle. We then repeated  this process, finding the midpoints in each of the enclosed triangles and connecting them to create smaller triangles within a larger triangle.

For our electives, we had the option to work to complete the mosaic, to play an intense game of Mafia, or to go on a relaxing Nature Hike through the Meditation Garden. Needless to say, today was a very busy day for all our campers.

Everyone arrived bright and early full of energy for the second day of CAMP! We began with a variety of warm-up activities to get our brains on track for more math and logic. We had teams learning to solve Rubik’s cubes, campers pairing up to play Rush Hour and other campers solving a variety of puzzles.

Soon after in computer science, we continued our challenge from the previous day with some groups going more in-depth to understand computers and other using NetLogo to make create variables such as turtles and cows that can draw squares in the language. They were challenged to be able to kill their turtles and perform various other actions on these variables. Their next challenge: Functions.

In Math class, campers reviewed information from yesterday and then dove deeper into fractals. They analyzed the rules for creating the Sierpinski Gasket fractal.  They began forming connections between the mathematical connection of fractals to their application in Computer Science.

Lastly, in Art, we began making our very own deck of cards! Each camper made their own set, with 4 houses. They had the option to make up their own houses or use the traditional hearts/spades/diamonds/clovers. We used stamps and various other art materials to create them.

At the end of the day we hiked to the Parliament of Reality and learned how to grass whistle. Others took their creativity to the studio and went painting and the last group had an intense Rubik’s cube championship.

-Tsitsi

It’s the first day and there’s lots of excitement and nervousness as old friends connect and meet new friends over an assortment of games including rush hour, human feline puzzles and huge 10 person rounds of Set.

In Computer Science, our teacher Yulia pretended to be a Robot and challenged the campers to right specific instructions that would lead her to draw a square onto the  board. We divided up into groups of three and our biggest challenge was to write instructions as specific as possible otherwise our robot had a lot of room for misinterpretation. The goal was to demonstrate how coding requires precision in wording, efficiency and thoroughness so that Yulia would follow their exact directions and draw a vertical line up instead of drawing a vertical line down. We then shifted to the computers and focused on the basics  of computer science and how it compares to mathematics.  After a brief review, we began exploring NetLogo, where we hope to be able to make our variables, turtles, draw a square  like we did our Robot Yulia.

In Mathematics, we started with listening to Michael Frame’s Yale TedX talk.  We learned about fractals, which are patterns made from infinite repeats, but do not exist in real life since there are a finite number of repeats. After the video, we moved on to creating the fractals. To create the fractals:

1. Draw a large Square on Graph Paper, labeling the x and y coordinates up to 1
2. Mark the coordinates(0,0),(0,1),(1,0),(1,1),20 other points within the square and three points on the edges

1. • To each point: Halve the x, and y and lightly plot in a new color and connect the two points
   • Add 1/2 in the x direction to the shrunken value from step 1 and plot in this same new color
   • Add 1/2 in the y  direction to the shrunken value from step 1 and plot in this same new color
   • Take a new color and apply the same rules to these new points . Repeat. Observe the movement of the point as it forms a fractal.

In Art, we explored centuries old puzzles including Tangrams, T puzzles, Mysto Squares and so much more. We collaborated with friends new and old to defeat the mystery behind each game.

The students ended their first day at CAMP with an intense games of 4 corners, sharks and minnows while also having the option to hike to Blithewood to view the lawn razing goats, or practice the lost art of paper folding: Origami.

-Tsitsi