Abstract: Did you know that hundreds of people use the Internet everyday for everything from e-commerce to sharing spicy memes with friends? One of the technologies that underpins this is encryption– the tool that allows data to be privately shared between two endpoints. We will briefly talk about the history of encryption from the Caesar cipher to the enigma machine before delving into modern cryptographic systems. In particular, we will look at how credit cards are secured, how websites secure traffic between host and users, the ins-and-outs of public key cryptography, and its uses in email and instant messaging (like PGP, Signal, or Whatsapp). This talk will be given by a graduate of the NYCCT math program and current student at the Graduate Center’s MS in Data Science program. We will spend the last 20 minutes discussing graduate school, the NYCCT math program (from the perspective of a graduate), and employment tips.
Author Archives: Johann Thiel
Have you ever considered being a seismologist?
Abstract: Seismology is the perfect mix of complex wave mechanics, high performance computing, and fieldwork. Geophysicists travel the world to exotic places deploying instruments to monitor Earth’s physical processes such as volcanoes, active faults, and even glaciers. For my current research, I study seismic waves that travel through Earth’s mantle and are recorded by seismometers on the seafloor. We use these signals to create images of Earth’s mantle miles below the surface, similar to a CAT scan, to better understand the elastic properties and dynamic processes of Earth’s tectonic plates and the underlying asthenosphere. My experiences as an IRIS and RESESS intern were crucial in my decision to pursue a PhD in the Earth Sciences. If you enjoy physics and computer programming and are excited by the idea of working outdoors, then geophysics might be for you!
Cooperation in the Iterated Prisoner’s Dilemma
Abstract: Suppose that two bank robbers are caught by the police after a heist. They are placed into separate rooms with no means of communication and given two options: confess to the crime, or blame the other person. If both robbers confess, the judge will be merciful and each will be given a 2-year sentence. If both blame the each other, they will be each be given a harsher 5-year sentence. If one confesses and the other does not, the one that confesses will get a 10-year sentence and the other one will go free. If you were in this situation, what would you do? This is known as the Prisoner’s Dilemma.
The Prisoner’s Dilemma is an interesting game that suggests that a rational individual’s best option is to avoid cooperating with others, even though it may cause more harm. While this game may be completely analyzed when played once, what happens if the game is played repeatedly by two individuals? Is there a strategy to improve one’s overall performance? Can this give rise to cooperation? We will examine this Iterated Prisoner’s Dilemma with some computer simulations.
Abstract: Suppose you have 5 pieces of fruit whose size, color, and label (the type of fruit it is) are known. Given the size and color of an unlabeled piece of fruit, is it possible to classify it given our previous observations? How sure can we be that we are right? This is a kind of classification problem.
Decision trees (used in machine learning) can be used to help with these types of problems. In this talk we will discuss how to construct a decision tree by hand and how to use the scikit-learn python module to create decision trees for larger data sets.
Faculty Presentations for SIAM meeting
• Services provided by the Professional Development Center
• Internship Information and opportunities
• Differential-Equations competition opportunity
• When 7=4?
“A 2-Dimensional Model for Ice and Alternating Sign Matrices” by Ezra Halleck
Date: April 26, 2018Speaker: Dr. Ezra Halleck (NYCCT)Title: A 2-Dimensional Model for Ice and Alternating Sign MatricesAbstract: In the later part of the 20th century, physicists developed the Ising and Potts models for ice and interacting spins on a crystalline lattice. Mathematicians noticed connections to several constructs, including the alternating sign matrices illustrated above. There was much interest on the growth of these objects as the size increased. A conjecture on an exact count for a given size quickly arose. Finding a proof was a hot problem for years, with many discrete mathematicians adding pieces towards its proof. Doron Zielberger put in the final piece in 1995.This picture-rich and proof-light treatment will begin with the bijection between the model and the matrix illustrated above but then focus on enumerative aspects of the matrix class. There will be several hands-on activities.
“Statistical Mechanics and Combinatorics” by Ezra Halleck
Date: April 19, 2018Speaker: Dr. Ezra Halleck (NYCCT)Title: Statistical Mechanics and CombinatoricsAbstract: In this picture-rich and proof-light treatment, I will begin with the connections between the 2 subjects but focus on enumerative and bijective aspects. One example is tiling using dimers. Another is a model of ice, again in a plane. There will be several hands-on activities as well as recursive programming examples in MATLAB, Python and R.
“The science of machine learning” by Viviana Acquaviva
Date: March 29, 2018Speaker: Dr. Viviana Acquaviva (NYCCT)Title: The science of machine learningAbstract: Machine learning is the discipline of teaching computers to recognize, classify and predict relationships within data. It has countless applications in the most diverse fields: it can be used to generate to recommend movies and articles, to generate poems in the style of Shakespeare, to accelerate diagnoses of dangerous diseases, to prevent insurance fraud, to improve system security, and many other endeavors. At their core though, machine learning algorithms are just a set of clever mathematical tools that allow us to re-map complicated questions onto simpler optimization problems. We discuss our ID course, Machine Learning for Physics and Astronomy, in which we use data sets from Physics and Astronomy and Python programming to learn machine learning from the ground up. We present a selection of algorithms to solve challenges such as discovering new elementary particles, finding dark energy, identifying variable stars, and understanding the origin of galaxy shapes.
“Roulette Wheel Betting” by Johann Thiel
Date: March 22, 2018
Speaker: Johann Thiel
Title: Roulette Wheel Betting
Abstract: A typical American roulette wheel has 38 different pockets. Two are colored green while the other 36 are split evenly between black and red. One way to bet on the roulette wheel is to bet on the color (black or red) of the next spin. The payout for this kind of bet is 1-to-1.
If we start out with $30 and want to try to double our money (or lose it all trying), what betting strategies can help improve our odds? What does this have to do with matrices? We will try to answer these questions and more in this introductory talk.
“Numbers: Real vs Imaginary” by Arthur Kramer
Date: March 15, 2018
Speaker: Arthur Kramer
Title: Numbers: Real vs Imaginary
Abstract: Imaginary numbers are as “real” as real numbers. Many of the greatest minds did not fully accept imaginary numbers as “real” mathematical quantities. It took a brilliant engineer to see in them as an elegant application to solving the problems of ac electricity. Such is the story with many scientific discoveries. Prof. Kramer will explore numbers and the evolution of imaginary numbers, the intriguing history surrounding them and their eventual acceptance as a “real” number system by the scientific community.