This year’s Awards Day Ceremony will take place on Friday April 26th at 3:30pm in Schenker Lecture Hall, followed by a talk given by Dr. Steven Miller.
The German Tank Problem: Math/Stats At War
Steven J Miller
Carnegie Mellon and Williams College
During World War II the German army used tanks to devastating advantage. The Allies needed accurate estimates of their tank production and deployment. They used two approaches to find these values: spies, and statistics. In this talk we describe the statistical approach and its generalization. Assuming the tanks are labeled consecutively starting at 1, if we observe $k$ serial numbers from an unknown number $N$ of tanks, with the maximum observed value $m$, what is the best estimate for $N$? This is now known as the German Tank Problem, and is a terrific example of the applicability of mathematics and statistics in the real world. We quickly review some needed combinatorial identities (which is why we are able to obtain clean, closed form expressions), give the proof for the standard problem, discuss the generalization, and show how if we were unable to do the algebra we could guess the formula by an application of linear regression, thus highlighting its power and applicability. Most of the talk only uses basic algebra and elementary knowledge of WWII.
We are pleased to announce that Jill Pipher (Elisha Benjamin Andrews Professor of Mathematics at Brown University) will deliver the inaugural UConn Mathematics Distinguished Lecture on Friday, April 19th at 3:30pm in the Schenker Lecture Hall.
Mathematical ideas in public key cryptography
Elisha Benjamin Andrews Professor of Mathematics, Brown University
President, American Mathematical Society
The problem solved by public key encryption is this: how can we create secure communication over an insecure channel (like the internet) between two people who have never met or shared a secret? The model application, unknown at the time of its invention, is you and any of your online vendors.
The concept of public key encryption was introduced in the famous 1976 paper “New Directions in Cryptography” by Diffie and Hellman. At the time it was indeed a “solution in search of a problem”: the application of encryption and authentication on a mass scale had yet to emerge from the Arpanet. In that paper, Diffie and Hellman posed an extraordinarily challenging mathematical problem and laid the foundation for a new field of mathematics/computer science. Then, in 1978, Rivest, Shamir and Adelman produced the first published example of a public key cryptosystem; their RSA encryption is still widely used for secure communication.
This lecture will provide some historical background on the subject of private and public key, encryption and explain some of the ideas involved in several different encryption systems. Particular attention will be focused on lattiice-based encryption schemes such as NTRU, an efficient public key system due to Hoffstein, Pipher, and Silverman, first disseminated in1996, which continues to remain secure against the potential speed-ups of quantum computers. In the last couple of years, national agencies and large financial institutions have recognized the urgent need for post-quantum cryptography; NIST has initiated a process to solicit, evaluate, and standardize one or more quantum-resistant public-key cryptographic algorithms. We will indicate some of the applications of lattice-based cryptosystems like NTRU to post-quantum computing and to cloud computing on private data.
On October 25th, 2018 the UConn graduate student chapter of the AMS held their Second Annual Integration Bee, where undergraduates of varying levels of mathematical background came together to test their knowledge of integrals. Students took turns in groups of six, going to the blackboard to compute various integrals on the spot. In each round a student had four minutes to compute an integral, and if time ran out or the answer was incorrect a student received a strike. After two strikes a student was out of the competition.
After an hour and half there were two finalists and five other students competing for third place. The rivalry was pretty intense among students for third place. They all stayed in the competition for round round after round until they were asked to integrate cos(ln(1/x)). Only Nick Juricic evaluated it correctly and he got third place.
The two finalists were Samuel Degnan-Morgenstern and Zhongwei Wang. The final battle between them was very dramatic and exhausting for both. After about another hour Samuel was the winner for successfully integrating 1/(e^2-x^2). Contestants who scored in the top three won prizes that were generously donated from our sponsors: Cengage, Lizzie’s Curbside Catering, and Moe’s Southwest Grill.
Although there were only three winners who officially won prizes, all students attending the Integration Bee received a nice meal compliments of the AMS and the joy of solving math problems.
Pictured from left to right: Samuel Degnan-Morgenstern (1st place), Zhongwei Wang (2nd place), and Nick Juricic (3rd place).