Can you do the Philippine candle dance, the Dirac belt trick, or the Feynman plate trick? Whether your answer is yes or no, this event will engage you in this and far beyond in discovering and understanding the most mathematically efficient way to untangle a double-twist in 3-space. Limber up!
Cryptology offers an ideal setting to give students a powerful and successful experience in mathematics. Cryptologic examples allow students to connect new content with prior knowledge, and provide students the opportunity for productive struggle with challenging material. Cryptologic contexts offer students multiple entry points to rich questions and provide all students an opportunity to engage with the material, to propose unique problem solving strategies, and to build upon the ideas and conjectures of their peers. Cryptologic applications allow students to take ownership of their problem solving strategies and increase their confidence as learners. Oh yeah...cryptology is fun!
In addition to providing some justification for the above claims, I will present a variety of examples from cryptology that could easily find their way into existing courses in probability, statistics, quantitative reasoning, linear algebra, and abstract algebra.
Sports drafts and divorce settlements are examples of situations where players take turns selecting indivisible goods. Like other topics in fair division, the situation is made more interesting because people may
value the goods in different ways. In this talk, we focus on the case of two players, where the machinery of permutations is surprisingly applicable. How many possible outcomes are there? In what circumstances do both players get their best possible outcomes? How can one best take advantage of knowing the other's preferences? What happens when a player's motivation switches from greed to spite, the common good, or selfless altruism? In this colorful talk, we'll sample some applied algebraic combinatorics and address these issues along with the provocative question of the title.
Whether a resource -- such as income -- is distributed evenly among members of a population is often an important political or economic question. The Occupy Movement has recently drawn more attention to the fact that income inequality in the United States is increasing. How can we measure this inequality? How can we decide whether the distribution of wealth in this country is becoming more or less equitable over time? How can we decide which country has the most equitable income distribution? This talk describes one tool, the Gini index, used to answer these questions. Aimed at students, will use integral calculus.
Karen is principal investigator on the NSF-funded Common Vision project, an initiative aimed at improving undergraduate learning in the mathematical sciences, especially in courses typically taken in the first two years. At the end of her talk, she will briefly describe the project. She will be happy to answer questions about the talk, Common Vision or both!