Math Seminar - Spring 2019

- Wednesday, February 13 - Dr. Wim Ruitenburg (Marquette),
*An Intro to Logic for Algebra*

This talk will discuss an introduction to logic for algebra. - Monday, February 18 - Dr. Wim Ruitenburg (Marquette),
*An Intro to Logic for Algebra (Part II)* - Monday, February 25 - Dr. Rachel Traylor (Marquette),
*Counterexamples, Subtleties, and Paradoxes in Probability*

Probability theory is a minefield of subtleties, and full of statements that seem so naturally true, but aren't. In this talk, we'll take a look at some subtle differences in definitions (e.g. random event v. random variable), the definition(s) of independence for random events and random variables, some counterexamples dealing with independence and conditional independence, and finally Borel's paradox, which cautions us to be very careful in dealing with conditional probability. - Monday, March 4 - Dr. Christopher Stocker (Marquette),
*Discharging via Friendships*

The friendship paradox was introduced by Sociologist Scott L. Feld in 1991 to explain why most people have fewer friends than their friends have, on average. The discharging method is a useful graph theoretical technique introduced by Paul Wernicke in 1904 as part of an attempt to prove the 4-color theorem. In this talk we will discuss variations of the friendship paradox, applications of the discharging method, and how they intersect. - Friday, April 5 - Unnar Erlendsson (Reykjavik University),
*Automatic Discovery of Polynomial-Time Enumeration Algorithms*

This talk will cover basic definitions of permutations and patterns as well as giving a short overview of how the field of permutation patterns started. I will then give a brief introduction of the CombSpecSearcher framework which has been created to aid mathematicians to find structure in combinatorial objects, and how we can use the "proof trees" it produces to automatically get polynomial-time algorithms to enumerate them. Finally I will show some examples of how we have used this framework in conjunction with HPC to enumerate almost all permutation classes with patterns of length 4. - Monday, April 15 - Dr. John Engbers (Marquette),
*Erdös' Proof of Bertrand's Postulate*

Bertrand's Postulate states that for all positive integers n > 1 there exists a prime p with n < p < 2n. We'll outline Paul Erdös' elementary proof of this result, which appeared in his first published paper (out of his over 1500 total published papers).

Previous Semesters:

Fall 2018

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