September 19: Hayden Jananthan
Title: Hilbert’s Hotel and Cardinality
Abstract: “Mathematics, in one view, is the science of infinity.” ~P. Davis and R. Hersh
A strong tradition in mathematics is encountering and taming the infinite. We will enter Hilbert’s Hotel to appreciate the intricacies of infinity, and then transition to a formal approach to pinning down what “size” and “infinity” mean. We won’t encounter just one infinity, but a great many of them – so many, in fact, that it defies our notion of size. We’ll also examine some subtleties of our notion of size, discussing the Axiom of Choice and the (Generalized) Continuum Hypothesis.
October 3: Alex Vlasiuk
Title: Speed-Data-ing with R
Abstract: We all learn by example. Human babies discover speech, space and gravity by carrying out millions of experiments day after day (and it takes years to figure out this whole potty business). Now with computers everyone is able to process large volumes of data in an instant, establishing subtle relations between huge numbers of factors. We will discuss some of the tools that are allowing humanity to learn faster and better, as well as mediocre newspapers to publish increasingly meaningless charts.
October 10: Jonathan Ashbrock
Title: Teaching Computers to See: Categorizing Images with Matrices and Derivatives
Abstract: Many technologies we dream of require the solution to the problem of computer vision. That is, we need to be able to teach a computer to recognize what it sees. We can use this to help medical professionals make diagnoses, to allow self-driving cars to distinguish between a plastic bag and a person, or to eliminate the task of hand-sorting objects on a conveyor belt in a factory. In this talk we explore how exactly computers work with images while also investigating and developing one of the leading algorithms used in classify images. We will discover that an image is nothing more than a matrix and that the algorithm we desire is an application of a technique learned in a student’s first semester of calculus.
October 17: Blake Dunshee
Title: The Burden of Proof
Abstract: Academic endeavors require a set of guidelines to govern how conclusions can be made in a certain field or area of study. Some require making inferences by what is “most likely” true or maybe what is true “beyond a reasonable doubt.” So what does it mean to arrive at a mathematical truth? We will introduce the requirements of mathematical logic and discuss what it means to prove something to a mathematician. We’ll also examine a few paradoxes and faulty proofs to put our skills as logicians to the test.
October 24: Zack Tripp
Title: Touring Computability with Turing
Abstract: In 1936, the 24 year-old mathematician Alan Turing came up with a machine that provided a possible answer to a basic question of mathematics: what does it mean to “compute”? While most people know him as the “father of computer science”, we will explore the ways in which Turing’s paper gave answers to problems that the most preeminent mathematicians at the time were asking. Additionally, we will explore some of the historical background of this discovery to provide a context for why it was such a fundamentally important result.
October 31: Frank Wagner
Title: Paranormal Paradoxes
Abstract: With Halloween upon us, we investigate all things spooky in mathematics. First, we look at paradoxes so strange they will leave you knowing only that you know nothing. Then, we examine some of the more mysterious people and terrifying stories in the history of math. Finally, we delve into eerily named mathematical objects and see how their sinister labels arose. Come enjoy a spooktacular evening and try not to be too scared by the mathematical frights.
November 7: Zach Gaslowitz
Title: The Trouble with Voting
Abstract: Each election day, we are reminded of how difficult it can be to form a representative government that, well, actually represents the population — from gerrymandered districts and the electoral college to a lack of (every kind of) diversity in our candidates. In this talk we’ll dive deep and question the very core of our electoral process: “each voter picks their favorite candidate, and whoever gets the most votes wins”. But… how else would we want to pick a winner? Our answer to this question will have far reaching implications for the balance of power in our democracy.
November 14: Ryan Solava
Title: Fractals all the way down
Abstract: Fractals are fascinating geometric objects, which are often bewildering and beautiful. But what exactly are they? While often described as “self-similar as we scale”, this is not exactly true of all fractals. Here we will take a journey to pin down exactly what we mean by a fractal, and in doing so, run into the concept of fractal dimension. Along the way, we will see some practical applications of fractals, as well as lots of pretty pictures.