Undergraduate Mathematics Seminar

The Undergraduate Mathematics Seminar has talks on a variety of topics at a level accessible to undergraduate students. Our speakers will include our faculty, our graduate students, our undergraduate students, and some visitors. Everyone is welcome and encouraged to come.
For more information contact Ross Chiquet.

Fall 2019

For the Fall 2019 semester we will meet every other Wednesday at 4:00 in 201 Maxim Doucet Hall.

• 4 September 2019
  Linear Search Problem with Low Sensing
  Argen West
  Abstract: We consider a generalization of the linear search problem where the searcher has low sensing capabilities. We first show the necessary conditions for an optimal search plan to exist. We then investigate properties of optimal search plans and show that optimal search plans are defined by an underlying recurrence relation.
• 18 September 2019
  Distance Sampling: A statistical ecology method
  Caleb Macdonald
  Abstract: Distance sampling is a statistical ecology technique widely used by biologists to estimate abundance or density of objects of interest, usually animals. This technique is especially useful in those circumstances where it is not reasonable to assume that all individuals of interest will be observed in the sample area. The method is so named because the information collected and used for statistical inference is the recorded distance from the observer to the objects of interest obtained by line or point surveys. In this talk we will give background and motivation for the technique; discuss the statistical considerations, and demonstrate how the method works using a simple example. No prior knowledge of statistics is assumed.

Spring 2019

For the Spring 2019 semester we will meet every other Wednesday at 4:00 in 201 Maxim Doucet Hall.

• 13 March 2019
  From Observation, to Pattern, to Conjecture, to Proof: A Simple Theorem from Calculus and Geometry
  Jonathon Hebert
  Mathematics Department, UL Lafayette
  Abstract: In this talk, we will explore a common observation made by calculus students and attempt to make a more general claim. We will do so by examining other cases, looking for a pattern, forming a conjecture from that pattern, and finally, proving our conjecture.

Fall 2018

For the Fall 2018 semester we will meet every other Tuesday at 3:30 in 201 Maxim Doucet Hall.

• 11 September 2018
  Cantor's Theorem and Infinite Cardinals
  Jonathon Hebert
  Mathematics Department, UL Lafayette
  Abstract: The measure of a set's size, in the sense of how many elements it contains, is called its cardinality. The notion of cardinality for finite sets is an intuitive concept, and this concept can be extended to compare the cardinalities of infinite sets. It turns out that for cardinality, some "infinities" are larger than others. In this talk we'll compare the cardinalities of various infinite sets, and we’ll discover a way to generate sets of higher cardinality.
• 25 September 2018
  Frogs and DEs and Chaos, Oh My!
  Ross Chiquet
  Mathematics Department, UL Lafayette
• 9 October 2018
  Science Day 2018 presentation preview
  Several undergraduate and graduate mathematics students will speak
• 6 November 2018
  Polyhedra: from Plato to present day
  Robin Koytcheff, UL Lafayette
  Abstract: Polyhedra are generalizations of polygons to dimension 3 (and higher). The platonic solids, which generalize regular polygons, were known at least as far back as the 5th century BCE. Polyhedra also appear in the forthcoming local film Bending Lines: the Sculpture of Robert Wiggs on the late Lafayette-based sculptor. We will describe the five platonic solids and show that they are the only regular polyhedra. We will then discuss related concepts, such as the question of tiling space with polyhedra and the question of embedding graphs in the plane.
• 20 November 2018
  Number-Theoretic Properties of the Golden Ratio
  Patrick Leleux, UL Lafayette
  Abstract: The golden ratio finds itself at the center of great mystification, often compromising its true uniqueness found in pure mathematics. It possesses several unique properties in several branches of mathematics, not the least of which being Number Theory. Designated for discussion will be the golden ratio as the extreme and mean ratio, the limit of several recursive sequences, it’s representation as a continued fraction and a continued radical, and a solution to an interesting equation.

Fall 2017

For the Fall 2017 semester we will meet at 4:00 on every other Monday in 201 Maxim Doucet Hall.

• 11 September 2017
  From Observation, to Pattern, to Conjecture, to Proof: A Simple Theorem from Calclulus and Geometry
  Jon Hebert
  Mathematics Department, UL Lafayette
  Abstract: In this talk we will explore a common observation made by calculus students and attempt to make a more general claim. We will do so by examining other cases, looking for a pattern, forming a conjecture from that pattern, and finally, proving our conjecture.
• 25 September 2017
  A statistical analysis of Bangkok traffic accident data
  Kanokwan Channgam
  Mathematics Department, UL Lafayette
• 16 October 2017
  Descartes and Fermat: an unlikely collaboration
  Caleb MacDonald
  Mathematics Department, UL Lafayette
  Abstract: Rene Descartes and Pierre Dr Fermat's mutual enmity is well known and was exacerbated by their near simultaneous publications of methods for finding tangents. We will work through a sample problem using Descartes circle method, Fermat's line method, and what has been termed 'Descartes line method', but which is really a clarification of Fermat's method. Time allowing we will gesture in the direction of a derivation of the power rule using this line method.

Spring 2017 -- archive

For the Spring 2017 semester we will meet at 4:00 on every other Wednesday in 201 Maxim Doucet Hall.

• 8 February 2017
  Algebraic Geometry: What is it and how is it used?
  James Kimball
  Mathematics Department, UL Lafayette
  Abstract: A central theme in Algebraic Geometry is the study of solutions of systems of polynomial equations in one or more variables. The solutions of these systems of equations form geometric objects called varieties. The corresponding algebraic objects are called ideals. In this talk, we will introduce these objects at the undergraduate level and provide many concrete and motivating examples. With these and algorithms for manipulating systems of polynomial equations, we can introduce a few fundamental results in the field of Algebraic Geometry.  Time permitting, we will introduce a few of the more interesting applications, such as robotics and error-correcting codes.
• 22 February 2017
  On p-adic numbers
  Leonel Robert
  Mathematics Department, UL Lafayette

Fall 2016 -- archive

• 7 September 2016
  How Much Math Does a Poker Player Need to Know?
  George Turcu
  Mathematics Department, UL Lafayette
• 21 September 2016
  e is transcendental
  Leonel Robert
  Mathematics Department, UL Lafayette
  Abstract: First I will discuss what it means to say that e is transcendental. Then I will go through the proof.
• 5 October 2016
  Irrational Numbers: From Ancient Greece to 20th Century France
  Henry Heatherly
  Mathematics Department, UL Lafayette
• 19 October 2016
  We will not meet this week. We will meet next week instead!
• 26 October 2016
  Science Day 2016 presentations
  Several students will give previews their Science Day presentations
• 16 November 2016
  A Quick Introduction to Goedel's Theorem
  Arturo Magidin
  Mathematics Department, UL Lafayette
  Abstract: Goedel's Theorem states that in certain types of axiomatic systems, we can either prove both a proposition and its negation, or else there are propositions that can neither be proven nor disproven. It was a major accomplishment, and Goedel is often called the greatest logician since Aristotle.
  We will give a quick overview of the history that led to Goedel's Theorem, as well as making precise exactly what it says (and what it does not say); we will also explain how the proof works. If time permits, we will go into some of the details of the proof.
• 30 November 2016
  The Cantor Set in the Context of Totally Disconnected Spaces
  Cody Nash
  Mathematics Department, UL Lafayette
  Abstract: The Cantor Set is a subset of the set of real numbers that has many very interesting properties. Georg Cantor was the first to introduce the Cantor Set. The Cantor Set was used extensively by Cantor and his colleagues when they were creating new, fundamental ideas in the field of point-set topology. One of these interesting topological properties of the Cantor Set is that it is a totally disconnected space. In this talk we will review some introductory material to aid in understanding what a totally disconnected space is. This introductory material will include equivalence relations, some ideas about what a topology on a set is, and some terminology used in the field of topology. After the introductory material, we will discuss what it means to be a totally disconnected space. This will lead to two supplementary theorems which will aid us in proving that the Cantor Set is a totally disconnected space.