The Mathematics Undergraduate Seminar Series presents a seminar by Josiah Reiswig on “k-Dependence on Hexagonal Boards.”

Combinatorial chessboard problems are a commonly studied topic in recreational mathematics. Rather than a standard chessboard, we examine one such problem using a rhomboidal board where each space is a hexagon. In particular, taking the standard movements of a king in hexagonal chess, we investigate the maximum number of kings that may be placed on a board so that no king is attacking more than k other kings. We develop both upper and lower bounds for this number for all appropriate values of k.

]]>Featuring MSUM students Pratik Dahal and Monica Maus

The Mathematics Undergraduate Seminar Series presents two student presentations by Pratik Dahal and Monica Maus

Pratik Dahal: The Generalized Dido Problem

The generalized Dido problem is considered. The problem deals with the classical isoperimetric inequality which is explained using concepts from the Calculus of Variations. The proof will show that the equality is unique to a circle. Moreover, the problem is generalized to curves in a sphere.

Monica Maus: Hat Puzzles

Hats are a common device in mathematical puzzles. In this presentation, we will explore both competitive and cooperative versions of hat puzzles. We will discuss cases in which someone could correctly guess the color/number of his hat using logic, and other cases where a strategy can be used to increase the chance of someone correctly guess the color of his hat. We will also take a look at Erbert’s version and what an optimal strategy would be for a correct guess, particularly in the case involving three players.

]]>Featuring MSUM students Ashley Borchardt and Paige Meyer

The Mathematics Undergraduate Seminar Series presents two student presentations by Ashley Borchardt and Paige Meyer

Ashley Borchardt: Opening Doors with de Bruijn Sequences

De Bruijn sequences are a fascinating topic in mathematics that can

be applied in a variety of different scientific, and conventional, spheres of study and application. De Bruijn sequences can be found in techniques for genetic coding, computer systems and programming, and even cracking the code to a locked door. In this presentation, we will explore what a de Bruijn sequence is and answer the questions “Can they be counted, and if so, how many are there?” We will aid our exploration by examining how de Bruijn sequences relate to directed graphs and Eulerian circuits, which will allow us to enumerate these sequences using Gustav Kirchhoff’s Matrix Tree Theorem.

Paige Meyer: The Traveling Salesman Problem

Suppose there is a salesman who needs to visit a selected set of cities. We want to find which order to visit these cities to minimize the total distance traveled by the salesman, in order to minimize the money spent on gas driving from city to city. It is not a difficult problem to calculate the total distance for a few cities, but as the number of cities increases, so does the time needed to solve this problem. We do not want to spend all day deciding on which order this salesman should visit the cities, so we want to find a way to quickly compute the route the salesman should take. During this seminar, we will discuss various algorithms that aid in solving or approximating a solution for this problem relatively quickly.

]]>The Mathematics Undergraduate Seminar Series presents two student presentations by Aaron Bohl and Samantha Landstrom.

**Aaron Bohl: The 5 Color Theorem**

We will be discuss the five color theorem — a result from graph theory about coloring the regions of a map in such a way that no two adjacent regions are assigned the same color. We will examine two different proofs of this result: one using proof by contradiction and another using proof by induction. We will also briefly discuss the four color theorem and its proof.

**Samantha Landstrom: The Golden Ratio**

This presentation will focus on the golden ratio. We will look at a couple of different ways that it can be defined. We will also examine connections to the Fibonacci sequence, along with a few of its more interesting qualities. Lastly, some examples of where the golden ratio appears in geometry, architecture and art will be shown.

]]>Talk 1: Samuel Erickson

Pattern avoidance, permutations, and the Wilf-equivalence

We will begin with a brief history of pattern avoidance, along with its roots in computer science. We will move on to discuss pattern avoidance in permutations along with Wilf-equivalence. We will then look at double-lists and pattern avoidance in double-lists. Finally, we will see results for specific cases that were obtained by my research group in the REU program at Valpo University.

Talk 2: Erin Giosta

Proofs that there are Infinitely Many Prime Numbers

Since every whole number greater than 1 can be uniquely written as the product of primes, primes can be regarded as the basic building blocks of whole numbers. How many of these building blocks are there? The fact that there are infinitely many prime numbers has been known for quite some time, but many different approaches can be used to prove this fact. During this talk we will go through the proof Euclid first used to establish this result and the ideas that he needed to develop his proof. We will then dive into different proofs found by Goldbach and Erdos that produce the same result.

Wednesday, Mar. 25 | 3-3:50 p.m. | Bridges 268

By Samuel Erickson and Erin Giosta, MSUM

Wednesday, Mar. 4 | 3-3:50 p.m. | Bridges 268

By Dr. Matthew Craig, MSUM

Wednesday, Feb. 25 | 3-3:50 p.m. | Bridges 268

By Trevor McGuire, NDSU

Mathematics Undergraduate Seminar Series presents: “Formal Languages, Finite State Automata, Regular Expressions, and Computational Problems in Mathematics (Part II)”

Wednesday, Feb. 18 | 3-3:50 p.m. | Bridges 268

By Justin James, MSUM

Mathematics Undergraduate Seminar Series presents: “Formal Languages, Finite State Automata, Regular Expressions, and Computational Problems in Mathematics (Part I)”

Wednesday, Feb. 11 | 3-3:50 p.m. | Bridges 268

By Justin James, MSUM

In this talk we will discuss de Bruijn sequences, which I claim manage this graceful dance between worlds. We will start in the world of entertainment and find ourselves naturally transported to the world of mathematics for the sake of mathematics.

In this world we will prove that de Bruijn sequences of any size exist and find out how many there are. We will then scratch our heads and wonder how we can apply de Bruijn sequences, and in an instant we will find ourselves in the world of mathematics as applied to computer science, engineering, and biology. A

short discussion about applications to computer science and engineering will quickly lead us whence we came.

We will finish by discussing a bit about how mathematicians are explorers, who move between these worlds as their needs arise. Whether they are solving problems in industry or have just found a curious object, mathematicians are explorers who search for truth, proof, and fun!

Mathematics Undergraduate Seminar Series presents: “The Magic of de Bruijn Sequences”

Wednesday, Feb. 4 | 3-3:50 p.m. | Bridges 268

By Adam Goyt, MSUM

Mathematics Undergraduate Seminar Series presents: “Introduction to Zermelo-Fraenkel Axioms (Part 2)”

Wednesday, Jan. 28 | 3-3:50 p.m. | Bridges 268

By Damiano Fulghesu, MSUM

can be written only in terms of sets and symbolic logic. But we have a problem. If sets are the fundaments of mathematics, what are the objects of which sets are made? They are sets as

well! As an example, consider the set N of natural numbers. Clearly 2 is an element of N, but can we see 2 as a set? Can we give a meaning to the expression 2∩3 ? The Zermelo-Fraenkel axioms allow us to present every mathematical object as a set and they provide a consistent theory for sets and ultimately for mathematics as a whole. In these two seminars, we present

the Zermelo-Fraenkel axioms and show how to write consistent definitions avoiding dangerous paradoxes.

Mathematics Undergraduate Seminar Series presents: “Introduction to Zermelo-Fraenkel Axioms (Part 1)”

Wednesday, Jan. 21 | 3-3:50 p.m. | Bridges 268

By Damiano Fulghesu, MSUM

Minnesota State University Moorhead will award degrees to 362 students during its fall commencement program Thursday, Dec. 18 at 1 p.m. in the university’s Nemzek Fieldhouse.

State Representative Ben Lien, a 2008 MSUM political science graduate, will deliver the commencement address. His district, 4A, is comprised of the city of Moorhead and Oakport Township. Lien will serve his second term in the Legislature after his re-election in 2014.

He grew up in Moorhead, attended Moorhead Senior High School and graduated from Minnesota State University Moorhead. During the last legislative session, he served on the House of Representatives Higher Education Finance and Policy Committee. He would like to continue serving on the Higher Education Finance and Policy Committee because of his passion for higher education as a driver of personal success for students and economic development for his district.

*Can’t attend commencement? **Watch the ceremony live.
*

Minnesota State University Moorhead is a comprehensive regional university and is a member of the Minnesota State Colleges and Universities system.

Tomorrow’s ceremony will also include live tweeting, so get your phones out and log in to Twitter! Follow @MSUMoorhead and use #MSUM2014 to show your support and excitement for the graduates!

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