## Section 1 Overall Schedule

All events are in the Ken Olsen Science Center, First Floor.

Time | Activity | Room |

9:00-9:30 | Arrival | Loggia |

9:30 | Mixer Activity |
Loggia |

9:45 | Welcome | 109 |

10:00-11:15 | 125,126,118 | |

11:15 | Break | Loggia |

11:30 | 109 | |

12:30 | Lunch | Loggia |

1:30 | Competition Begins |
109 |

2:30 | Competition Ends/Break |
109 |

2:40 | Second Short Activity |
109 |

3:00 | Closing, Winners, Thank-Yous |
109 |

## Section 2 Talks

### Subsection 2.1 Keynote Address

¶Scott Taylor, Colby College

*Title*: Almost Unknotted Mathematical Creatures

*Abstract*: Knots appear in science, culture, and mathematics. What does it mean for something to be knotted and how can we quantify the amount of knotting? I’ll give a quick survey of a few of my favorite instances of knotting and explain how mathematics can be used to quantify the knottedness of an object. I’ll introduce you to some mysterious mathematical creatures living at the border between knotting and unknotting. I will highlight work with undergraduates and other collaborators that sheds light on these objects, while raising more questions about them.

### Subsection 2.2 Contributed Papers

¶Contributed student papers will be held in three parallel sessions. Click within each talk for the abstract, or see Contributed Paper Abstracts.

Time | Speakers | Topic | Room |

10:00 |
John Kenney Iesina Tupouniua SNHU |
Bromochloromethane (Abstract) |
KOS 125 |

10:00 |
Brian Jordan Jessica McElwain SNHU |
Global Sensitivity Analysis of a PBPK Model of Bromochloromethane (Abstract) |
KOS 126 |

10:00 |
Rachel O'Connor Gordon |
Number Theory and Paul Erdos (Abstract) |
KOS 118 |

10:20 |
Marisa Jellison SNHU |
Validating a Physiologically-based Pharmokinetic Bromochloromethane Model (Abstract) |
KOS 125 |

10:20 |
Xuan Yang Gordon |
Non-Classical Logic (Abstract) |
KOS 126 |

10:20 |
Amanda Paiva Gordon |
Pythagorean Triples (Abstract) |
KOS 118 |

10:40 |
Hyunjun Park Gordon |
The prime number theorem and beyond (Abstract) |
KOS 125 |

10:40 |
Samuel Paquette Gordon |
Number Theory in Medieval Islam (Abstract) |
KOS 126 |

10:40 |
Charles Parham Qidong He Colby |
‘Knot’ Your Average Research: Knot Invariants (Abstract) |
KOS 118 |

11:00 |
Samantha Bates SNHU |
The Uncertainty of the Stock Market (Abstract) |
KOS 125 |

11:00 |
Xiang Feng Gordon |
The Chinese Remainder Theorem (Abstract) |
KOS 126 |

11:00 |
Julianne McKay Gordon |
Charlotte Angas Scott: Her Work and Women’s Mathematical Education (Abstract) |
KOS 118 |

### Subsection 2.3 Contributed Paper Abstracts

¶##### Bromochloromethane.

John Kenney and Iesina Tupouniua (SNHU)

Bromochloromethane (BCM) is a dihalomethane that is not currently regulated by the EPA for toxicity. There has been very little research done about the dihalomethane and it has mainly been examined for the inhalation into rats. Our research is to examine the effect of dermal absorption of BCM in rats. Through incorporating published data and models, we will produce a model for skin absorption of BCM to extrapolate toxicity in the body. This will add to previously gathered information on BCM and environmental impact.

(Back to Contributed Papers.)

##### Global Sensitivity Analysis of a PBPK Model of Bromochloromethane.

Brian Jordan and Jessica McElwain (SNHU)

Bromochloromethane (BCM) is an understudied chemical which is produced as a byproduct of water chlorination. As such, it is important to understand if the compound may cause undesirable effects on humans when ingested or inhaled. A 2012 paper by Cuello et al. examines the effects of BCM when inhaled by rats via a physiologically based pharmacokinetic (PBPK) model. We were tasked with performing global sensitivity analysis on the model to discern which parameters are most influential.

(Back to Contributed Papers.)

##### Number Theory and Paul Erdos.

Rachel O'Connor (Gordon)

Paul Erdos is considered one of the most prolific and eccentric mathematicians of the 20th century. His 1,500 papers prove that he made significant contributions to mathematics, particularly the fields of number theory and combinatorics. From a very young age, he was very fascinated with prime numbers and kept working until the day of his death.

(Back to Contributed Papers.)

##### Validating a Physiologically-based Pharmokinetic Bromochloromethane Model.

Marisa Jellison (SNHU)

Bromochloromethane (BCM) is a byproduct of water disinfection and is potentially toxic to humans. Several studies have been done to determine metabolic parameters. This project is centered around validating a physiologically-based pharmacokinetic (PBPK) BCM model in rats, presented in Cuello et al (2012). Confidence intervals around parameters will be discussed as well as a general assessment of the model.

(Back to Contributed Papers.)

##### Non-Classical Logic.

Xuan Yang (Gordon)

We often touch the logic. We are always applying logic in mathematical proof and life. Learning logic can even convey information more effectively in life. But in logic we find only two values, true and false. But in fact, we all know that we will encounter many statements that we don't actually know, or even do not have the ability to answer, or we can't simply describe them with true and false. What should we do at this time? I will briefly introduce the classic logic and ask some interesting questions. Later I will mainly introduce the framework of three-valued logic to solve these problems, or to expand more values in the classic logic. Finally, I will briefly introduce the fuzzy logic as the expansion of the three-valued logic.

(Back to Contributed Papers.)

##### Pythagorean Triples.

Amanda Paiva (Gordon)

We all know that sides of lengths 3, 4, and 5 make up a right triangle. But, do you know of any right triangles with sides of lengths with 3 digits? Come learn how you can create your own Pythagorean triple and a little about the history of the famous Pythagorean Theorem.

(Back to Contributed Papers.)

##### The prime number theorem and beyond.

Hyunjun Park (Gordon)

One of the most interesting sets of a number in number theory is the prime number. It provides us strong tools for proving miscellaneous theorems, but also used in our daily life like cryptography. One of the reasons for its usefulness is based on two facts. First, we can relatively easy to find a big prime number, while extremely hard to factor large numbers back into primes. It has a pattern, yet it is not obvious. Today, we will study a beautiful pattern behind prime numbers by introducing the prime number theorem. By using theorem, we can predict the nth prime number, distribution and average distance between prime numbers. After that, we will study the method used to prove this theorem, Riemann Zeta function. This will give us an important idea that prime number can be related to the complex number and beyond.

(Back to Contributed Papers.)

##### Number Theory in Medieval Islam.

Samuel Paquette

The mathematical accomplishments in Dar al-Islam are a topic which have been brought to increasing prominence in recent years. My project shall focus on the history of mathematics in the Islamic world, particularly number theory. Though most Medieval Muslim Number theory was based off of that of the Ancient Greeks, such as Diophantus, they did make their own innovations; some important figures include al-Mamum, al-Haytham, and al-Karaji.

(Back to Contributed Papers.)

##### ‘Knot’ Your Average Research: Knot Invariants.

Qidong He and Charles Parham

In knot theory, two-dimensional diagrams are extremely useful in studying the properties of knots. In particular, they help knot theorists define quantities known as ‘knot invariants’, numbers assigned to knots according to a specific rule set that not only make it possible to determine if two monstrosities actually represent the same object, but also capture the fundamental features of some very specific knots. This past summer, we explored the properties of two new knot invariants ‘net extent’, and ‘width’ with pictures, equations, and computer programs. We seek in particular to understand how the global structure of a knot is associated with the two knot invariants, as well as what characteristics of a knot we may glean from one invariant compared to the other.

Though our explorations are ongoing, we have successfully found ways to understand the behavior of both width and net extent with respect to knot structure and how the invariants can be minimized or maximized under particular conditions. In sharing our work, we shall untangle some of the theory for knots you encounter each day.

(Back to Contributed Papers.)

##### The Uncertainty of the Stock Market.

Samantha Bates (SNHU)

Since its introduction in 1792, the New York Stock Exchange has been a huge conversation point. Allowing investors to buy shares of publicly traded companies keeps the NYSE in its thriving position, but it has certainly had its ups-and-downs. There is no real way to tell whether or not it will be a good or bad day, month, or even year for the NYSE, but the concept of predictive mathematics has allowed some to think that it is actually possible to anticipate such changes. Predictive mathematics, and techniques such as data mining and predictive modelling, allow an individual to analyze past trends within a company. Analysis of data extrapolates trends and certain patterns which allows an individual to predict a future change in the Stock Market. This presentation will explore how exactly predictive mathematics and analysis can lead to one actually guessing future trends within the Stock Market. Specific techniques of predictive mathematics will be described, as long as how they are useful for the Stock Market’s anticipators.

(Back to Contributed Papers.)

##### The Chinese Remainder Theorem.

Xiang Feng (Gordon)

The Chinese Remainder Theorem

(Back to Contributed Papers.)

##### Charlotte Angas Scott: Her Work and Women’s Mathematical Education.

Julianne McKay (Gordon)

Charlotte Angas Scott (1858-1931) was a British algebraic geometer who spent her career at Bryn Mawr College in Pennsylvania. She was one of the first women to receive a PhD in mathematics, and she utilized her influence to create opportunities for the women who came after her. In this presentation we explore not only Scott’s role in women’s higher education in mathematics, but also her contributions to the field of algebraic geometry through the historical study of plane curves and their singularities.

(Back to Contributed Papers.)