Hudson River Undergraduate Mathematics Conference XIV

Siena College, April 2007

Morning sessions:

Knot Theory I, 9:50-10:45AM, Siena Hall 218

ABSTRACT: Hands-on exploration of Brunnian links and fashion design as described in the article "Brunnian Clothes on the Runway: Not for the Bashful" by Colin Adams, Thomas Fleming and Christopher Koegel.
Level: I

Applied Mathematics I, 9:50-10:45AM, Roger Bacon Hall 210

ABSTRACT: Understanding the concept of projectile motion for a skating jump can help coaches and skaters most successfully master complex figure skating jumps. In this presentation we will examine the axel jump and see how the speed and initial velocity directly affect the success of the completion of the jump. By applying Newton’s Second Law of Motion to many mathematical relations we will be able to find the skaters position in the air at any give time (t) as the skater completes their jump. This will help us see the most desirable way to achieve the best skating jump.
Level: I

Computer Science I, 9:50-10:45, Roger Bacon Hall 328

ABSTRACT: Computers are getting small: so small that soon we will reach a road block known as quantum mechanics. The next logical step would be to research quantum computing. How far are we in the research? How powerful are these machines? How can they be used? In this talk we will see just how powerful they are and the consequences it brings with this computing power.
Level: I

Mathematics Education, 9:50-10:45AM, Roger Bacon Hall 302

ABSTRACT: This talk will discuss the creation of a high school mathematics course for upper-classmen based upon some existing college courses at Westfield State College. This course will be a discussion course that takes a deeper look at mathematics than "just numbers in a book." It is the hope that this course will promote mathematics in a positive way to high school students, when what they know of mathematics seem to be what is presented to them for preparation of standardized testing.
Level: I

ABSTRACT: The presentation will chronicle a class of Algebra 2 high school students who are guided along the path to discovering Euler Characteristic. What happens and how the students react to what they discover will be shared. A copy of the lesson plan and worksheets will be available to all who attend.
Level: I

Early afternoon sessions:

Number Theory II, 1:45-2:40PM, Siena Hall 119

ABSTRACT: ABSTRACT: Have you ever thought there is a pattern to the prime numbers? This talk will include an explanation of prime numbers and how Mersenne Primes are one pattern that can be used to find prime number candidates. Mersenne Primes can be used as a guideline to lead to other patterns. The search for the highest Mersenne is in progress, however in this talk you will learn how to find prime candidates using other patterns Mersenne Primes neglect.
Level: I

Applied Mathematics II, 1:45-2:40PM, Roger Bacon Hall 250

ABSTRACT: Newton's Law of Heating and Cooling states that the rate an object heats or cools is directly proportional to the difference in temperature between the object and its environment. I investigate if and how this law can be used to model the temperature in a small reservoir. I start with air and water temperature data collected on the Westfield River, western Massachusetts, over a period of 8 months. I address the problem of 'cleaning up' the data, measurement accuracy, external influences, and other factors that may affect the model's validity. Finally, I will show a simple model and demonstrate how well it fits the actual temperatures.
Level: I

ABSTRACT: Casual observations show that river water levels jump during October, concurrent with the seasonal fall of leaves. On the West Branch of the Westfield River (western Massachusetts), this jump is approximately 0.5 m. It is likely that this jump is a direct result of trees and other plants stopping photosynthesis. As trees become less productive (less photosynthesis) they use less water for respiration and transpiration. This increases runoff, infiltration, and hence river base flow. To verify the existence of this step jump, I used SPSS to analyze historical flow records using time series analysis and hypothesis testing. Next, I determined the amount of water used by plants for respiration and transpiration, and the resulting biomass storage associated with photosynthesis (literature review). The water increase in the river is correlated to this biomass storage resulting in an estimate of the total primary productivity for the watershed. This measure is also expressed per unit area, given the watershed area. This method / tool will be useful to foresters, biologists, watershed managers, and ecologists studying productivity of remote areas.
Level: I

Statistics II, 1:45-2:40PM, Siena Hall 317

ABSTRACT: Deal or No Deal is a game show craze that has swept the nation, who would not want the chance to play in a win-win situation. However, are the contestants really making the most of their time on the show? This talk will discuss the mathematical strategies of taking the largest prize home from the game, how the banker calculates his mysterious offers, and how the financial theories behind the game are deeper than picking the right suitcase.
Level: I

Late afternoon sessions:

Abstract Algebra II, 3:30-4:45pm, Roger Bacon Hall 302

ABSTRACT: Lego Bricks are very good at making rectangular structures: they have right angles built right into them. But have you ever tried to build diagonals at different angles? Pythagoras can help in a very obvious way, but we will extend classical results using something called a continued fraction. We'll learn just what that is, and get very good at approximating irrational numbers. A warning to participants: During this talk, you will play with Lego bricks.
Level: I

Applied Mathematics III, 3:30-4:45PM, Roger Bacon Hall 250

ABSTRACT: Do you know how to solve a Sudoku puzzle? If so, you may already know the theory behind one of the most ground breaking pieces of modern medicine: the CAT scan. In this talk we will be solving a variety of puzzles from Sudoku and Challenger to transforms and CAT scans. We will take a brief look into the CAT scan procedure and how images are produced while giving the audience a chance to interpret and 'solve' these puzzles together.
Level: I

Computer Science III, 3:30-4:45PM, Roger Bacon Hall 328

ABSTRACT: An overview of Hakin's algorithm and the unsolved problem of developing a computer program to apply it: Determining if any given knot projection is the unknot. Demonstration of a program's attempt at it, and identifying the points in Hakin's algorithm that cannot be achieved with the program.
Level: II

Statistics III, 3:30-4:45PM, Siena Hall 315

ABSTRACT: In "The Wisdom of Crowds," James Surowiecki claims that the average of all guesses is more reliable than any indivdual guess. We will see if Surowiecki is wrong by using inference testing on data gathered from the audience and as well as inference testing on data colelcted in recent statistics classes.
Level: I

Topology, 1:45-2:40PM, Siena Hall 220

ABSTRACT: If you lived on a torus, and took a long journey in some direction, how would that differ from a long journey on a sphere in the same direction? Will your explorers return home? If so in how long? Every surface has characteristics that change the distance an explorer will travel. We will be examining these characteristics and imagining living in such a universe. We will also briefly discuss space-finnling curves. If you are interested in learning what kind of a world Homer Simpson would prefer to live in, tune in!
Level: I