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Full-Text Articles in Physical Sciences and Mathematics
The Mathematics Of Spot It, Marcus Heemstra
The Mathematics Of Spot It, Marcus Heemstra
The Journal of Undergraduate Research
Spot It™ is a fun, fast paced game for people of all ages. The game appears to have a rich mathematical structure, which we investigated, using combinatorial analysis. We constructed some similar Spot It type games with a different number of cards, and displayed that some games are impossible to complete. In particular, the original Spot It game has eight objects on each card; however, it is impossible to construct a complete game (a game in which every object appears with every other object) in which every card has seven objects. We have investigated the mathematics behind the game.
Theory And Applications Of Correspondences, Heather Olson
Theory And Applications Of Correspondences, Heather Olson
The Journal of Undergraduate Research
Throughout this paper, we will examine correspondences, also known as set-valued functions. A definition of correspondences and their graphs are given. Properties of correspondences including continuity, optimization, and existence of fixed points are considered. Examples are considered demonstrating these properties. Applications in the field of Economics are introduced. Specifically the optimization of consumer utility is examined through examples.
Real Number Rado Numbers For The Equation ∑_(I=1)^(M-1)▒X_(I+C=X_M ), Melanie Zinter
Real Number Rado Numbers For The Equation ∑_(I=1)^(M-1)▒X_(I+C=X_M ), Melanie Zinter
The Journal of Undergraduate Research
This paper will examine the type of Ramsey theory concerned with the preservation of solution to specific linear equations under set partition. That is, if a solution to a linear equation exists in the natural numbers, must one also exist within one set of a partition of the natural numbers? To differentiate sets of a partition of the natural numbers from one another, it is convenient to use colors. Then a solution in just one set of a partition of the natural numbers can be referred to as monochromatic solution, or a solution in a single color. [Page 1]
Xenakis' Combination Of Music And Mathematics, Janelle Anderson
Xenakis' Combination Of Music And Mathematics, Janelle Anderson
The Journal of Undergraduate Research
My interest in using mathematics in music composition stems from the works of the contemporary composer Iannis Xenakis. As a physics and music education major I am able to combine both fields of study for this topic. Although Xenakis wrote many orchestral compositions it is his vocal music that I have concentrated on as I too am a singer. Graphic representation and new music notation are among the methods used to analyze his music. I found that his first choral work was called “Nuits,” which I proceeded to analyze. I also found myself interested in the analysis of a more …
Modeling Immune Response To Bacterial Infection, Carla Roth
Modeling Immune Response To Bacterial Infection, Carla Roth
The Journal of Undergraduate Research
Mathematical models have begun to play an important role in the study of biology. We will examine this role further by analyzing a specific model of the innate immune system's response to a bacterial infection. Beginning with the biological background of the model, we will move into an explanation of a specific model of this situation followed by a critique of the model and future work to be done with the topic.