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Full-Text Articles in Physical Sciences and Mathematics
Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter
Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter
Scripps Senior Theses
Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.
Emergence And Complexity In Music, Zoe Tucker
Emergence And Complexity In Music, Zoe Tucker
HMC Senior Theses
How can we apply mathematical notions of complexity and emergence to music, and how can these mathematical ideas then inspire new musical works? Using Steve Reich's Clapping Music as a starting point, we look for emergent patterns in music by considering cases where a piece's complexity is significantly different from the total complexity of each of the individual parts. Definitions of complexity inspired by information theory, data compression, and musical practice are considered. We also consider the number of distinct musical pieces that could be composed in the same manner as Clapping Music. Finally, we present a new musical …
Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations, Tracy Layden
Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations, Tracy Layden
Scripps Senior Theses
This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.
Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff
Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff
CMC Senior Theses
For a long time, women have struggled to gain complete acceptance in the mathematics field. The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field, through literature review and personal interviews. This paper looks at the lives of four famous female mathematicians, as well as female mathematicians in the Claremont Colleges who were interviewed for this paper. Specifically this paper examines the discrimination they faced and how they overcame this discrimination, as well as the …