Physical Sciences and Mathematics

Torus Knots

This is a self-contained paper assuming no background knowledge of knot theory. A knot is a closed curve in three-dimensional space that does not intersect itself anywhere. A (double) crossing is where two strands of the knot meet; a triple crossing is where three strands of the knot meet. In this paper, a specic family of knots, called torus knots, is studied. This paper explores different properties of knots and how they are realized in torus knots. The relationship between the number of double crossings and triple crossings is investigated for a specic type of torus knot.
WHDL ID: 
WHDL-00015222

Homomorphic Encryption

A homomorphic encryption scheme built on polynomial rings is studied. The construction of irreducible polynomials in a given field is considered and implemented. Isomorphisms between two fields are found, and the method is evaluated. The scheme is ultimately implemented in SageMath, which is largely built on Python, and this is demonstrated.
WHDL ID: 
WHDL-00015213

Radiation Shielding Using Magnetic Fields

Download the PDF version of the honors project.

WHDL ID: 
WHDL-00014940

Pages

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