Introductory physics is one of the most difficult course sequences one can take as an undergraduate, due in no small part to the prerequisite knowledge of mathematics. Over the past six years, David Meltzer and his research group have developed a diagnostic meant to test students’ abilities in core mathematical concepts believed to be crucial foundations for learning physics. Concepts tested include the ability to solve systems of equations, work with trigonometric functions, manipulate fractions, and interpret information from graphs among others. With over 7000 students having taken the diagnostic, some patterns have begun to emerge, confirming work from other studies that suggest there is in fact a link between prerequisite math knowledge and success in an introductory physics course. However, most students take the diagnostic either in a classroom setting or online, so student responses are largely limited to being categorized as simply correct or incorrect. Even when students’ work is present it is impossible to assess their mindset when working through a problem without making inferences and logical leaps. In an attempt to better understand the nature of students’ misconceptions in mathematics I have conducted seven semi-formal interviews with introductory physics students just after they have completed the diagnostic where they walked me through their solutions and thought processes.

This is a primer on the mathematic foundation of quantum mechanics. It seeks to introduce the topic in such a way that it is useful to both mathematicians and physicists by providing an extended example of abstract math concepts to work through and by going more in-depth in the math formalism than would normally be covered in a quantum mechanics class. The thesis begins by investigating functional analysis topics such as the Hilbert space and operators acting on them. Then it goes on to the postulates of quantum mechanics which extends the math formalism covered before to physics and works as the foundation for the rest of quantum mechanics.

As the search for life in our universe grows, it is important to not only locate planets outside of our solar system, but also to work towards the ability to understand and characterize their nature. Many current research endeavors focus on the discovery of exoplanets throughout the surrounding universe; however, we still know very little about the characteristics of these exoplanets themselves, particularly their atmospheres. Observatories, such as the Hubble Space Telescope and the Spitzer Space Telescope, have made some of the first observations which revealed information about the atmospheres of exoplanets but have yet to acquire complete and detailed characterizations of exoplanet atmospheres. The EXoplanet Climate Infrared TElescope (EXCITE) is a mission specifically designed to target key information about the atmospheres of exoplanets - including the global and spatially resolved energy budget, chemical bulk-compositions, vertical temperature profiles and circulation patterns across the surface, energy distribution efficiency as a function of equilibrium temperatures, and cloud formation and distribution - in order to generate dynamic and detailed atmospheric characterizations. EXCITE will use phase-resolved transit spectroscopy in the 1-4 micron wavelength range to accomplish these science goals, so it is important that the EXCITE spectrograph system is designed and tested to meet these observational requirements. For my thesis, I present my research on the EXCITE mission science goals and the design of the EXCITE spectrograph system to meet these goals, along with the work I have done in the beginning stages of testing the EXCITE spectrograph system in the lab. The primary result of my research work is the preparation of a simple optics setup in the lab to prepare a laser light source for use in the EXCITE spectrograph system - comparable to the preparation of incoming light by the EXCITE telescope system - which successfully yields an F# = 12.9 and a spot size of s = 39 ± 7 microns. These results meet the expectations of the system and convey appropriate preparation of a light source to begin the assembly and testing of the EXCITE spectrograph optics in the lab.

The Micro-g NExT 2019 challenge set out to find a new device to replace the Apollo mission lunar contingency sampler in preparation for the 2024 Artemis mission. The 2019 challenge set a series of requirements that would enable compatibility with the new xEMU suit and enable astronauts to effectively collect and secure an initial sample upon landing. The final prototype developed by the team features a sliding plate design with each plate slightly shorter than the previous. The device utilizes the majority of the xEMU suit’s front pocket volume while still allowing space for the astronaut’s hand and the bag for the sample. Considering safety concerns, the device satisfies NASA’s requirements for manual handheld devices and poses no threat to the astronaut under standard operation. In operation, the final design experiences an acceptable level stress in the primary use direction, and an even less in the lateral direction. Using assumptions such as the depth and density of lunar soil to be sampled, the working factor of safety is about 2 for elastic deformation, but the tool can still be operated and even collapsed at roughly double that stress. Unfortunately, the scope of this thesis only covers the effectiveness of resin prototypes and simulations of aluminum models, but properly manufactured aluminum prototypes are the next step for validating this design as a successor to the design used on the Apollo missions.

Single molecule FRET experiments are important for studying processes that happen on the molecular scale. By using pulsed illumination and collecting single photons, it is possible to use information gained from the fluorescence lifetime of the chromophores in the FRET pair to gain more accurate estimates of the underlying FRET rate which is used to determine information about the distance between the chromophores of the FRET pair. In this paper, we outline a method that utilizes Bayesian inference to learn parameter values for a model informed by the physics of a immobilized single-molecule FRET experiment. This method is unique in that it combines a rigorous look at the photophysics of the FRET pair and a nonparametric treatment of the molecular conformational statespace, allowing the method to learn not just relevant photophysical rates (such as relaxation rates and FRET rates), but also the number of molecular conformational states.

Mutations in the DNA of somatic cells, resulting from inaccuracies in DNA<br/>replication or exposure to harsh conditions (ionizing radiation, carcinogens), may be<br/>loss-of-function mutations, and the compounding of these mutations can lead to cancer.<br/>Such mutations can come in the form of thymine dimers, N-𝛽 glycosyl bond hydrolysis,<br/>oxidation by hydrogen peroxide or other radicals, and deamination of cytosine to uracil.<br/>However, many cells possess the machinery to counteract the deleterious effects of<br/>such mutations. While eukaryotic DNA repair enzymes decrease the incidence of<br/>mutations from 1 mistake per 10^7 nucleotides to 1 mistake per 10^9 nucleotides, these<br/>mutations, however sparse, are problematic. Of particular interest is a mutation in which<br/>uracil is incorporated into DNA, either by spontaneous deamination of cysteine or<br/>misincorporation. Such mutations occur about one in every 107 cytidine residues in 24<br/>hours. DNA uracil glycosylase (UDG) recognizes these mutations and cleaves the<br/>glycosidic bond, creating an abasic site. However, the rate of this form of DNA repair<br/>varies, depending on the nucleotides that surround the uracil. Most enzyme-DNA<br/>interactions depend on the sequence of DNA (which may change the duplex twist),<br/>even if they only bind to the sugar-phosphate backbone. In the mechanism of uracil<br/>excision, UDG flips the uracil out of the DNA double helix, and this step may be<br/>impaired by base pairs that neighbor the uracil. The deformability of certain regions of<br/>DNA may facilitate this step in the mechanism, causing these regions to be less<br/>mutable. In DNA, base stacking, a form of van der Waals forces between the aromatic<br/>nucleic bases, may make these uracil inclusions more difficult to excise. These regions,<br/>stabilized by base stacking interactions, may be less susceptible to repair by<br/>glycosylases such as UDG, and thus, more prone to mutation.

This paper outlines the design and testing of a z-scan spectrometer capable of measuring the third order refraction index of liquids. The spectrometer underwent multiple redesigns, with each explored in this paper with their benefits and drawbacks discussed. The first design was capable of measuring the third order refraction index for glass, and found a value of 8.43 +- 0.392 x 10^(-16) cm^2/W for the glass sample, with the literature stating glass has a refraction index between 1-100 x 10^(-16) cm^2/W. The second design was capable of measuring the third order refraction index of liquids, and found values of 1.23 $\pm$ 0.121 $\e{-16}$ and 9.43 +- 1.00 x 10^(-17) cm^2/W for water and ethanol respectively, with literature values of 2.7 x 10^(-16) and 5.0 x 10^(-17) cm^2/W respectively. The third design gave inconclusive results due to extreme variability in testing, and and the fourth design outlined has not been tested yet due to time constraints.