Mike's Book lists

I spend a lot of my time reading books and studies that I don't circulate outside of my academic spheres. In an attempt to make the internet a better place, I've decided to make my work more public access. I'll be complining my abstracts and bibliographies over the years into one page. While a lot of this work was preliminary in my academic career and thus doesn't stand up to close scrutiny, the sources I used are still valuble! I hope others find as much value.

Fermat-Torcelli Introductory Mathematics Research. 2021. https://www.youtube.com/watch?v=hTDP1GHpl5c

Abstract:

The Fermat-Torricelli is an interesting problem with an interesting abstract solution. The question itself asks: can you find a point that defines the minimum sum of the distance between it and a finite number of points in any dimension? In my talk, I will explain not just how to find the general solution for the problem, but we will also look at solutions bound by a number of variables such as the number of finite points, the dimensional space it occupies, the shapes created by the points, and more. We will explore the varying simplicity of these different solutions in contrast to the general one, and the different types of math they use.

X-Ray entanglement Communcation Project. 2023. https://www.youtube.com/watch?v=xRd_6qs3IYo

Abstract:

In 2019, a study was published in the journal Science titled “X-Ray Imaging Goes Quantum.” The study discussed the findings of a small group of researchers using quantum optics to enhance X-Ray imaging in the simplest way possible. In my talk we will be looking at this one study in particular and what it means for the future of X-Ray imaging. By hooking the long-range RIKEN SPring-8 X-Ray up to a diamond unitary crystal with an ancilla detector and object detector, the team was able to split the X-Ray beam into two low-photon beams. These beams had successfully been quantum entangled, which they confirmed by measuring quantum activity in the ancilla detector. At the same time, a normal image was taken of a metal object with small slits. The physicists found a significant statistical decrease in “coincidence counts,” photons being imaged in positions inaccurate to the object’s known location. This means their X-Ray images were significantly clearer, using half the photons. How was this possible?

To explain this study, we will discuss Heisenberg’s Uncertainty Principle and what it means for quantum physics and light entanglement. Light behaves both as individual indivisible photons, and as divisible waves. Because an individual photon is indivisible, the shared “divided” photons when waves are split can become entangled. The definition of quantum entanglement used here is any two particles who’s quantum states can’t be described as separate from each other, but more specifically, the photon is in two locations at once. We will then discuss photon entanglement across split beams of polarized light and how a particle’s quantum state can be described with quantum statistics. In specifics, we will discuss quantum wavefunction and how it relates to a photon’s phase. In order to increase the image quality in an X-Ray, you would want to split a long-range X-Ray beam in half and entangle the two resulting beams so they share certain qualities. In this case, the team managed to entangle the light’s angular momentum going through the object detector, so the contrast on the resulting image was higher. Much clearer to see injuries with!

In terms of the build itself, the X-Ray uses a diamond crystal as a unitary space. We will be discussing what a unity space is and the importance of “measurement.” The unitary space makes sure no measurement is occurring during the split, so the quantum process can occur. By utilizing an ancilla detector to detect produced q-bits during entanglement, we guarantee the entangled photon exists in the object detector at the same moment. These real photons from the beam will all have very consistent angular momentum, in stark comparison to normal X-Rays. The coincidence counter hooked up records this data. By measuring the q-bits, we are forcing the particles to exist at the detector, fully utilizing quantum mechanics to organize the light.

There are a lot of benefits of this research, but the clearest thing shown is that the field of quantum optics has a huge future in imaging. Light is clearly influenced by basic quantum mechanics and hospitals with long-range X-rays could run their own tests with their own X-rays, as long as they have splitter crystals and ancilla detectors. This is also great because developing X-rays that use less and less photons limits hospital exposure to radiation as much as possible. If half the photons don’t have to go into the patient, that’s potentially half the radiation exposure eliminated for technicians overtime. But the true benefit is the statistical clarity, what they found occurring in the 2019 study is genuinely shocking. The coincidence counts were recorded without quantum entanglement at around 50-150 at any given location, but with quantum radiation, that number drops to ZERO at over a fourth of the data points. That’s a substantial increase in clarity. These statistics alone make me excited for the future applications of this technology in imaging.

Nonrelativistic Quantum X-Ray Physics. John Wiley & Sons. https://ebookcentral.proquest.com/lib/psu/detail.action?docID=1812460&pq-origsite=primo

Experimental Realization of Quantum Illumination. 110(15). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.153603

Enhanced sensitivity of photodetection via quantum illumination. Science. https://www.science.org/doi/10.1126/science.1160627

X-Ray Imaging Goes Quantum. Physics, 12. https://physics.aps.org/articles/v12/95

Schrodinger equation. (n.d.). HyperPhysics. Georgia State University. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html

Focus Study:

Sofer, S., Strizhevsky, E., Schori, A., Tamasaku, K., & Shwartz, S. (2019). Quantum Enhanced X-ray Detection. Physical Review X, 9(3). https://journals.aps.org/prx/abstract/10.1103/PhysRevX.9.031033

Racism + Mathematics '24 teaching project

Abstract:

This can't be put online without heavy edits due to the final project including the personal details of local middle school children, such as their race, demanors, likes and dislikes, and other such things. My analysis also included descriptions of local school interiors and how they aided teaching equitably, and thus I don't feel right sharing my work outside of Portland academic spheres. Since the project discussed minors who identified with a gender other then what they were assigned at birth, I especially don't feel comfortable posting this research online on the off-chance some delusional freak tries to find the kids. Stranger things happened to me when I was on social media, so, better safe then sorry. But I CANNOT reccomend these frameworks enough.

Young, J., Cunningham, J., Ortiz, N., Frank, T., Hamilton, C., & Mitchell, T. (2021). Mathematics Dispositions and the Mathematics Learning Outcomes of Black Students: How are They Related? Investigations in Mathematics Learning, 13(2), 77–90. https://doi.org/10.1080/19477503.2020.1845537.

Jackson, C., Mohr-Schroeder, M. J., Bush, S. B., Maiorca, C., Roberts, T., Yost, C., & Fowler, A. (2021). Equity-Oriented Conceptual Framework for K-12 STEM literacy. International Journal of STEM Education, 8(1), 38. https://doi.org/10.1186/s40594-021-00294-z

These go together

Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional Noticing of Children’s Mathematical Thinking. Journal for Research in Mathematics Education, 41(2), 169–202. https://doi.org/10.5951/jresematheduc.41.2.0169

Textbooks:

Golasx-Boza, Tanya Maria. (2021). Race & racisms:a critical approach. New York: Oxford University Press

Curren, R. R., & Blackwell Publishing. (2012). Philosophy of education : an anthology. Blackwell Publishing.

Basic Math Education

If you're interested in learning math in a college setting I reccomend these books. There is a difference between passing the standard DEQ path and studying theoretical mathematics, and proofs from THE BOOK is the easiest way to tell if pure math is for you. If you're interested in starting quanphys research, try the G Raymer book, and move on to the calculus early transcendentals and thornton texts. They're difficult but the more time you put in the more you get out.

Aigner, M., & Ziegler, G. M. (2013). Proofs from THE BOOK. Springer Science & Business Media.

Raymer, M. G. (2017). Quantum physics : what everyone needs to know. Oxford University Press.

Rogawski, J., Adams, C., & Franzosa, R. (2018). Calculus: Early Transcendentals. Macmillan Higher Education.

Thornton, S. T. (2019). Modern physics for scientists and engineers.

MY BOY PAUL

I'd basically only direct my tutors to Paul's website working at UO because it's so great if you want to learn any calc at all

Pauls Online Math Notes. (n.d.). Tutorial.math.lamar.edu. https://tutorial.math.lamar.edu/

Books I just like

Ritchie, H. (2024). Not the End of the World. Little, Brown Spark.

Zhu, X. (2016). GIS for environmental applications : a practical approach. Routledge.

creative project, sources I used for redesigning Ceyan https://docs.google.com/document/d/1GVil8oq6to6x3KollQolydc-ojpRPwWnd3uqRL7hbtg/edit?usp=sharing