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PhD in Theoretical Physics with a minor in Pure Mathematics
Keegan C.

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About Keegan

Bio

If you're looking for a math or physics tutor—welcome! I love learning about both subjects; in my free time, I still watch educational videos on YouTube and solve a problem here and there. I've gone over the basics many times and been taught by many different voices, and I have taught students at all kinds of different skill levels. All this makes it possible for me to find the perfect interpretation you need for everything to click, and to deliver it with an enthusiasm that keeps you...

If you're looking for a math or physics tutor—welcome! I love learning about both subjects; in my free time, I still watch educational videos on YouTube and solve a problem here and there. I've gone over the basics many times and been taught by many different voices, and I have taught students at all kinds of different skill levels. All this makes it possible for me to find the perfect interpretation you need for everything to click, and to deliver it with an enthusiasm that keeps you engaged.

My Bachelor's degree was in Mathematical Physics, with a minor in Pure Mathematics. In addition to your standard slate of physics courses—general relativity, statistical mechanics, fluid mechanics, particle physics—and the math required to back those up (probability, linear algebra, calculus, and more), I also studied real and complex analysis, group theory, chaos theory, and differential geometry. In grad school, I obtained a Master's and eventually a PhD in physics from Carnegie Mellon University. My thesis was on a topic in theoretical quantum field theory, which is like a step beyond quantum physics.

As teachers go, I am more than capable. While I was a student, I earned a reputation as the guy to seek out if you didn't get something, and I got skilled in being able to state the key ideas in several different ways to make myself understood. That experience was instrumental when I started tutoring, and even more so once I became a TA in grad school. In that role, I hosted office hours and tutorial sections, getting to help hundreds and hundreds of students learn. More than once, I stepped in for the professor of a course and taught my students something from scratch. I always enjoyed those moments the most.

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Education

University of Waterloo
Mathematical Physics
Carnegie Mellon University
PhD
Carnegie Mellon University
Masters

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Approved Subjects

Calculus

Calculus

I have taken at least five calculus courses across high school and university, and regularly use vector calculus in my graduate school work. I have studied real analysis and learned how to formalize the intuitive definition of a limit in terms of sequences alongside epsilon-deltas; generally, I have a strong grasp of what it means to work with infinities in this context. I also was a teaching assistant for a calculus course in graduate school.
Differential Equations

Differential Equations

I have taken multiple university-level courses on ordinary and partial differential equations, including one on numerical methods for solving differential equations. My doctorate thesis involved finding an analytical approximation to the solution of a nonlinear system of coupled differential equations using perturbation theory. My quantum mechanics knowledge provides a good understanding of Sturm-Liouville problems.
GRE

GRE

I had to take the GRE myself, and I found the general exam to be very straightforward. The accumulated experience of standardized testing throughout my decades in school makes it easy to identify the root of the question and how to quickly find the answer among the multiple-choice options. In some sense, standardized testing is as much an exercise in gaming the test itself as it is in learning the material, and I can help underscore the importance of both.
Linear Algebra

Linear Algebra

I took not only linear algebra, but a whole host of courses that required linear algebra as a prerequisite that turned the subject into a solid foundation for almost every other abstract mathematics topic I studied. In particular, my doctoral thesis was on the subject of quantum mechanics, a field that models physical reality in the language of Hermitian operators, projections, and linear superpositions. I am practiced at interpretation of matrices and vectors, abstract linear mappings, and even mathematical groups and algebras whose structures are similar to vector spaces.
Physics

Physics

I took AP physics in high school, majored in mathematical physics in university, and obtained a doctorate in theoretical physics. I have been a teaching assistant for about a dozen different physics courses, with which I was able to help hundreds of students learn material in a way that suited them. I once produced a simple simulation of Newtonian gravity just because it seemed like fun, and still hold a lot of enthusiasm for teaching physics to interested students.
Prealgebra

Prealgebra

I have a knack for viewing ideas from a number of different perspectives, and that is typically the kind of thinking Prealgebra seeks to cultivate. A student needs to work out how to translate word problems into math, and I can help walk them through it by identifying words with operations and finding relatable problems to drill. Together, we can identify specific hurdles and find ways of thinking around them until the problems become second-nature to solve.
Precalculus

Precalculus

With these late-middle- and early-high-school level subjects, teaching is more about meeting the student where they are and figuring out the right language to make everything click. I have spent many years practicing different ways of thinking about math problems, understanding why a certain operation or system of equations is the correct way to model a real-world problem. Working together with students, I can identify the best way to contextualize the math, step by step.
Probability

Probability

I have studied probability on its own, but also in the context of statistical and quantum mechanics, which both rely heavily on probabilistic methods and require an airtight understanding of how distributions work. There are a number of nice, diagrammatic ways of understanding basic operations in probability that I can share, and I am equipped with a few interesting, high-level examples of it being slightly counterintuitive as a cautionary tale. My experiences with being a teaching assistant for university students provide a solid foundation to draw upon when it comes to equipping students with a working understanding of mathematical materials.
Quantum Physics

Quantum Physics

My thesis was in quantum field theory, which builds on the fundamentals of quantum physics. I have passed courses on quantum mechanics at the undergraduate and graduate level with flying colors, so I know what questions to expect and have familiarity with both the Griffiths and Sakurai textbooks. I can help visualize the linear algebra underpinning the subject and interpret the wavelike character of the solutions to the Schrodinger equation in an intuitive way.
SAT Math

SAT Math

SAT math is meant to test the competency of all students, including non-mathematicians, and as a result the material is rather trivial for someone with any university-level mathematics background, much less a post-graduate doctor of theoretical physics. However, it can be intimidating for a lot of students, but it does not have to be. I can help students identify what exactly the questions want of them, and at that point it is usually no more difficult than basic arithmetic.
Trigonometry

Trigonometry

Trigonometry requires mainly the Pythagorean identities and the angle-sum formulas, alongside the basic definitions of each of the six main functions, and is something that every student of calculus is required to know inside and out. I have practiced deriving all the main identities from scratch to the point where it is faster to re-derive some obscure relationships than it is to look them up. My experiences teaching basic calculus and physics to students has necessitated some reminders of how to solve problems in trigonometry, and I feel quite comfortable explaining everything from radians and the unit circle to offering a visual proof of the angle sum formulas to items of possible interest beyond the standard scope of trigonometry.
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Hourly Rate: $40
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