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Math, Physics & Python Tutor | College Instructor
Juan O.

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Hourly Rate: $60

About Juan


Bio

I completed bachelor’s degrees in Mathematics and Physics at Universidad de los Andes with a 4.42/5.00 GPA. My advanced coursework includes Measure Theory, Functional Analysis, Differential Geometry, Honors Probability, Mathematical Statistics, Stochastic Processes, Numerical Analysis, Complex Variables, Quantum Mechanics, and Statistical Mechanics. I am also currently conducting research in mathematical physics.

I have six years of teaching and tutoring experience in both classroom and...

I completed bachelor’s degrees in Mathematics and Physics at Universidad de los Andes with a 4.42/5.00 GPA. My advanced coursework includes Measure Theory, Functional Analysis, Differential Geometry, Honors Probability, Mathematical Statistics, Stochastic Processes, Numerical Analysis, Complex Variables, Quantum Mechanics, and Statistical Mechanics. I am also currently conducting research in mathematical physics.

I have six years of teaching and tutoring experience in both classroom and one-on-one settings. At Universidad de los Andes, I independently taught a Vector Calculus section, worked as an in-person tutor in mathematics, physics, and Python, and served as a teaching assistant for courses ranging from Differential Equations and Classical Mechanics to Particle Physics, General Relativity, and Modern Cosmology. I have also provided paid private Python tutoring to a university student. In 2024, I provided live online tutoring through Pear Deck Learning, primarily helping college students with mathematics, physics, Python, machine learning, and introductory C++.

My goal is to help students understand why a method works, not simply memorize steps. I identify the precise point causing difficulty, rebuild the necessary intuition, and guide the student toward increasingly independent problem solving. I specialize in college-level mathematics and physics, AP Calculus, AP Physics, and Python. I can teach in either English or Spanish and adapt each session to the student’s goals and learning style.


Education

Universidad de los Andes (Bogotá, Colombia)
Math, Physics

Additional Languages

Spanish

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Schedule

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Approved Subjects

Logic

Logic

I completed bachelor’s degrees in Mathematics and Physics with a 4.42/5.00 GPA, including an upper-level course in Mathematical Logic. My formal logic training covered propositional and first-order logic, syntax and semantics, formal deductive systems, completeness and compactness, model theory, computability, and Gödel’s incompleteness theorem. Additionally, coursework in Functional Analysis, Abstract Algebra I and II, Real Analysis, Measure and Integration, Differential Geometry and Topology, together with two theses graded 5.0/5.0, gave me extensive experience constructing and evaluating rigorous proofs. With six years of university teaching and tutoring experience, I help students translate statements into symbolic form, work confidently with quantifiers, analyze arguments, and write clear logical proofs.
Quantum Physics

Quantum Physics

I completed bachelor’s degrees in Mathematics and Physics, including Quantum Mechanics I and II, Particle Physics (which I also TA'd) and advanced training in mathematical physics. Both my mathematics and physics theses were in quantum physics: my mathematics thesis examined Berry and Wilczek-Zee geometric phases using holonomy on vector bundles. My physics thesis studied emergent gauge symmetries on the fuzzy sphere using the algebraic formalism of quantum mechanics and noncommutative geometry; both theses received the highest possible grade of 5.0/5.0. I currently conduct research in mathematical physics and quantum field theory, and my six years of university teaching and tutoring experience allow me to explain both the physical intuition and mathematical structure underlying quantum mechanics.
Real Analysis

Real Analysis

I completed bachelor’s degrees in Mathematics and Physics with a 4.42/5.00 GPA, which included advanced coursework in Real Analysis, Measure and Integration, Functional Analysis, Complex Variables, and Differential Geometry. My research in algebraic quantum mechanics uses advanced tools from operator theory and differential geometry, both of which are grounded in real analysis. My mathematics thesis used holonomy on vector bundles, while my physics thesis used transformation-group C*-algebras and operator-algebraic methods to study emergent gauge symmetries on the fuzzy sphere; both received the highest possible grade of 5.0/5.0. With six years of university teaching and tutoring experience, including work as an in-person mathematics tutor, I help students develop the intuition and proof-writing skills needed to succeed in real analysis.
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