Currently Teaching
Beginning Grammar (2026)
Latest: The Pronoun: Personal & Possessive – Lesson 5 (Grammar)
9/24/2026
Linear Algebra (2026)
Latest: Linear Transformations, Matrices, and Linear Models – Lecture 4 (Linear Algebra)
10/6/2026
University Physics II (2026) – Electricity & Magnetism
Latest: Inductance – Lecture 13 (University Physics II)
10/8/2026
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Beginning Grammar (2026)
5 videos
An introductory grammar course following "Elementary Grammar and Composition" by Thomas Wadleigh Harvey.
Linear Algebra (2026)
5 videos
This is a standard university-level linear algebra course.
University Physics II (2026) – Electricity & Magnetism
14 videos
This playlist is designed to mirror a standard college-level University Physics II course in Electricity & Magnetism. Unlike a typical E&M course, however, this series is structured to function as a fully stand-alone course, with integrated coverage of the necessary calculus and Newtonian mechanics as they are needed throughout the material. To get the most out of this course, or to view extra materials, please visit: https://timpson-lyceum.vercel.app/courses/cmp4n6v650004h3uxd68xbvp8
University Physics I (2025)
22 videos
A standard college-level University Physics I course covering Newtonian and Classical Mechanics.
Discrete Math (2025)
22 videos
This is a standard college-level course in Discrete Mathematics. The course is being taught to high school students, and so an entire year is spent on the course (as opposed to a single semester), allowing more time to be spent on each topic.
History of Rome – Titus Livius (2025)
24 videos
A course following Livy's History of Rome. Get a detailed explanation of the Roman Republic, the history leading to its founding, and hopefully how The Republic fell. The course is in progress, and so I'm unsure how far it'll go.
First-Order Predicate Logic (2024)
15 videos
This course goes entirely through Propositional and First-Order Predicate Logic with Identity. Several examples of Axiomatic Systems are given along the way. There is NO prerequisite knowledge required! This course was developed with Mathematics and Philosophy majors in mind. The course continues into Axiomatic Set Theory.
Calculus 1 (2024)
22 videos
This is a standard college-level Calculus 1 course. The textbook being used is Thomas Calculus ISBN-13: 978-0-321-87896-0.
Geometry (2024)
18 videos
This course is intended as a high school-level Euclidean Geometry course. The course begins by briefly covering Propositional Logic, Predicate Logic with Identity, and Set Theory before beginning Geometry proper using Hilbert's axioms (or close approximations). Upon finishing Planer Geometry, we will briefly cover Solid Geometry and Analytic Geometry. Time permitting, I will then lay the foundations of Trigonometry, followed by briefly looking at the Axioms of Arithmetic.
History of Philosophy (2024)
33 videos
This is a History of Ancient Western Philosophy course. I start with a crash course on logic, quickly set up a historical context, and the cover everything from Thales going forward. As the class is in progress, I do not know how far it will go.
Intermediate Algebra (2023)
22 videos
A full Intermediate Algebra course, taught over a year to high school students, covering the ground between a first algebra course and college algebra. The course opens with integers, rationals, order of operations, and the properties of algebra, then works through solving linear equations, absolute value equations, and applications; graphs and equations of lines; inequalities and absolute value inequalities; and systems of equations. The second half turns to properties of exponents, operations on polynomials, factoring, rational expressions, and radicals — including radicals and exponents together — before taking up quadratic equations by radicals, by exponents, and by the quadratic formula, along with their applications. It closes with functions and function operations, logarithms, compound interest, and an introduction to the trigonometric functions. Every topic gets the time it needs, and the test and midterm reviews are included as their own lectures.
General Topology (Point Set Topology)
22 videos
This is intended as an undergraduate-level, first-semester, General Topology course. We begin with Set Theory, and work our way through the three Cs of Topology (Continuity, Connectedness, and Compactness). The course is a continuation of my Logic playlist, and so it starts with Set Theory and a review of Relations and Functions, then gets into Topology proper starting on Lecture 5. Logic playlist: https://www.youtube.com/playlist?list=PLJWhXkxQzDF58EHPCuxHS-iaMpom9qTqg
Computation Theory
18 videos
An undergraduate course in the Theory of Computation, taken from first principles to the limits of what a machine can decide. We start with the tools: propositional and predicate logic, set theory and functions, and enough graph theory to work with machines as diagrams. Then the hierarchy, in order — finite automata, nondeterministic finite automata, and regular expressions, with the pumping lemma to prove a language is not regular; right linear grammars, context-free grammars, and pushdown automata, with a second pumping lemma for the languages that are not context-free. The last third is Turing machines and their variants, the Church-Turing thesis and what it means to define "algorithm" at all, decidable and undecidable languages, and reducibility — ending with proofs that particular problems cannot be solved by any machine whatsoever. No prior computer science is assumed. The logic and set theory you need are built in the opening lectures.
College Algebra
12 videos
A college-level College Algebra course that does not start where most algebra courses start. Before any algebra, we build the logic the subject is written in — propositional logic, then predicate logic — and then state the ten field axioms and prove the basic theorems of arithmetic from them. Only then does the algebra begin, on a foundation the student has actually seen laid. From there the course works through the standard material: real numbers and decimals, the four operations, absolute value, inequalities and the real number line, exponents, monomials and polynomials, products of binomials, factoring, rational expressions, radicals and rational exponents, and rationalizing denominators. It then takes up sets and linear inequalities in one variable, coordinates in the plane, inclination and slope, functions and relations, and equations of lines — with a look at the basics of trigonometry along the way. The course is in progress.
Real Analysis (2020)
26 videos
A first course in Real Analysis, equivalent to an Analysis 1 course — the rigorous rebuilding of single-variable calculus from the axioms up. We open with preliminaries: logic, sets, functions, and then the field and positivity axioms for the real numbers, along with the distribution of the integers and rationals and the standard inequalities and identities. From there the course follows the usual arc. Convergent sequences: the definition of convergence, sequences and sets, the Monotone Convergence Theorem, and the Sequential Compactness Theorem. Continuous functions: continuity, the Extreme Value and Intermediate Value Theorems, uniform continuity, the epsilon-delta criterion, images and inverses, monotone functions, and limits. Differentiation: the algebra of derivatives, differentiating inverses and compositions, the Mean Value Theorem and Cauchy's, and Leibniz notation. Integration: upper and lower integrals, the Archimedes-Riemann Theorem, additivity, monotonicity and linearity, continuity and integrability, and both Fundamental Theorems of Calculus. Proofs throughout — this is the course where the theorems from calculus finally get argued for.