Calculus foundations
Limits, continuity, derivatives, and integrals as tools for change and accumulation.
Higher mathematics, explained without the fog
Higher Math Guide is a calm, original map of calculus, linear algebra, probability, analysis habits, and differential equations — written for students who want intuition and precision, not jargon for its own sake.
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Original explainers
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Six topic pillars
Start with any pillar. Each page stands alone and links to related explainers, pathways, and glossary terms.
Multivariable & vector calculus
Partial derivatives, gradients, and how several variables interact in space.
Linear algebra
Vectors, matrices, eigenvalues, and the geometry of linear maps.
Probability & statistics
Uncertainty, conditional probability, and how data updates beliefs.
Real analysis & proof habits
Sequences, rigor, and how to write arguments that actually prove something.
Differential equations
A first look at equations that describe how systems evolve over time.
Featured explainers
Long-form introductions to sticky ideas — each with outbound citations to textbooks, notes, or open educational resources.
Epsilon-delta intuition without terror
What “for every ε there exists δ” is really asking of a function.
What a derivative actually measures
Instantaneous rate of change without treating the definition as a magic spell.
Eigenvalues in plain language
Stretch factors and invariant directions for linear maps.
All explainers →
Bayes, series, separable DEs, and more.
Tools, pathways & references
Math calculators
Derivatives, Riemann sums, matrices, vectors, binomial & normal tools, sequences, and more — all in your browser.
Glossary
About thirty core terms with anchors for quick jumps from any page.
Learning pathways
AP Calc AB bridge, linear algebra first course, and intro to proofs.
Sources
Directory of open notes, textbooks, and primary references cited on this site.
Disclaimer. This site is educational. It is not a substitute for a course, tutor, exam board materials, or professional advice. See the full disclaimer.