writing

My writing is released under the GNU General Public License (3.0 or later), so that anyone can make edits to the work provided it stays free.

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Arithmetic of the Continuum

The target audience for this book is threefold: graduate students in technical fields (not necessarily math); math majors at liberal arts colleges; and the occasional precocious teenager.

0. Introduction
   (released: 11 Nov 2025)
   [src | pdf]
1. Logic, Sets, and Order
   (released: 11 Nov 2025)
   [src | pdf]
2. The Topological Perspective
   (released: 24 Dec 2025)
   [src | pdf]
3. Products of the Line
   (upcoming: 3 Mar 2026)
4. Functional Analysis
   (upcoming: TBA)
5. Distributions
   (upcoming: TBA)
6. Harmonic Oscillation
   (upcoming: TBA)

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Rhapsody in C

This is my planned attempt at treating complex analysis, differential geometry, and electromagnetism as a unified conceptual body. Expect to see something on this by the end of 2026.

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4NAND

An experimental four-valued logic system with imaginary truth values, inspired by G. Spencer Brown's Laws of Form.
(released: 5 Jan 2026)
[src | pdf]

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Elementary NT Notes

I grew disenchanted with how voluminous the later editions of Rosen's elementary number theory book became, and how difficult it can be to find a print copy of the original in good condition. So, I wrote a set of mini notes in the spirit of Rosen's original.
(released: 26 Jul 2025)
[src | pdf]

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Calculus: Integrals Tutorial

A quick how-to on the basic techniques of integration from high school calculus: substitution, integration by parts, and avoiding trigonometric identities via complexponentials.
(released: 18 Jul 2025)
[src | pdf]

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Calculus: Divergence of a Binomial Series

A "perturbation theory" solution to a series that resists the usual tests.
(released: 19 Jul 2025)
[src | pdf]

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Calculus: Integrating (x⁸+1)^-1

Wolfram Alpha chickens out on giving the answer in terms of radicals.
(released: 6 Jan 2026, originally from Jul 2025)
[src | pdf]

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Finite implies (Injective iff Surjective)

Two environments, one solution: just count.
(released: 18 Jul 2025)
[src | pdf]

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Connection and Curvature

Maxwell's equations in the language of differential forms, including how to write the Faraday 2-form as a matrix. Written in the mostly-plus convention, due to many of us not being particle physicists.
(released: 26 Jul 2025)
[src | pdf]