- maths page
some useful mathematical concepts, definitions, and results
- Properties of the Real Numbers
= a PDF file (2.1 MB) containing slides and notes from a Keynote presentation about construction of the real number line.
Also included: cardinality, complex numbers without an imaginary unit, and a mini-biography of David Hilbert.
- A Graphical Derivation of the Legendre Transform
= a PDF file (224 KB) explaining a geometrical interpretation of the Legendre transform and convex functions.
Intended as an introduction or refresher for graduate students and undergraduate upperclassmen in quantitative subjects.
- How To Calculate Interest
= a PDF file (280 KB) explaining simple and compound interest, exponential growth, expectation value and the Kelly criterion.
Includes "magic formulas" and example spreadsheets for calculating mortgage and student loan payments, credit card bills, and savings account balances.
- Too Much Information
= a PDF file (1.4 MB) containing slides from a Keynote presentation about Shannon and Von Neumann entropy.
This talk was intended to cover enough material to sensibly introduce density matrix theory, offer hints for
those taking qualifying exams, and review some undergraduate statistical mechanics for new students.
- A Crash Course In Group Theory
= a PDF file (180 KB) containing a 20-page introduction to finite group theory.
Intended for any reader who is familiar with high-school algebra. (Knowledge of vectors, matrices, and modular arithmetic is helpful but not necessary.)
- Matrix Cheat Sheet
= a PDF file (360 KB) one-page quick-reference guide to common matrix terminology and properties.
Includes basic rules of matrix algebra, Hermitian and unitary matrices, eigensystems and the spectral theorem, and some rules for matrix exponentiation.
- Degenerate Systems of Capacitively-Coupled Josephson Junctions: paper and presentation
= two PDF files (12 MB paper, 7 MB presentation) from my PhD qualifier, including the printed report and pdf versions of slides.
Explains the basic physics of phase qubits, the Josephson effects, and an analogous driven-pendulum system from classical mechanics.
(Slides were originally an animated Keynote presentation and are missing some minor details.)