Greek Letters

Greek letters are used throughout this course as variable names, function symbols, indices, and bound parameters. This page collects every Greek letter that appears in the notes so you can recognize each one on sight, distinguish its visual variants, and pronounce it without hesitation.

The list is intentionally not the full Greek alphabet — only letters actually in use are included. As new letters appear in later chapters, they are added here.

Letters used in this course

The “Pronunciation” column gives a phonetic spelling that is widely used in mathematical English. Where two pronunciations are common, the more typical one is listed first.

For uppercase letters whose form coincides with a Latin capital ($A$, $E$, $P$, $T$), there is no separate LaTeX command — just type the Latin letter.

Visual variants

Four of the letters above have two distinct printed lowercase forms that look quite different at a glance. They denote the same letter — knowing both prevents misreading one for an entirely different symbol.

Epsilon: $\epsilon$ vs $ϵ$

• $\varepsilon$ (\varepsilon) — the open, script-like form. The form used throughout this course, e.g. for the radius of an ε-ball $B_\varepsilon(\mathbf{x}_0)$ and for tolerances in iterative algorithms.
• $\epsilon$ (\epsilon) — the lunate form, shaped like a thin backward “3”. Common in physics texts but not used here.

The two are interchangeable as letters. Whichever your slides or sources use, treat it as the same epsilon.

Theta: $\theta$ vs $\vartheta$

• $\theta$ (\theta) — the standard oval form. Used for generic angles, e.g. the angle between two vectors in the inner product and cross product formulas.
• $\vartheta$ (\vartheta) — the script form, more like a curly handwritten d. Used in our content for the polar angle in spherical coordinates, where it needs to be visually distinct from the azimuthal angle $\varphi$.

Reserve the variant form for when a second, different theta is needed in the same expression — otherwise default to $\theta$.

Phi: $\varphi$ vs $\phi$

• $\phi$ (\phi) — the closed-loop form, a vertical bar through a circle. Used in our content for vector-field-style functions, e.g. coordinate transformations $\boldsymbol{\phi}(u, v)$.
• $\varphi$ (\varphi) — the open, cursive form with a descender. Used for the azimuthal angle in polar and spherical coordinates.

The two forms are interchangeable as letters; the split here is purely a local convention to keep “the function $\boldsymbol{\phi}$” visually distinct from “the angle $\varphi$” when both appear in the same context.

Rho: $\rho$ vs $\varrho$

• $\rho$ (\rho) — the standard form: a closed loop with a straight stem dropping below the baseline, much like a Latin lowercase “p”. Used in our content for density — charge density and fluid density — in the Maxwell and Navier–Stokes equations.
• $\varrho$ (\varrho) — the tailed form, where the descender curls forward into a hook. Used for the preference relation on a set of candidates in group decision making.

The two are interchangeable as letters; the split here is incidental — each context simply picked whichever form was conventional for its own subject.

Pronunciation notes

A few of the letters above have multiple pronunciations in active use. None is “wrong” — pick one and stay consistent.

• $\xi$ (xi). Most common in English math is KSY (rhyming with “sky”), occasionally ZIE or SIE. The original Greek is closer to KSEE, but mathematicians rarely use that.
• $\psi$ (psi). The p is usually silent in modern English math, giving SIE (rhyming with “sky”). Some speakers — especially in physics — keep the p and say PSY. Both are accepted.
• $\phi$ (phi). Two equally common pronunciations: FIE (rhymes with “sky”, more typical in American math) and FEE (rhymes with “see”, more typical in British English and physics). Either is fine.
• $\theta$ (theta). Pronounced THAY-tə in American English and THEE-tə in British English. Both are widespread.

When in doubt, listen for what your lecturer says and match that — in a classroom the value of consistency outweighs any particular regional preference.