generate-math-flashcards

name	generate-math-flashcards
description	Use when creating, editing, or reviewing Anki math flashcards in this repository's custom .note format.

Generate Math Flashcards

Purpose

Create technically correct, active-recall math flashcards in this repository's custom .note format. The goal is conceptual reinforcement: cards should help the learner explain, derive, compare, interpret, check assumptions, and recognize failure cases.

Repository Context

• Source files are .note files organized by topic directories such as 01-algebra/, 03-calculus/, and 04-linalgebra/.
• The model definitions live in math.model.
• Import is handled by the Notatki Anki addon; do not invent new syntax, build steps, or generated artifacts.
• Follow nearby files for deck names, tags, notation, and topic granularity.

File Format

A .note file is plain text. It contains file-level or section-level metadata followed by card records. Cards are separated by a line containing exactly:

~~~

Common metadata fields:

!type: Basic Math
!deck: Math::Calculus::Limits
!tags: Math Calculus Limits Theory

Available note types:

• Basic Math: one front-to-back card.
• Basic Math (and reversed card): creates a forward and reverse card. Use only when both directions are pedagogically useful, such as formulas, identities, and equivalences.

Card fields:

!id: AbC123xYz9
!front: A precise prompt
!back:
Answer text, formulas, derivation, or explanation.
!related:
Optional closely related facts, identities, or comparisons.
!extra:
Optional caveats, examples, assumptions, or context.
~~~

Rules:

• Preserve existing !id values when editing existing cards.
• For new cards, omit !id; it is generated by the note tooling.
• !front: may be one line or introduce a multi-line field. !back:, !related:, and !extra: may be multi-line.
• Metadata such as !type, !deck, and !tags can appear at the top of a file and again later when the value changes for subsequent cards.
• Use !related: for material that is helpful to see after answering but should not be required for the answer.
• Use !extra: for assumptions, edge cases, examples, or warnings that would clutter the main answer.

LaTeX and Text Style

• Use inline math as \( ... \) and display math as \[ ... \].
• Use align* for multi-line derivations:

\[
\begin{align*}
    a^2 - b^2 &= (a - b)(a + b) \\
    a^3 - b^3 &= (a - b)(a^2 + ab + b^2)
\end{align*}
\]

• Keep notation consistent within a file and with nearby topic files.
• State assumptions explicitly, such as domains, nonzero denominators, differentiability, invertibility, convergence conditions, or matrix dimensions.
• Use Markdown bullets sparingly when they improve readability.
• Keep answers direct. Avoid filler, motivational language, and long exposition.

Card-Writing Standards

Prefer prompts that test understanding rather than recall. Good fronts often start with:

• Why does ...
• Under what conditions ...
• What breaks if ...
• How are ... related?
• Give a geometric interpretation of ...
• Derive ...
• Compare ...
• Construct a counterexample to ...
• Explain why ...

Use a small number of substantial cards per concept instead of many shallow variants. Increase depth within a topic by moving from definitions to consequences, assumptions, derivations, and failure cases.

Avoid by default:

• trivial definition regurgitation,
• repeated cards that ask the same thing with different wording,
• purely computational drill unless computation is the point,
• vague fronts with no clear mathematical target,
• reverse cards where the reverse direction is ambiguous or unhelpful.

Mathematical Rigor

• Check every formula, theorem statement, and implication before writing it.
• Do not conflate intuition with proof.
• Do not state converses unless they are true under the stated assumptions.
• If a result has hypotheses, include them in the front or back.
• If compressing a proof, say what is being omitted without making the shortened argument false.
• Prefer a short derivation or reason over an unsupported formula when the card is conceptual.

Workflow

1. Inspect nearby .note files for deck, tags, notation, and local style.
2. Decide whether the topic needs Basic Math or Basic Math (and reversed card).
3. Draft cards around conceptual targets, not just topic headings.
4. Verify mathematical correctness and assumptions.
5. Ensure every card ends with ~~~ and fields are spelled exactly as used in this repository.

Examples

Conceptual card:

!type: Basic Math
!deck: Math::Algebra
!tags: Math Algebra Inequality

!front: Why does \( |x| \le c \), with \( c \ge 0 \), imply both an upper and a lower bound for \( x \)?
!back:
Because \( |x| \le c \) means the distance from \( x \) to \( 0 \) is at most \( c \). Equivalently,
\[
-c \le x \le c.
\]
So it gives the upper bound \( x \le c \) and the lower bound \( x \ge -c \).
!extra:
The assumption \( c \ge 0 \) is necessary because \( |x| \) is always nonnegative.
~~~

Formula card with a justified reverse:

!type: Basic Math (and reversed card)
!deck: Math::Algebra
!tags: Math Algebra Identity

!front: \[ a^2 - b^2 \]
!back: \[ (a - b)(a + b) \]
!related:
\[
\begin{align*}
    a^2 - b^2 &= (a - b)(a + b) \\
    a^2 + b^2 &= (a - ib)(a + ib)
\end{align*}
\]
~~~