fix: convert plain-text math to laTex only for 04-calculus-for-ml docs

[sawgatio]

Changes

• Converted plain-text math in phases/01-math-foundations/04-calculus-for-ml/docs/en.md to LaTeX
• Inline formulas wrapped in $...$
• Standalone formulas converted from plain code fences to $$...$$ blocks

[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

Plan: Pro

Run ID: 0b960d1c-a07d-43db-b97b-85e0bef385b6

📥 Commits

Reviewing files that changed from the base of the PR and between 4415dc8 and 7236530.

📒 Files selected for processing (1)

• phases/01-math-foundations/04-calculus-for-ml/docs/en.md

---

📝 Walkthrough

Walkthrough

A single documentation file for calculus-for-ML content converts all mathematical notation from plain-text and ASCII formats into consistent LaTeX-style inline and block equations. The update spans learning objectives, derivative definitions, optimization methods, second-order analysis, integral concepts, and exercise prompts with no changes to program logic or structure.

Changes

Calculus-for-ML Documentation Math Formatting

Layer / File(s)	Summary
Derivative and Optimization Foundations phases/01-math-foundations/04-calculus-for-ml/docs/en.md	Learning objectives, derivative limit definition, partial derivatives, gradient notation, contour-plot labels, gradient descent update rules, and analytical/numerical derivative formulas (including central difference form) are all converted to LaTeX. Example derivative prompts for $x^2$ and $f(w)=wx+b$ are formatted consistently.
Advanced Topics and Applications phases/01-math-foundations/04-calculus-for-ml/docs/en.md	Hessian matrix definition, saddle and bowl function captions, Newton's method and optimization comparison tables (including $O(N^3)$ notation), Taylor series expansion with first-order/second-order mappings, integral expressions for probability/expected value/KL divergence/Bayesian constants, Jacobian notation ($\mathbb{R}^n \to \mathbb{R}^m$ and $m \times n$ shape), and exercise prompts are all rendered in LaTeX.

🎯 1 (Trivial) | ⏱️ ~3 minutes

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title accurately describes the main change: converting plain-text math to LaTeX in the 04-calculus-for-ml documentation file.
Description check	✅ Passed	The description is directly related to the changeset, detailing the specific LaTeX conversion work performed on the calculus documentation.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

---

Thanks for using CodeRabbit! It's free for OSS, and your support helps us grow. If you like it, consider giving us a shout-out.

❤️ Share

• X
• Mastodon
• Reddit
• LinkedIn

_{Comment @coderabbitai help to get the list of available commands and usage tips.}