Calculus with Julia

Original Article ↗ Hacker News Discussion ↗

Site and materials

  • PDF link in header returns 404; text explains PDF is intentionally not provided due to size and must be built locally with Quarto.
  • Some readers find the book interesting and would recommend it to learners; others find the formatting and progression confusing.

Why Julia for calculus

  • Advocates: Julia targets numerical/mathematical computing, has math-like syntax, Unicode operators, first-class vectors/matrices, built‑in rationals, broadcasting, multiple dispatch, and reactive notebooks (e.g., sliders updating dependencies).
  • It interoperates with symbolic tools (e.g., SymPy) and supports convenient mathematical notation (e.g., postfix derivatives, √, π).

Comparisons with other languages and tools

  • Python: Seen as easier to adopt and with a stronger general ecosystem, especially deep learning (PyTorch/TensorFlow). Critics cite clumsy math syntax, reliance on NumPy/SymPy, weaker type system for numerics, and performance gaps.
  • NumPy vs MATLAB/Julia: Debate over whether NumPy’s syntax is “the same” as MATLAB’s. Some argue Python syntax makes array operations verbose and semantically different; others say differences are minor.
  • MATLAB: Julia is viewed as a strong replacement for many numerical tasks, with similar array idioms and higher performance, but MATLAB’s decades of toolboxes and examples remain a major practical advantage.
  • Mathematica/Sage/Maxima: Mathematica widely praised for symbolic work but seen as overkill or too “magical” for learning; Sage/Maxima and Emacs Calc mentioned as FOSS alternatives.
  • Other math languages mentioned: Haskell, F#, APL/J, LuaJIT; one tangent notes LuaJIT beating Julia in some older benchmarks.

Language design debates

  • 1‑ vs 0‑based indexing: Long subthread; some insist 1‑based matches most math literature and Julia’s goals; others claim 0‑based is more fundamental and consistent with computing.
  • OOP vs multiple dispatch: Some miss method-chaining syntax (array.mean().round()), others argue function style and multiple dispatch are more natural for mathematics.
  • Rich operator and Unicode support in Julia versus Python’s fixed operator set is highlighted.

Pedagogy and target audience

  • Concern that courses mixing new math and new language can overload beginners; recommended as optional or for motivated self‑learners.
  • Mixed views on suitability for high‑school calculus: some say fine even without prior Julia; others say the mathematical exposition assumes too much maturity.
  • Several suggest first learning calculus by hand (traditional texts like standard calculus books or “Quick Calculus”), then using Julia or Python to deepen understanding.
  • Alternative teaching resources: MOOCulus (liked for writing, exercises), calculus texts using J, books combining math with functional programming or physical models.

Ecosystem and industry adoption

  • Julia seen as strong in research and numerical/engineering niches (ODEs, differential equations, scientific ML), with growing but still smaller industrial footprint.
  • Some argue commercial support and indemnification are key reasons MATLAB (and paid tools generally) remain easier to justify in corporate environments than pure FOSS languages.