Computer algebra systems and the optional bridge

Sage, WolframAlpha, SymPy, MATLAB/Octave, Maple, and more

Optional content. Computer algebra systems (CAS) are not required for the core course. The course’s required pillars are LaTeX, R, technical workflow (Quarto / reproducibility), and generative AI literacy. This page exists because (a) mathematicians often want a CAS for symbolic work, and (b) the course’s optional second-tool exploration in Week 13 may be a CAS for some students.

What a CAS is

A computer algebra system lets you manipulate mathematical expressions symbolically — factoring polynomials, computing derivatives and integrals, solving equations exactly, working with matrices and groups symbolically.

R is great for numerics. CAS is great for exact symbolic work.

Options worth knowing

SageMath / SageMathCell

• What it is. A free, open-source mathematics platform that unifies many CAS tools (Maxima, GAP, PARI/GP, SymPy, etc.) under one Python-flavored syntax.
• Where to use it.
  • In a browser: https://sagecell.sagemath.org — no install, no account, no save (copy your code into a .sage or .txt file if you want to keep it). Great for the Week 13 bridge exploration.
  • CoCalc: https://cocalc.com — Sage worksheets in the browser, savable, free tier exists.
  • Local install: https://www.sagemath.org/download.html.
• Why use it. Free, powerful, browser-accessible, ties in with Python.

Python + SymPy

• What it is. A Python library for symbolic computation. If you’re already comfortable with Python, this is the lightest weight way to do CAS work.
• Where to use it.
  • Google Colab: https://colab.research.google.com — browser, free, savable to your Google Drive.
  • Locally: pip install sympy once you have Python.
• Why use it. Programming-friendly. Plays well with NumPy, pandas, and other Python tools you might use elsewhere.

WolframAlpha

• What it is. A computational knowledge engine. Type a natural- language math query, get a worked answer.
• Where to use it. https://www.wolframalpha.com. Free for most short queries; a paid tier shows step-by-step solutions.
• Why use it. Fast lookup for one-off calculations and sanity checks. Not ideal for a real bridge mini-report — output isn’t scripted or reproducible.

Maple / Maple Learn

• What it is. Maplesoft’s commercial CAS.
  • Maple — full desktop application; available on lab machines when the institution provides it.
  • Maple Learn — a free browser-based mini-version. Note: the free tier does not save worksheets, which makes it awkward for sustained projects; screenshots are the workaround.
• Why use it. Familiar if you’ve taken UA Little Rock’s calculus sequence on the labs. Otherwise probably not worth a fresh investment.

MATLAB / Octave

• What it is.
  • MATLAB — commercial numerical computing language. Heavily used in engineering programs. Symbolic Math Toolbox adds CAS functionality.
  • GNU Octave — free, mostly MATLAB-compatible.
• Where to use it.
  • MATLAB Online (limited free tier): https://matlab.mathworks.com.
  • Octave locally: https://octave.org/download — or https://octave-online.net in a browser.
• Why use it. Most natural choice for engineering students who already work in MATLAB.

Which one should you pick?

The Week 13 second-tool exploration is flexible — no single tool is locked. Quick orientation:

• Mathematics or math-education student, no prior CAS experience: SageMathCell has the lightest setup (browser, no install).
• You already program in Python: Python + SymPy in Colab.
• You’re an engineering or science student in MATLAB-heavy courses: Octave (or MATLAB Online if you have access).
• You’ve used Maple in calculus: Maple Learn is fine, but expect the no-save constraint to be annoying.

If Week 13 includes a written deliverable, the brief calls for a short mini-report (≤ 2 pp) exploring one problem in your chosen second tool — not a full project. Pick whichever tool you can get running fastest.

Minimum reproducibility expectation

Whatever tool you pick, your bridge mini-report should:

• include the commands or code you used, copy-pasteable,
• include the output or a screenshot of it,
• name the tool and version at the top, and
• be rendered as a PDF (you can put the screenshots and code in a Quarto document and render).

A note on Maple in this course

In previous terms, this course required Maple as one of three core tools. It is no longer required content. The institution doesn’t make Maple universally available to students, and Maple Learn’s no-save constraint makes it awkward for sustained work. If you have Maple access (lab machines, personal license) and prefer it, fine — otherwise pick a free option above.